| Title: | R to Symbolic Data Analysis |
|---|---|
| Description: | Symbolic Data Analysis (SDA) was proposed by professor Edwin Diday in 1987, the main purpose of SDA is to substitute the set of rows (cases) in the data table for a concept (second order statistical unit). This package implements, to the symbolic case, certain techniques of automatic classification, as well as some linear models. |
| Authors: | Oldemar Rodriguez [aut, cre], Jose Emmanuel Chacon [cph], Carlos Aguero [cph], Jorge Arce [cph] |
| Maintainer: | Oldemar Rodriguez <[email protected]> |
| License: | GPL (>=2) |
| Version: | 3.1.1 |
| Built: | 2024-11-13 05:31:32 UTC |
| Source: | https://github.com/PROMiDAT/RSDA |
$ operator for histograms
## S3 method for class 'symbolic_histogram' x$name## S3 method for class 'symbolic_histogram' x$name
x |
..... |
name |
... |
$ operator for modals
## S3 method for class 'symbolic_modal' x$name = c("cats", "props", "counts")## S3 method for class 'symbolic_modal' x$name = c("cats", "props", "counts")
x |
..... |
name |
... |
$ operator for set
## S3 method for class 'symbolic_set' x$name = c("levels", "values")## S3 method for class 'symbolic_set' x$name = c("levels", "values")
x |
..... |
name |
... |
Example of SODAS XML data file converted in a CSV file in RSDA format.
data(abalone)data(abalone)
An object of class symbolic_tbl (inherits from tbl_df, tbl, data.frame) with 24 rows and 7 columns.
http://www.info.fundp.ac.be/asso/sodaslink.htm
Bock H-H. and Diday E. (eds.) (2000).Analysis of Symbolic Data. Exploratory methods for extracting statistical information fromcomplex data. Springer, Germany.
data(abalone) res <- sym.pca(abalone, 'centers') plot(res, choix = "ind") plot(res, choix = "var")data(abalone) res <- sym.pca(abalone, 'centers') plot(res, choix = "ind") plot(res, choix = "var")
a data.frame
## S3 method for class 'symbolic_histogram' as.data.frame(x, ...)## S3 method for class 'symbolic_histogram' as.data.frame(x, ...)
x |
..... |
... |
... |
convertir a data.frame
## S3 method for class 'symbolic_interval' as.data.frame(x, ...)## S3 method for class 'symbolic_interval' as.data.frame(x, ...)
x |
a symbolic interval vector |
... |
further arguments passed to or from other methods. |
Extract values
## S3 method for class 'symbolic_modal' as.data.frame(x, ...)## S3 method for class 'symbolic_modal' as.data.frame(x, ...)
x |
An object to be converted |
... |
Further arguments to be passed from or to other methods. |
convertir a data.frame
## S3 method for class 'symbolic_set' as.data.frame(x, ...)## S3 method for class 'symbolic_set' as.data.frame(x, ...)
x |
a symbolic interval vector |
... |
further arguments passed to or from other methods. |
Burt Matrix
calc.burt.sym(sym.data, pos.var)calc.burt.sym(sym.data, pos.var)
sym.data |
ddd |
pos.var |
ddd |
Cardiological interval data example.
data(Cardiological)data(Cardiological)
An object of class symbolic_tbl (inherits from tbl_df, tbl, data.frame) with 11 rows and 3 columns.
Billard L. and Diday E. (2006).Symbolic data analysis: Conceptual statistics and data mining. Wiley, Chichester.
data(Cardiological) res.cm <- sym.lm(formula = Pulse~Syst+Diast, sym.data = Cardiological, method = 'cm') pred.cm <- sym.predict(res.cm, Cardiological) RMSE.L(Cardiological$Pulse, pred.cm$Fitted) RMSE.U(Cardiological$Pulse,pred.cm$Fitted) R2.L(Cardiological$Pulse,pred.cm$Fitted) R2.U(Cardiological$Pulse,pred.cm$Fitted) deter.coefficient(Cardiological$Pulse,pred.cm$Fitted)data(Cardiological) res.cm <- sym.lm(formula = Pulse~Syst+Diast, sym.data = Cardiological, method = 'cm') pred.cm <- sym.predict(res.cm, Cardiological) RMSE.L(Cardiological$Pulse, pred.cm$Fitted) RMSE.U(Cardiological$Pulse,pred.cm$Fitted) R2.L(Cardiological$Pulse,pred.cm$Fitted) R2.U(Cardiological$Pulse,pred.cm$Fitted) deter.coefficient(Cardiological$Pulse,pred.cm$Fitted)
Cardiological interval data example.
data(Cardiological)data(Cardiological)
An object of class symbolic_tbl (inherits from tbl_df, tbl, data.frame) with 44 rows and 5 columns.
Billard L. and Diday E. (2006).Symbolic data analysis: Conceptual statistics and data mining. Wiley, Chichester.
Compute centers of the interval
centers.interval(sym.data)centers.interval(sym.data)
sym.data |
Symbolic interval data table. |
Centers of teh intervals.
Jorge Arce.
Arce J. and Rodriguez O. (2015) 'Principal Curves and Surfaces to Interval Valued Variables'. The 5th Workshop on Symbolic Data Analysis, SDA2015, Orleans, France, November.
Hastie,T. (1984).Principal Curves and Surface. Ph.D Thesis Stanford University.
Hastie,T. & Weingessel,A. (2014). princurve - Fits a Principal Curve in Arbitrary Dimension.R package version 1.1–12 http://cran.r-project.org/web/packages/princurve/index.html.
Hastie,T. & Stuetzle, W. (1989). Principal Curves. Journal of the American Statistical Association, Vol. 84-406, 502–516.
Hastie, T., Tibshirani, R. & Friedman, J. (2008). The Elements of Statistical Learning; Data Mining, Inference and Prediction. Springer, New York.
sym.interval.pc
Generate a symbolic data table from a classic data table.
classic.to.sym( x = NULL, concept = NULL, variables = tidyselect::everything(), default.numeric = sym.interval, default.categorical = sym.modal, ... )classic.to.sym( x = NULL, concept = NULL, variables = tidyselect::everything(), default.numeric = sym.interval, default.categorical = sym.modal, ... )
x |
A data.frame. |
concept |
These are the variable that we are going to use a concepts. |
variables |
These are the variables that we want to include in the symbolic data table. |
default.numeric |
function to use for numeric variables |
default.categorical |
function to use for categorical variables |
... |
A vector with names and the type of symbolic data to use, the available types are type_histogram (), type_continuous (), type.set (), type.modal (), by default type_histogram () is used for numeric variables and type_modal () for the categorical variables. |
a [tibble][tibble::tibble-package]
Bock H-H. and Diday E. (eds.) (2000). Analysis of Symbolic Data. Exploratory methods for extracting statistical information from complex data. Springer, Germany.
This function compute the symbolic correlation
cor(x, ...) ## Default S3 method: cor( x, y = NULL, use = "everything", method = c("pearson", "kendall", "spearman"), ... ) ## S3 method for class 'symbolic_interval' cor(x, y, method = c("centers", "billard"), ...) ## S3 method for class 'symbolic_tbl' cor(x, ...)cor(x, ...) ## Default S3 method: cor( x, y = NULL, use = "everything", method = c("pearson", "kendall", "spearman"), ... ) ## S3 method for class 'symbolic_interval' cor(x, y, method = c("centers", "billard"), ...) ## S3 method for class 'symbolic_tbl' cor(x, ...)
x |
A symbolic variable. |
... |
As in R cor function. |
y |
A symbolic variable. |
use |
An optional character string giving a method for computing covariances in the presence of missing values. This must be (an abbreviation of) one of the strings 'everything', 'all.obs', 'complete.obs', 'na.or.complete', or 'pairwise.complete.obs'. |
method |
The method to be use. |
Return a real number in [-1,1].
Oldemar Rodriguez Rojas
Billard L. and Diday E. (2006). Symbolic data analysis: Conceptual statistics and data mining. Wiley, Chichester.
Rodriguez, O. (2000). Classification et Modeles Lineaires en Analyse des Donnees Symboliques. Ph.D. Thesis, Paris IX-Dauphine University.
This function compute the symbolic covariance.
cov(x, ...) ## Default S3 method: cov( x, y = NULL, use = "everything", method = c("pearson", "kendall", "spearman"), ... ) ## S3 method for class 'symbolic_interval' cov(x, y, method = c("centers", "billard"), na.rm = FALSE, ...) ## S3 method for class 'symbolic_tbl' cov(x, ...)cov(x, ...) ## Default S3 method: cov( x, y = NULL, use = "everything", method = c("pearson", "kendall", "spearman"), ... ) ## S3 method for class 'symbolic_interval' cov(x, y, method = c("centers", "billard"), na.rm = FALSE, ...) ## S3 method for class 'symbolic_tbl' cov(x, ...)
x |
First symbolic variables. |
... |
As in R cov function. |
y |
Second symbolic variables. |
use |
an optional character string giving a method for computing covariances in the presence of missing values. This must be (an abbreviation of) one of the strings 'everything', 'all.obs', 'complete.obs', 'na.or.complete', or 'pairwise.complete.obs'. |
method |
The method to be use. |
na.rm |
As in R cov function. |
Return a real number.
Oldemar Rodriguez Rojas
Billard L. and Diday E. (2006). Symbolic data analysis: Conceptual statistics and data mining. Wiley, Chichester.
Rodriguez, O. (2000). Classification et Modeles Lineaires en Analyse des Donnees Symboliques. Ph.D. Thesis, Paris IX-Dauphine University.
The determination coefficient represents a goodness-of-fit measure commonly used in regression analysis to capture the adjustment quality of a model.
deter.coefficient(ref, pred)deter.coefficient(ref, pred)
ref |
Variable that was predicted. |
pred |
The prediction given by the model. |
Return the determination cosfficient.
Oldemar Rodriguez Rojas
LIMA-NETO, E.A., DE CARVALHO, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis 52, 1500-1515.
LIMA-NETO, E.A., DE CARVALHO, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347.
sym.glm
data(int_prost_test) data(int_prost_train) res.cm <- sym.lm(lpsa ~ ., sym.data = int_prost_train, method = "cm") pred.cm <- sym.predict(res.cm, int_prost_test) deter.coefficient(int_prost_test$lpsa, pred.cm$Fitted)data(int_prost_test) data(int_prost_train) res.cm <- sym.lm(lpsa ~ ., sym.data = int_prost_train, method = "cm") pred.cm <- sym.predict(res.cm, int_prost_test) deter.coefficient(int_prost_test$lpsa, pred.cm$Fitted)
Compute a distance vector
dist.vect(vector1, vector2)dist.vect(vector1, vector2)
vector1 |
First vector. |
vector2 |
Second vector. |
Eclidean distance between the two vectors.
Jorge Arce
Arce J. and Rodriguez O. (2015) 'Principal Curves and Surfaces to Interval Valued Variables'. The 5th Workshop on Symbolic Data Analysis, SDA2015, Orleans, France, November.
Hastie,T. (1984). Principal Curves and Surface. Ph.D. Thesis Stanford University.
Hastie,T. & Weingessel,A. (2014). princurve - Fits a Principal Curve in Arbitrary Dimension.R package version 1.1–12 http://cran.r-project.org/web/packages/princurve/index.html.
Hastie,T. & Stuetzle, W. (1989). Principal Curves. Journal of the American Statistical Association, Vol. 84-406, 502–516.
Hastie, T., Tibshirani, R. & Friedman, J. (2008). The Elements of Statistical Learning; Data Mining, Inference and Prediction. Springer, New York.
sym.interval.pc
Compute the distance vector matrix.
dist.vect.matrix(vector, Matrix)dist.vect.matrix(vector, Matrix)
vector |
An n dimensional vector. |
Matrix |
An n x n matrix. |
The distance.
Jorge Arce.
Arce J. and Rodriguez O. (2015) 'Principal Curves and Surfaces to Interval Valued Variables'. The 5th Workshop on Symbolic Data Analysis, SDA2015, Orleans, France, November.
Hastie,T. (1984). Principal Curves and Surface. Ph.D Thesis Stanford University.
Hastie,T. & Weingessel,A. (2014). princurve - Fits a Principal Curve in Arbitrary Dimension.R package version 1.1–12 http://cran.r-project.org/web/packages/princurve/index.html.
Hastie,T. & Stuetzle, W. (1989). Principal Curves. Journal of the American Statistical Association, Vol. 84-406, 502–516.
Hastie, T., Tibshirani, R. & Friedman, J. (2008). The Elements of Statistical Learning; Data Mining, Inference and Prediction. Springer, New York.
sym.interval.pc
Correspondence Analysis for Symbolic MultiValued Variables example.
data(ex_cfa1)data(ex_cfa1)
An object of class symbolic_tbl (inherits from tbl_df, tbl, data.frame) with 4 rows and 4 columns.
Rodriguez, O. (2011). Correspondence Analysis for Symbolic MultiValued Variables. Workshop in Symbolic Data Analysis Namur, Belgium
Correspondence Analysis for Symbolic MultiValued Variables example.
data(ex_cfa2)data(ex_cfa2)
An object of class symbolic_tbl (inherits from tbl_df, tbl, data.frame) with 6 rows and 5 columns.
Rodriguez, O. (2011). Correspondence Analysis for Symbolic MultiValued Variables. Workshop in Symbolic Data Analysis Namur, Belgium
example for the sym.mcfa function.
example for the sym.mcfa function.
data(ex_mcfa1) ex_mcfa1data(ex_mcfa1) ex_mcfa1
An object of class data.frame with 130 rows and 5 columns.
An object of class data.frame with 130 rows and 5 columns.
data("ex_mcfa1") sym.table <- classic.to.sym(ex_mcfa1, concept = suspect, hair = sym.set(hair), eyes = sym.set(eyes), region = sym.set(region)) res <- sym.mcfa(sym.table, c(1,2)) mcfa.scatterplot(res[,1], res[,2], sym.data = sym.table, pos.var = c(1,2)) data("ex_mcfa1") sym.table <- classic.to.sym( x = ex_mcfa1, concept = "suspect", variables = c(hair, eyes, region), hair = sym.set(hair), eyes = sym.set(eyes), region = sym.set(region) ) sym.tabledata("ex_mcfa1") sym.table <- classic.to.sym(ex_mcfa1, concept = suspect, hair = sym.set(hair), eyes = sym.set(eyes), region = sym.set(region)) res <- sym.mcfa(sym.table, c(1,2)) mcfa.scatterplot(res[,1], res[,2], sym.data = sym.table, pos.var = c(1,2)) data("ex_mcfa1") sym.table <- classic.to.sym( x = ex_mcfa1, concept = "suspect", variables = c(hair, eyes, region), hair = sym.set(hair), eyes = sym.set(eyes), region = sym.set(region) ) sym.table
example for the sym.mcfa function.
data(ex_mcfa2)data(ex_mcfa2)
An object of class data.frame with 130 rows and 7 columns.
data("ex_mcfa2") ex <- classic.to.sym(ex_mcfa2, concept = employee_id, variables = c(employee_id, salary, region, evaluation, years_worked), salary = sym.set(salary), region = sym.set(region), evaluation = sym.set(evaluation), years_worked = sym.set(years_worked)) res <- sym.mcfa(ex, c(1,2,3,4)) mcfa.scatterplot(res[,1], res[,2], sym.data = ex, pos.var = c(1,2,3,4))data("ex_mcfa2") ex <- classic.to.sym(ex_mcfa2, concept = employee_id, variables = c(employee_id, salary, region, evaluation, years_worked), salary = sym.set(salary), region = sym.set(region), evaluation = sym.set(evaluation), years_worked = sym.set(years_worked)) res <- sym.mcfa(ex, c(1,2,3,4)) mcfa.scatterplot(res[,1], res[,2], sym.data = ex, pos.var = c(1,2,3,4))
This is a small data example to generate symbolic objets.
data(ex1_db2so)data(ex1_db2so)
An object of class data.frame with 19 rows and 5 columns.
Bock H-H. and Diday E. (eds.) (2000). Analysis of Symbolic Data. Exploratory methods for extracting statistical information from complex data. Springer, Germany.
data(ex1_db2so) ex1 <- ex1_db2so result <- classic.to.sym( x = ex1_db2so, concept = c(state, sex), variables = c(county, group, age), county = mean(county), age_hist = sym.histogram(age, breaks = pretty(ex1_db2so$age, 5)) ) resultdata(ex1_db2so) ex1 <- ex1_db2so result <- classic.to.sym( x = ex1_db2so, concept = c(state, sex), variables = c(county, group, age), county = mean(county), age_hist = sym.histogram(age, breaks = pretty(ex1_db2so$age, 5)) ) result
This a symbolic data table with variables of continuos, interval, histogram and set types.
data(example1)data(example1)
The labels $C means that follows a continuous variable, $I means an interval
variable, $H means a histogram variables and $S means set variable. In the
first row each labels should be follow of a name to variable and to the case
of histogram a set variables types the names of the modalities (categories).
In data rows for continuous variables we have just one value, for interval
variables we have the minimum and the maximum of the interval, for histogram
variables we have the number of modalities and then the probability of each
modality and for set variables we have the cardinality of the set and next
the elements of the set.
The format is the *.csv file is:
$C F1 $I F2 F2 $M F3 M1 M2 M3 $S F4 e a 2 3 g b 1 4 i k c d
Case1 $C 2.8 $I 1 2 $M 3 0.1 0.7 0.2 $S 12 1 0 0 0 1 0 0 0 1 1 0 0
Case2 $C 1.4 $I 3 9 $M 3 0.6 0.3 0.1 $S 12 0 1 0 0 0 1 0 0 0 0 1 1
Case3 $C 3.2 $I -1 4 $M 3 0.2 0.2 0.6 $S 12 0 0 1 0 0 1 1 0 0 0 1 0
Case4 $C -2.1 $I 0 2 $M 3 0.9 0.0 0.1 $S 12 0 1 0 1 0 0 0 1 0 0 1 0
Case5 $C -3.0 $I -4 -2 $M 3 0.6 0.0 0.4 $S 12 1 0 0 0 1 0 0 0 1 1 0 0
The internal format is:
$N
[1] 5
$M
[1] 4
$sym.obj.names
[1] 'Case1' 'Case2' 'Case3' 'Case4' 'Case5'
$sym.var.names
[1] 'F1' 'F2' 'F3' 'F4'
$sym.var.types
[1] '$C' '$I' '$H' '$S'
$sym.var.length
[1] 1 2 3 4
$sym.var.starts
[1] 2 4 8 13
$meta
$C F1 $I F2 F2 $M F3 M1 M2 M3 $S F4 e a 2 3 g b 1 4 i k c d
Case1 $C 2.8 $I 1 2 $M 3 0.1 0.7 0.2 $S 12 1 0 0 0 1 0 0 0 1 1 0 0
Case2 $C 1.4 $I 3 9 $M 3 0.6 0.3 0.1 $S 12 0 1 0 0 0 1 0 0 0 0 1 1
Case3 $C 3.2 $I -1 4 $M 3 0.2 0.2 0.6 $S 12 0 0 1 0 0 1 1 0 0 0 1 0
Case4 $C -2.1 $I 0 2 $M 3 0.9 0.0 0.1 $S 12 0 1 0 1 0 0 0 1 0 0 1 0
Case5 $C -3.0 $I -4 -2 $M 3 0.6 0.0 0.4 $S 12 1 0 0 0 1 0 0 0 1 1 0 0
$data
F1 F2 F2.1 M1 M2 M3 e a 2 3 g b 1 4 i k c d
Case1 2.8 1 2 0.1 0.7 0.2 1 0 0 0 1 0 0 0 1 1 0 0
Case2 1.4 3 9 0.6 0.3 0.1 0 1 0 0 0 1 0 0 0 0 1 1
Case3 3.2 -1 4 0.2 0.2 0.6 0 0 1 0 0 1 1 0 0 0 1 0
Case4 -2.1 0 2 0.9 0.0 0.1 0 1 0 1 0 0 0 1 0 0 1 0
Case5 -3.0 -4 -2 0.6 0.0 0.4 1 0 0 0 1 0 0 0 1 1 0 0
Bock H-H. and Diday E. (eds.) (2000). Analysis of Symbolic Data. Exploratory methods for extracting statistical information from complex data. Springer, Germany.
data(example1) example1data(example1) example1
This a symbolic data table with variables of continuos, interval, histogram and set types.
data(example2)data(example2)
$C F1 $I F2 F2 $M F3 M1 M2 M3 $C F4 $S F5 e a 2 3 g b 1 4 i k c d
Case1 $C 2.8 $I 1 2 $M 3 0.1 0.7 0.2 $C 6.0 $S 12 1 0 0 0 1 0 0 0 1 1 0 0
Case2 $C 1.4 $I 3 9 $M 3 0.6 0.3 0.1 $C 8.0 $S 12 0 1 0 0 0 1 0 0 0 0 1 1
Case3 $C 3.2 $I -1 4 $M 3 0.2 0.2 0.6 $C -7.0 $S 12 0 0 1 0 0 1 1 0 0 0 1 0
Case4 $C -2.1 $I 0 2 $M 3 0.9 0.0 0.1 $C 0.0 $S 12 0 1 0 1 0 0 0 1 0 0 1 0
Case5 $C -3.0 $I -4 -2 $M 3 0.6 0.0 0.4 $C -9.5 $S 12 1 0 0 0 1 0 0 0 1 1 0 0
data(example2) example2data(example2) example2
This a symbolic data table with variables of continuos, interval, histogram and set types.
data(example3)data(example3)
$C F1 $I F2 F2 $M F3 M1 M2 M3 $C F4 $S F5 e a 2 3 g b 1 4 i k c d $I F6 F6 $I F7 F7 Case1 $C 2.8 $I 1 2 $M 3 0.1 0.7 0.2 $C 6.0 $S 12 1 0 0 0 1 0 0 0 1 1 0 0 $I 0.00 90.00 $I 9 24 Case2 $C 1.4 $I 3 9 $M 3 0.6 0.3 0.1 $C 8.0 $S 12 0 1 0 0 0 1 0 0 0 0 1 1 $I -90.00 98.00 $I -9 9 Case3 $C 3.2 $I -1 4 $M 3 0.2 0.2 0.6 $C -7.0 $S 12 0 0 1 0 0 1 1 0 0 0 1 0 $I 65.00 90.00 $I 65 70 Case4 $C -2.1 $I 0 2 $M 3 0.9 0.0 0.1 $C 0.0 $S 12 0 1 0 1 0 0 0 1 0 0 1 0 $I 45.00 89.00 $I 25 67 Case5 $C -3.0 $I -4 -2 $M 3 0.6 0.0 0.4 $C -9.5 $S 12 1 0 0 0 1 0 0 0 1 1 0 0 $I 20.00 40.00 $I 9 40 Case6 $C 0.1 $I 10 21 $M 3 0.0 0.7 0.3 $C -1.0 $S 12 1 0 0 0 0 0 1 0 1 0 0 0 $I 5.00 8.00 $I 5 8 Case7 $C 9.0 $I 4 21 $M 3 0.2 0.2 0.6 $C 0.5 $S 12 1 1 1 0 0 0 0 0 0 0 0 0 $I 3.14 6.76 $I 4 6
data(example3) example3data(example3) example3
data(example4) example4
data(example4)data(example4)
$C 2.8 $I 1 2 $M 3 0.1 0.7 0.2 $C 6 $S F4 e a 2 3 g b 1 4 i k c d $I 0 90 Case2 $C 1.4 $I 3 9 $M 3 0.6 0.3 0.1 $C 8.0 $S 12 1 0 0 0 1 0 0 0 1 1 0 0 $I -90.00 98.00 Case3 $C 3.2 $I -1 4 $M 3 0.2 0.2 0.6 $C -7.0 $S 12 0 1 0 0 0 1 0 0 0 0 1 1 $I 65.00 90.00 Case4 $C -2.1 $I 0 2 $M 3 0.9 0.0 0.1 $C 0.0 $S 12 0 0 1 0 0 1 1 0 0 0 1 0 $I 45.00 89.00 Case5 $C -3.0 $I -4 -2 $M 3 0.6 0.0 0.4 $C -9.5 $S 12 0 1 0 1 0 0 0 1 0 0 1 0 $I 90.00 990.00 Case6 $C 0.1 $I 10 21 $M 3 0.0 0.7 0.3 $C -1.0 $S 12 1 0 0 0 1 0 0 0 1 1 0 0 $I 5.00 8.00 Case7 $C 9.0 $I 4 21 $M 3 0.2 0.2 0.6 $C 0.5 $S 12 1 1 0 0 0 0 1 0 0 0 0 1 $I 3.14 6.76
data(example4) example4data(example4) example4
This a symbolic data matrix wint continuos, interval, histograma a set data types.
data(example5)data(example5)
$H F0 M01 M02 $C F1 $I F2 F2 $H F3 M1 M2 M3 $S F4 E1 E2 E3 E4
Case1 $H 2 0.1 0.9 $C 2.8 $I 1 2 $H 3 0.1 0.7 0.2 $S 4 e g k i
Case2 $H 2 0.7 0.3 $C 1.4 $I 3 9 $H 3 0.6 0.3 0.1 $S 4 a b c d
Case3 $H 2 0.0 1.0 $C 3.2 $I -1 4 $H 3 0.2 0.2 0.6 $S 4 2 1 b c
Case4 $H 2 0.2 0.8 $C -2.1 $I 0 2 $H 3 0.9 0.0 0.1 $S 4 3 4 c a
Case5 $H 2 0.6 0.4 $C -3.0 $I -4 -2 $H 3 0.6 0.0 0.4 $S 4 e i g k
data(example5) example5data(example5) example5
This a symbolic data matrix wint continuos, interval, histograma a set data types.
data(example6)data(example6)
$C F1 $M F2 M1 M2 M3 M4 M5 $I F3 F3 $M F4 M1 M2 M3 $C F5 $S F4 e a 2 3 g b 1 4 i k c d Case1 $C 2.8 $M 5 0.1 0.1 0.1 0.1 0.6 $I 1 2 $M 3 0.1 0.7 0.2 $C 6.0 $S 12 1 0 0 0 1 0 0 0 1 1 0 0 Case2 $C 1.4 $M 5 0.1 0.1 0.1 0.1 0.6 $I 3 9 $M 3 0.6 0.3 0.1 $C 8.0 $S 12 0 1 0 0 0 1 0 0 0 0 1 1 Case3 $C 3.2 $M 5 0.1 0.1 0.1 0.1 0.6 $I -1 4 $M 3 0.2 0.2 0.6 $C -7.0 $S 12 0 0 1 0 0 1 1 0 0 0 1 0 Case4 $C -2.1 $M 5 0.1 0.1 0.1 0.1 0.6 $I 0 2 $M 3 0.9 0.0 0.1 $C 0.0 $S 12 0 1 0 1 0 0 0 1 0 0 1 0 Case5 $C -3.0 $M 5 0.1 0.1 0.1 0.1 0.6 $I -4 -2 $M 3 0.6 0.0 0.4 $C -9.5 $S 12 1 0 0 0 1 0 0 0 1 1 0 0
data(example6) example6data(example6) example6
This a symbolic data matrix wint continuos, interval, histograma a set data types.
data(example6)data(example6)
$C F1 $H F2 M1 M2 M3 M4 M5 $I F3 F3 $H F4 M1 M2 M3 $C F5
Case1 $C 2.8 $H 5 0.1 0.2 0.3 0.4 0.0 $I 1 2 $H 3 0.1 0.7 0.2 $C 6.0
Case2 $C 1.4 $H 5 0.2 0.1 0.5 0.1 0.2 $I 3 9 $H 3 0.6 0.3 0.1 $C 8.0
Case3 $C 3.2 $H 5 0.1 0.1 0.2 0.1 0.5 $I -1 4 $H 3 0.2 0.2 0.6 $C -7.0
Case4 $C -2.1 $H 5 0.4 0.1 0.1 0.1 0.3 $I 0 2 $H 3 0.9 0.0 0.1 $C 0.0
Case5 $C -3.0 $H 5 0.6 0.1 0.1 0.1 0.1 $I -4 -2 $H 3 0.6 0.0 0.4 $C -9.5
data(example7) example7data(example7) example7
Symbolic data matrix with all the variables of interval type.
data('facedata')data('facedata')
$I;AD;AD;$I;BC;BC;.........
HUS1;$I;168.86;172.84;$I;58.55;63.39;.........
HUS2;$I;169.85;175.03;$I;60.21;64.38;.........
HUS3;$I;168.76;175.15;$I;61.4;63.51;.........
INC1;$I;155.26;160.45;$I;53.15;60.21;.........
INC2;$I;156.26;161.31;$I;51.09;60.07;.........
INC3;$I;154.47;160.31;$I;55.08;59.03;.........
ISA1;$I;164;168;$I;55.01;60.03;.........
ISA2;$I;163;170;$I;54.04;59;.........
ISA3;$I;164.01;169.01;$I;55;59.01;.........
JPL1;$I;167.11;171.19;$I;61.03;65.01;.........
JPL2;$I;169.14;173.18;$I;60.07;65.07;.........
JPL3;$I;169.03;170.11;$I;59.01;65.01;.........
KHA1;$I;149.34;155.54;$I;54.15;59.14;.........
KHA2;$I;149.34;155.32;$I;52.04;58.22;.........
KHA3;$I;150.33;157.26;$I;52.09;60.21;.........
LOT1;$I;152.64;157.62;$I;51.35;56.22;.........
LOT2;$I;154.64;157.62;$I;52.24;56.32;.........
LOT3;$I;154.83;157.81;$I;50.36;55.23;.........
PHI1;$I;163.08;167.07;$I;66.03;68.07;.........
PHI2;$I;164;168.03;$I;65.03;68.12;.........
PHI3;$I;161.01;167;$I;64.07;69.01;.........
ROM1;$I;167.15;171.24;$I;64.07;68.07;.........
ROM2;$I;168.15;172.14;$I;63.13;68.07;.........
ROM3;$I;167.11;171.19;$I;63.13;68.03;.........
Billard L. and Diday E. (2006). Symbolic data analysis: Conceptual statistics and data mining. Wiley, Chichester.
## Not run: data(facedata) res.vertex.ps <- sym.interval.pc(facedata,'vertex',150,FALSE,FALSE,TRUE) class(res.vertex.ps$sym.prin.curve) <- c('sym.data.table') sym.scatterplot(res.vertex.ps$sym.prin.curve[,1], res.vertex.ps$sym.prin.curve[,2], labels=TRUE,col='red',main='PSC Face Data') ## End(Not run)## Not run: data(facedata) res.vertex.ps <- sym.interval.pc(facedata,'vertex',150,FALSE,FALSE,TRUE) class(res.vertex.ps$sym.prin.curve) <- c('sym.data.table') sym.scatterplot(res.vertex.ps$sym.prin.curve[,1], res.vertex.ps$sym.prin.curve[,2], labels=TRUE,col='red',main='PSC Face Data') ## End(Not run)
Symbolic modal conversion functions to and from Character
## S3 method for class 'symbolic_histogram' format(x, ...)## S3 method for class 'symbolic_histogram' format(x, ...)
x |
An object to be converted |
... |
Further arguments to be passed from or to other methods. |
Symbolic interval conversion functions to and from Character
## S3 method for class 'symbolic_interval' format(x, ...)## S3 method for class 'symbolic_interval' format(x, ...)
x |
An object to be converted |
... |
Further arguments to be passed from or to other methods. |
Symbolic modal conversion functions to and from Character
## S3 method for class 'symbolic_modal' format(x, ...)## S3 method for class 'symbolic_modal' format(x, ...)
x |
An object to be converted |
... |
Further arguments to be passed from or to other methods. |
Symbolic set conversion functions to and from Character
## S3 method for class 'symbolic_set' format(x, ...)## S3 method for class 'symbolic_set' format(x, ...)
x |
An object to be converted |
... |
Further arguments to be passed from or to other methods. |
Extract categories
get_cats(x, ...)get_cats(x, ...)
x |
An object to be converted |
... |
Further arguments to be passed from or to other methods. |
Extract prop
get_props(x, ...)get_props(x, ...)
x |
An object to be converted |
... |
Further arguments to be passed from or to other methods. |
Linear regression model interval-valued data example.
data(int_prost_test)data(int_prost_test)
An object of class symbolic_tbl (inherits from tbl_df, tbl, data.frame) with 30 rows and 9 columns.
HASTIE, T., TIBSHIRANI, R. and FRIEDMAN, J. (2008). The Elements of Statistical Learning: Data Mining, Inference and Prediction. New York: Springer.
Linear regression model interval-valued data example.
data(int_prost_train)data(int_prost_train)
An object of class symbolic_tbl (inherits from tbl_df, tbl, data.frame) with 67 rows and 9 columns.
HASTIE, T., TIBSHIRANI, R. and FRIEDMAN, J. (2008). The Elements of Statistical Learning: Data Mining, Inference and Prediction. New York: Springer.
calcula centros
interval.centers(x)interval.centers(x)
x |
tabla simbolica todos intervalos |
Histogram plot for an interval variable
interval.histogram.plot(x, n.bins, ...)interval.histogram.plot(x, n.bins, ...)
x |
An symbolic data table. |
n.bins |
Numbers of breaks of the histogram. |
... |
Arguments to be passed to the barplot method. |
A list with componets : frequency and histogram
data(oils) res <- interval.histogram.plot(x = oils[, 3], n.bins = 3) resdata(oils) res <- interval.histogram.plot(x = oils[, 3], n.bins = 3) res
calcula maximos
interval.max(x)interval.max(x)
x |
tabla simbolica todos intervalos |
calcula minimos
interval.min(x)interval.min(x)
x |
tabla simbolica todos intervalos |
calcula rangos
interval.ranges(x)interval.ranges(x)
x |
tabla simbolica todos intervalos |
Symbolic histogram
is.sym.histogram(x)is.sym.histogram(x)
x |
an object to be tested |
returns TRUE if its argument's value is a symbolic_histogram and FALSE otherwise.
x <- sym.histogram(iris$Sepal.Length) is.sym.histogram(x)x <- sym.histogram(iris$Sepal.Length) is.sym.histogram(x)
Symbolic interval
is.sym.interval(x)is.sym.interval(x)
x |
an object to be tested |
returns TRUE if its argument's value is a symbolic_vector and FALSE otherwise.
x <- sym.interval(1:10) is.sym.interval(x) is.sym.interval("d")x <- sym.interval(1:10) is.sym.interval(x) is.sym.interval("d")
Symbolic modal
is.sym.modal(x)is.sym.modal(x)
x |
an object to be tested |
returns TRUE if its argument's value is a symbolic_modal and FALSE otherwise.
x <- sym.modal(factor(c("a", "b", "b", "l"))) is.sym.modal(x)x <- sym.modal(factor(c("a", "b", "b", "l"))) is.sym.modal(x)
Symbolic set
is.sym.set(x)is.sym.set(x)
x |
an object to be tested |
returns TRUE if its argument's value is a symbolic_set and FALSE otherwise.
x <- sym.set(factor(c("a", "b", "b", "l"))) is.sym.set(x)x <- sym.set(factor(c("a", "b", "b", "l"))) is.sym.set(x)
Symbolic data matrix with all the variables of interval type.
data(lynne1)data(lynne1)
An object of class tbl_df (inherits from tbl, data.frame) with 10 rows and 4 columns.
Billard L. and Diday E. (2006). Symbolic data analysis: Conceptual statistics and data mining. Wiley, Chichester.
data(lynne1) lynne1data(lynne1) lynne1
Plot Interval Scatterplot
mcfa.scatterplot(x, y, sym.data, pos.var)mcfa.scatterplot(x, y, sym.data, pos.var)
x |
symbolic table with only one column. |
y |
symbolic table with only one column. |
sym.data |
original symbolic table. |
pos.var |
column number of the variables to be plotted. |
data("ex_mcfa1") sym.table <- classic.to.sym(ex_mcfa1, concept = suspect, hair = sym.set(hair), eyes = sym.set(eyes), region = sym.set(region) ) res <- sym.mcfa(sym.table, c(1, 2)) mcfa.scatterplot(res[, 2], res[, 3], sym.data = sym.table, pos.var = c(1, 2))data("ex_mcfa1") sym.table <- classic.to.sym(ex_mcfa1, concept = suspect, hair = sym.set(hair), eyes = sym.set(eyes), region = sym.set(region) ) res <- sym.mcfa(sym.table, c(1, 2)) mcfa.scatterplot(res[, 2], res[, 3], sym.data = sym.table, pos.var = c(1, 2))
This function compute the symbolic mean for intervals
## S3 method for class 'symbolic_interval' mean(x, method = c("centers", "interval"), trim = 0, na.rm = F, ...) ## S3 method for class 'symbolic_tbl' mean(x, ...)## S3 method for class 'symbolic_interval' mean(x, method = c("centers", "interval"), trim = 0, na.rm = F, ...) ## S3 method for class 'symbolic_tbl' mean(x, ...)
x |
A symbolic interval. |
method |
The method to be use. |
trim |
As in R mean function. |
na.rm |
As in R mean function. |
... |
As in R mean function. |
Oldemar Rodriguez Rojas
Billard L. and Diday E. (2006). Symbolic data analysis: Conceptual statistics and data mining. Wiley, Chichester.
Rodriguez, O. (2000). Classification et Modeles Lineaires en Analyse des Donnees Symboliques. Ph.D. Thesis, Paris IX-Dauphine University.
This function compute the median for symbolic intervals.
## S3 method for class 'symbolic_interval' median(x, na.rm = FALSE, method = c("centers", "interval"), ...) ## S3 method for class 'symbolic_tbl' median(x, ...)## S3 method for class 'symbolic_interval' median(x, na.rm = FALSE, method = c("centers", "interval"), ...) ## S3 method for class 'symbolic_tbl' median(x, ...)
x |
A symbolic interval. |
na.rm |
As in R median function. |
method |
The method to be use. |
... |
As in R median function. |
Oldemar Rodriguez Rojas
Billard L. and Diday E. (2006). Symbolic data analysis: Conceptual statistics and data mining. Wiley, Chichester.
Rodriguez, O. (2000). Classification et Modeles Lineaires en Analyse des Donnees Symboliques. Ph.D. Thesis, Paris IX-Dauphine University.
Summary method to CM and CRM regression model
method_summary(ref, pred)method_summary(ref, pred)
ref |
Real values |
pred |
Predicted values |
Maxima and Minima
## S3 method for class 'symbolic_interval' min(x, ...) ## S3 method for class 'symbolic_interval' max(x, ...) ## S3 method for class 'symbolic_interval' x$name = c("min", "max", "mean", "median")## S3 method for class 'symbolic_interval' min(x, ...) ## S3 method for class 'symbolic_interval' max(x, ...) ## S3 method for class 'symbolic_interval' x$name = c("min", "max", "mean", "median")
x |
symbolic interval vector |
... |
further arguments passed to or from other methods. |
name |
... |
a new symbolic interval with the minimum of the minima and the minimum of the maxima
Compute neighbors vertex
neighbors.vertex(vertex, Matrix, num.neig)neighbors.vertex(vertex, Matrix, num.neig)
vertex |
Vertes of the hipercube |
Matrix |
Interval Data Matrix. |
num.neig |
Number of vertices. |
Jorge Arce
Arce J. and Rodriguez O. (2015) 'Principal Curves and Surfaces to Interval Valued Variables'. The 5th Workshop on Symbolic Data Analysis, SDA2015, Orleans, France, November.
Hastie,T. (1984). Principal Curves and Surface. Ph.D Thesis Stanford University.
Hastie,T. & Weingessel,A. (2014). princurve - Fits a Principal Curve in Arbitrary Dimension.R package version 1.1–12 http://cran.r-project.org/web/packages/princurve/index.html.
Hastie,T. & Stuetzle, W. (1989). Principal Curves. Journal of the American Statistical Association, Vol. 84-406, 502–516.
Hastie, T., Tibshirani, R. & Friedman, J. (2008). The Elements of Statistical Learning; Data Mining, Inference and Prediction. Springer, New York.
sym.interval.pc
Compute the norm of a vector.
norm.vect(vector1)norm.vect(vector1)
vector1 |
An n dimensional vector. |
The L2 norm of the vector.
Jorge Arce
Arce J. and Rodriguez O. (2015) 'Principal Curves and Surfaces to Interval Valued Variables'. The 5th Workshop on Symbolic Data Analysis, SDA2015, Orleans, France, November.
Hastie,T. (1984). Principal Curves and Surface. Ph.D Thesis Stanford University.
Hastie,T. & Weingessel,A. (2014). princurve - Fits a Principal Curve in Arbitrary Dimension.R package version 1.1–12 http://cran.r-project.org/web/packages/princurve/index.html.
Hastie,T. & Stuetzle, W. (1989). Principal Curves. Journal of the American Statistical Association, Vol. 84-406, 502–516.
Hastie, T., Tibshirani, R. & Friedman, J. (2008). The Elements of Statistical Learning; Data Mining, Inference and Prediction. Springer, New York.
sym.interval.pc
Symbolic data matrix with all the variables of interval type.
data(oils)data(oils)
$I GRA GRA $I FRE FRE $I IOD IOD $I SAP SAP
L $I 0.930 0.935 $I -27 -18 $I 170 204 $I 118 196
P $I 0.930 0.937 $I -5 -4 $I 192 208 $I 188 197
Co $I 0.916 0.918 $I -6 -1 $I 99 113 $I 189 198
S $I 0.920 0.926 $I -6 -4 $I 104 116 $I 187 193
Ca $I 0.916 0.917 $I -25 -15 $I 80 82 $I 189 193
O $I 0.914 0.919 $I 0 6 $I 79 90 $I 187 196
B $I 0.860 0.870 $I 30 38 $I 40 48 $I 190 199
H $I 0.858 0.864 $I 22 32 $I 53 77 $I 190 202
Cazes P., Chouakria A., Diday E. et Schektman Y. (1997). Extension de l'analyse en composantes principales a des donnees de type intervalle, Rev. Statistique Appliquee, Vol. XLV Num. 3 pag. 5-24, France.
data(oils) oilsdata(oils) oils
Plot UMAP for symbolic data tables
## S3 method for class 'sym_umap' plot(x, ...)## S3 method for class 'sym_umap' plot(x, ...)
x |
sym_umap object |
... |
params for plot |
Function for plotting a symbolic object
## S3 method for class 'symbolic_tbl' plot( x, col = NA, matrix.form = NA, border = FALSE, size = 1, title = TRUE, show.type = FALSE, font.size = 1, reduce = FALSE, hist.angle.x = 60, ... )## S3 method for class 'symbolic_tbl' plot( x, col = NA, matrix.form = NA, border = FALSE, size = 1, title = TRUE, show.type = FALSE, font.size = 1, reduce = FALSE, hist.angle.x = 60, ... )
x |
The symbolic object. |
col |
A specification for the default plotting color. |
matrix.form |
A vector of the form c(num.rows,num.columns). |
border |
A logical value indicating whether border should be plotted. |
size |
The magnification to be used for each graphic. |
title |
A logical value indicating whether title should be plotted. |
show.type |
A logical value indicating whether type should be plotted. |
font.size |
The font size of graphics. |
reduce |
A logical value indicating whether values different from zero should be plotted in modal and set graphics. |
hist.angle.x |
The angle of labels in y axis. Only for histogram plot |
... |
Arguments to be passed to methods. |
A plot of the symbolic data table.
Andres Navarro
## Not run: data(oils) plot(oils) plot(oils, border = T, size = 1.3) ## End(Not run)## Not run: data(oils) plot(oils) plot(oils, border = T, size = 1.3) ## End(Not run)
Compute the lower boundary correlation coefficient for two interval variables.
R2.L(ref, pred)R2.L(ref, pred)
ref |
Variable that was predicted. |
pred |
The prediction given by the model. |
The lower boundary correlation coefficient.
Oldemar Rodriguez Rojas
LIMA-NETO, E.A., DE CARVALHO, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis 52, 1500-1515.
LIMA-NETO, E.A., DE CARVALHO, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347.
sym.glm
data(int_prost_train) data(int_prost_test) res.cm <- sym.lm(lpsa ~ ., sym.data = int_prost_train, method = "cm") pred.cm <- sym.predict(res.cm, int_prost_test) R2.L(int_prost_test$lpsa, pred.cm$Fitted)data(int_prost_train) data(int_prost_test) res.cm <- sym.lm(lpsa ~ ., sym.data = int_prost_train, method = "cm") pred.cm <- sym.predict(res.cm, int_prost_test) R2.L(int_prost_test$lpsa, pred.cm$Fitted)
Compute the upper boundary correlation coefficient for two interval variables.
R2.U(ref, pred)R2.U(ref, pred)
ref |
Variable that was predicted. |
pred |
The prediction given by the model. |
The upper boundary correlation coefficient.
Oldemar Rodriguez Rojas
LIMA-NETO, E.A., DE CARVALHO, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis 52, 1500-1515.
LIMA-NETO, E.A., DE CARVALHO, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347.
sym.glm
data(int_prost_train) data(int_prost_test) res.cm <- sym.lm(lpsa ~ ., sym.data = int_prost_train, method = "cm") pred.cm <- sym.predict(res.cm, int_prost_test) R2.U(int_prost_test$lpsa, pred.cm$Fitted)data(int_prost_train) data(int_prost_test) res.cm <- sym.lm(lpsa ~ ., sym.data = int_prost_train, method = "cm") pred.cm <- sym.predict(res.cm, int_prost_test) R2.U(int_prost_test$lpsa, pred.cm$Fitted)
It reads a symbolic data table from a CSV file.
read.sym.table(file, header = TRUE, sep, dec, row.names = NULL)read.sym.table(file, header = TRUE, sep, dec, row.names = NULL)
file |
The name of the CSV file. |
header |
As in R function read.table |
sep |
As in R function read.table |
dec |
As in R function read.table |
row.names |
As in R function read.table |
The labels $C means that follows a continuous variable, $I means an interval variable, $H means a histogram variables and $S means set variable. In the first row each labels should be follow of a name to variable and to the case of histogram a set variables types the names of the modalities (categories) . In data rows for continuous variables we have just one value, for interval variables we have the minimum and the maximum of the interval, for histogram variables we have the number of modalities and then the probability of each modality and for set variables we have the cardinality of the set and next the elements of the set.
The format is the CSV file should be like:
$C F1 $I F2 F2 $H F3 M1 M2 M3 $S F4 E1 E2 E3 E4
Case1 $C 2.8 $I 1 2 $H 3 0.1 0.7 0.2 $S 4 e g k i
Case2 $C 1.4 $I 3 9 $H 3 0.6 0.3 0.1 $S 4 a b c d
Case3 $C 3.2 $I -1 4 $H 3 0.2 0.2 0.6 $S 4 2 1 b c
Case4 $C -2.1 $I 0 2 $H 3 0.9 0.0 0.1 $S 4 3 4 c a
Case5 $C -3.0 $I -4 -2 $H 3 0.6 0.0 0.4 $S 4 e i g k
The internal format is:
$N
[1] 5
$M
[1] 4
$sym.obj.names
[1] 'Case1' 'Case2' 'Case3' 'Case4' 'Case5'
$sym.var.names
[1] 'F1' 'F2' 'F3' 'F4'
$sym.var.types
[1] '$C' '$I' '$H' '$S'
$sym.var.length
[1] 1 2 3 4
$sym.var.starts
[1] 2 4 8 13
$meta
$C F1 $I F2 F2 $H F3 M1 M2 M3 $S F4 E1 E2 E3 E4
Case1 $C 2.8 $I 1 2 $H 3 0.1 0.7 0.2 $S 4 e g k i
Case2 $C 1.4 $I 3 9 $H 3 0.6 0.3 0.1 $S 4 a b c d
Case3 $C 3.2 $I -1 4 $H 3 0.2 0.2 0.6 $S 4 2 1 b c
Case4 $C -2.1 $I 0 2 $H 3 0.9 0.0 0.1 $S 4 3 4 c a
Case5 $C -3.0 $I -4 -2 $H 3 0.6 0.0 0.4 $S 4 e i g k
$data
F1 F2 F2.1 M1 M2 M3 E1 E2 E3 E4
Case1 2.8 1 2 0.1 0.7 0.2 e g k i
Case2 1.4 3 9 0.6 0.3 0.1 a b c d
Case3 3.2 -1 4 0.2 0.2 0.6 2 1 b c
Case4 -2.1 0 2 0.9 0.0 0.1 3 4 c a
Case5 -3.0 -4 -2 0.6 0.0 0.4 e i g k
Return a symbolic data table structure.
Oldemar Rodriguez Rojas
Bock H-H. and Diday E. (eds.) (2000). Analysis of Symbolic Data. Exploratory methods for extracting statistical information from complex data. Springer, Germany.
display.sym.table
## Not run: data(example1) write.sym.table(example1, file = "temp4.csv", sep = "|", dec = ".", row.names = TRUE, col.names = TRUE ) ex1 <- read.sym.table("temp4.csv", header = TRUE, sep = "|", dec = ".", row.names = 1) ## End(Not run)## Not run: data(example1) write.sym.table(example1, file = "temp4.csv", sep = "|", dec = ".", row.names = TRUE, col.names = TRUE ) ex1 <- read.sym.table("temp4.csv", header = TRUE, sep = "|", dec = ".", row.names = 1) ## End(Not run)
Compute the lower boundary root-mean-square error.
RMSE.L(ref, pred)RMSE.L(ref, pred)
ref |
Variable that was predicted. |
pred |
The prediction given by the model. |
The lower boundary root-mean-square error.
Oldemar Rodriguez Rojas.
LIMA-NETO, E.A., DE CARVALHO, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis 52, 1500-1515.
LIMA-NETO, E.A., DE CARVALHO, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347.
sym.glm
Compute the upper boundary root-mean-square error.
RMSE.U(ref, pred)RMSE.U(ref, pred)
ref |
Variable that was predicted. |
pred |
The prediction given by the model. |
The upper boundary root-mean-square error.
Oldemar Rodriguez Rojas
LIMA-NETO, E.A., DE CARVALHO, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis 52, 1500-1515.
LIMA-NETO, E.A., DE CARVALHO, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347.
sym.glm
This work is framed inside the Symbolic Data Analysis (SDA). The objective of this work is to implement in R to the symbolic case certain techniques of the automatic classification, as well as some lineal models. These implementations will always be made following two fundamental principles in Symbolic Data Analysis like they are: Classic Data Analysis should always be a case particular case of the Symbolic Data Analysis and both, the exit as the input in an Symbolic Data Analysis should be symbolic. We implement for variables of type interval the mean, the median, the mean of the extreme values, the standard deviation, the deviation quartil, the dispersion boxes and the correlation also three new methods are also presented to carry out the lineal regression for variables of type interval. We also implement in this R package the method of Principal Components Analysis in two senses: First, we propose three ways to project the interval variables in the circle of correlations in such way that is reflected the variation or the inexactness of the variables. Second, we propose an algorithm to make the Principal Components Analysis for variables of type histogram. We implement a method for multidimensional scaling of interval data, denominated INTERSCAL.
| Package: | RSDA |
| Type: | Package |
| Version: | 3.1.0 |
| Date: | 2023-04-21 |
| License: | GPL (>=2) |
Most of the function of the package stars from a symbolic data table that can be store in a CSV file withe follwing forma: In the first row the labels $C means that follows a continuous variable, $I means an interval variable, $H means a histogram variables and $S means set variable. In the first row each labels should be follow of a name to variable and to the case of histogram a set variables types the names of the modalities (categories) . In data rows for continuous variables we have just one value, for interval variables we have the minimum and the maximum of the interval, for histogram variables we have the number of modalities and then the probability of each modality and for set variables we have the cardinality of the set and next the elements of the set.
Oldemar Rodriguez Rojas
Maintainer: Oldemar Rodriguez Rojas <[email protected]>
Billard L. and Diday E. (2006). Symbolic data analysis: Conceptual statistics and data mining. Wiley, Chichester.
Billard L., Douzal-Chouakria A. and Diday E. (2011) Symbolic Principal Components For Interval-Valued Observations, Statistical Analysis and Data Mining. 4 (2), 229-246. Wiley.
Bock H-H. and Diday E. (eds.) (2000). Analysis of Symbolic Data. Exploratory methods for extracting statistical information from complex data. Springer, Germany.
Carvalho F., Souza R.,Chavent M., and Lechevallier Y. (2006) Adaptive Hausdorff distances and dynamic clustering of symbolic interval data. Pattern Recognition Letters Volume 27, Issue 3, February 2006, Pages 167-179
Cazes P., Chouakria A., Diday E. et Schektman Y. (1997). Extension de l'analyse en composantes principales a des donnees de type intervalle, Rev. Statistique Appliquee, Vol. XLV Num. 3 pag. 5-24, France.
Diday, E., Rodriguez O. and Winberg S. (2000). Generalization of the Principal Components Analysis to Histogram Data, 4th European Conference on Principles and Practice of Knowledge Discovery in Data Bases, September 12-16, 2000, Lyon, France.
Chouakria A. (1998) Extension des methodes d'analysis factorialle a des donnees de type intervalle, Ph.D. Thesis, Paris IX Dauphine University.
Makosso-Kallyth S. and Diday E. (2012). Adaptation of interval PCA to symbolic histogram variables, Advances in Data Analysis and Classification July, Volume 6, Issue 2, pp 147-159. Rodriguez, O. (2000). Classification et Modeles Lineaires en Analyse des Donnees Symboliques. Ph.D. Thesis, Paris IX-Dauphine University.
Compute the symbolic standard desviation.
sd(x, ...) ## Default S3 method: sd(x, na.rm = FALSE, ...) ## S3 method for class 'symbolic_interval' sd(x, method = c("centers", "interval", "billard"), na.rm = FALSE, ...) ## S3 method for class 'symbolic_tbl' sd(x, ...)sd(x, ...) ## Default S3 method: sd(x, na.rm = FALSE, ...) ## S3 method for class 'symbolic_interval' sd(x, method = c("centers", "interval", "billard"), na.rm = FALSE, ...) ## S3 method for class 'symbolic_tbl' sd(x, ...)
x |
A symbolic variable. |
... |
As in R sd function. |
na.rm |
As in R sd function. |
method |
The method to be use. |
return a real number.
Oldemar Rodriguez Rojas
Billard L. and Diday E. (2006). Symbolic data analysis: Conceptual statistics and data mining. Wiley, Chichester.
Rodriguez, O. (2000). Classification et Modeles Lineaires en Analyse des Donnees Symboliques. Ph.D. Thesis, Paris IX-Dauphine University.
To convert SDS SODAS files to RSDA files.
SDS.to.RSDA(file.path, labels = FALSE)SDS.to.RSDA(file.path, labels = FALSE)
file.path |
Disk path where the SODAS *.SDA file is. |
labels |
If we want to include SODAS SDA files lebels in RSDA file. |
A RSDA symbolic data file.
Olger Calderon and Roberto Zuniga.
Bock H-H. and Diday E. (eds.) (2000). Analysis of Symbolic Data. Exploratory methods for extracting statistical information from complex data. Springer, Germany.
SODAS.to.RSDA
## Not run: # We can read the file directly from the SODAS SDA file as follows: # We can save the file in CSV to RSDA format as follows: setwd('C:/Program Files (x86)/DECISIA/SODAS version 2.0/bases/') result <- SDS.to.RSDA(file.path='hani3101.sds') # We can save the file in CSV to RSDA format as follows: write.sym.table(result, file='hani3101.csv', sep=';',dec='.', row.names=TRUE, ## End(Not run)## Not run: # We can read the file directly from the SODAS SDA file as follows: # We can save the file in CSV to RSDA format as follows: setwd('C:/Program Files (x86)/DECISIA/SODAS version 2.0/bases/') result <- SDS.to.RSDA(file.path='hani3101.sds') # We can save the file in CSV to RSDA format as follows: write.sym.table(result, file='hani3101.csv', sep=';',dec='.', row.names=TRUE, ## End(Not run)
To convert XML SODAS files to RSDA files.
SODAS.to.RSDA(XMLPath, labels = T)SODAS.to.RSDA(XMLPath, labels = T)
XMLPath |
Disk path where the SODAS *.XML file is. |
labels |
If we want to include SODAS XML files lebels in RSDA file. |
A RSDA symbolic data file.
Olger Calderon and Roberto Zuniga.
Bock H-H. and Diday E. (eds.) (2000). Analysis of Symbolic Data. Exploratory methods for extracting statistical information from complex data. Springer, Germany.
SDS.to.RSDA
## Not run: # We can read the file directly from the SODAS XML file as follows: # abalone<-SODAS.to.RSDA('C:/Program Files (x86)/DECISIA/SODAS version 2.0/bases/abalone.xml) # We can save the file in CSV to RSDA format as follows: # write.sym.table(sodas.ex1, file='abalone.csv', sep=';',dec='.', row.names=TRUE, # col.names=TRUE) # We read the file from the CSV file, # this is not necessary if the file is read directly from # XML using SODAS.to.RSDA as in the first statement in this example. data(abalone) res <- sym.interval.pca(abalone, "centers") sym.scatterplot(sym.var(res$Sym.Components, 1), sym.var(res$Sym.Components, 2), labels = TRUE, col = "red", main = "PCA Oils Data" ) sym.scatterplot3d(sym.var(res$Sym.Components, 1), sym.var(res$Sym.Components, 2), sym.var(res$Sym.Components, 3), color = "blue", main = "PCA Oils Data" ) sym.scatterplot.ggplot(sym.var(res$Sym.Components, 1), sym.var(res$Sym.Components, 2), labels = TRUE ) sym.circle.plot(res$Sym.Prin.Correlations) ## End(Not run)## Not run: # We can read the file directly from the SODAS XML file as follows: # abalone<-SODAS.to.RSDA('C:/Program Files (x86)/DECISIA/SODAS version 2.0/bases/abalone.xml) # We can save the file in CSV to RSDA format as follows: # write.sym.table(sodas.ex1, file='abalone.csv', sep=';',dec='.', row.names=TRUE, # col.names=TRUE) # We read the file from the CSV file, # this is not necessary if the file is read directly from # XML using SODAS.to.RSDA as in the first statement in this example. data(abalone) res <- sym.interval.pca(abalone, "centers") sym.scatterplot(sym.var(res$Sym.Components, 1), sym.var(res$Sym.Components, 2), labels = TRUE, col = "red", main = "PCA Oils Data" ) sym.scatterplot3d(sym.var(res$Sym.Components, 1), sym.var(res$Sym.Components, 2), sym.var(res$Sym.Components, 3), color = "blue", main = "PCA Oils Data" ) sym.scatterplot.ggplot(sym.var(res$Sym.Components, 1), sym.var(res$Sym.Components, 2), labels = TRUE ) sym.circle.plot(res$Sym.Prin.Correlations) ## End(Not run)
Plot the symbolic circle of correlations.
sym.circle.plot(prin.corre)sym.circle.plot(prin.corre)
prin.corre |
A symbolic interval data matrix with correlations between the variables and the principals componets, both of interval type. |
Plot the symbolic circle
Oldemar Rodriguez Rojas
Rodriguez O. (2012). The Duality Problem in Interval Principal Components Analysis. The 3rd Workshop in Symbolic Data Analysis, Madrid.
data(oils) res <- sym.pca(oils, "centers") sym.circle.plot(res$Sym.Prin.Correlations)data(oils) res <- sym.pca(oils, "centers") sym.circle.plot(res$Sym.Prin.Correlations)
This function computes and returns the distance matrix by using the specified distance measure to compute distance between symbolic interval variables.
sym.dist.interval( sym.data, gamma = 0.5, method = "Minkowski", normalize = TRUE, SpanNormalize = FALSE, q = 1, euclidea = TRUE, pond = rep(1, length(variables)) )sym.dist.interval( sym.data, gamma = 0.5, method = "Minkowski", normalize = TRUE, SpanNormalize = FALSE, q = 1, euclidea = TRUE, pond = rep(1, length(variables)) )
sym.data |
A symbolic object |
gamma |
gamma value for the methods ichino and minkowski. |
method |
Method to use (Gowda.Diday, Ichino, Minkowski, Hausdorff) |
normalize |
A logical value indicating whether normalize the data in the ichino or hausdorff method. |
SpanNormalize |
A logical value indicating whether |
q |
q value for the hausdorff method. |
euclidea |
A logical value indicating whether use the euclidean distance. |
pond |
A numeric vector |
variables |
Numeric vector with the number of the variables to use. |
An object of class 'dist'
Generalized Boosted Symbolic Regression
sym.gbm( formula, sym.data, method = c("cm", "crm"), distribution = "gaussian", interaction.depth = 1, n.trees = 500, shrinkage = 0.1 )sym.gbm( formula, sym.data, method = c("cm", "crm"), distribution = "gaussian", interaction.depth = 1, n.trees = 500, shrinkage = 0.1 )
formula |
A symbolic description of the model to be fit. The formula may include an offset term (e.g. y~offset(n)+x). If keep.data = FALSE in the initial call to gbm then it is the user's responsibility to resupply the offset to gbm.more. |
sym.data |
symbolic data table |
method |
cm crm |
distribution |
distribution |
interaction.depth |
Integer specifying the maximum depth of each tree (i.e., the highest level of variable interactions allowed). A value of 1 implies an additive model, a value of 2 implies a model with up to 2-way interactions, etc. Default is 1. |
n.trees |
Integer specifying the total number of trees to fit. This is equivalent to the number of iterations and the number of basis functions in the additive expansion. Default is 100. |
shrinkage |
A shrinkage parameter applied to each tree in the expansion. Also known as the learning rate or step-size reduction; 0.001 to 0.1 usually work, but a smaller learning rate typically requires more trees. Default is 0.1. |
Lima-Neto, E.A., De Carvalho, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis52, 1500-1515
Lima-Neto, E.A., De Carvalho, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347
Lima Neto, E.d.A., de Carvalho, F.d.A.T. Nonlinear regression applied to interval-valued data. Pattern Anal Applic 20, 809–824 (2017). https://doi.org/10.1007/s10044-016-0538-y
Rodriguez, O. (2018). Shrinkage linear regression for symbolic interval-valued variables.Journal MODULAD 2018, vol. Modulad 45, pp.19-38
Execute Lasso, Ridge and and Elastic Net Linear regression model to interval variables.
sym.glm(sym.data, response = 1, method = c('cm', 'crm'), alpha = 1, nfolds = 10, grouped = TRUE)sym.glm(sym.data, response = 1, method = c('cm', 'crm'), alpha = 1, nfolds = 10, grouped = TRUE)
sym.data |
Should be a symbolic data table read with the function read.sym.table(...). |
response |
The number of the column where is the response variable in the interval data table. |
method |
'cm' to generalized Center Method and 'crm' to generalized Center and Range Method. |
alpha |
alpha=1 is the lasso penalty, and alpha=0 the ridge penalty. 0<alpha<1 is the elastic net method. |
nfolds |
Number of folds - default is 10. Although nfolds can be as large as the sample size (leave-one-out CV), it is not recommended for large datasets. Smallest value allowable is nfolds=3 |
grouped |
This is an experimental argument, with default TRUE, and can be ignored by most users. |
An object of class 'cv.glmnet' is returned, which is a list with the ingredients of the cross-validation fit.
Oldemar Rodriguez Rojas
Rodriguez O. (2013). A generalization of Centre and Range method for fitting a linear regression model to symbolic interval data using Ridge Regression, Lasso and Elastic Net methods. The IFCS2013 conference of the International Federation of Classification Societies, Tilburg University Holland.
sym.lm
Create an symbolic_histogram type object
sym.histogram(x = double(), breaks = NA_real_)sym.histogram(x = double(), breaks = NA_real_)
x |
character vector |
breaks |
a vector giving the breakpoints between histogram cells |
a symbolic histogram
sym.histogram(iris$Sepal.Length)sym.histogram(iris$Sepal.Length)
Create an symbolic_interval type object
sym.interval(x = numeric(), .min = min, .max = max)sym.interval(x = numeric(), .min = min, .max = max)
x |
numeric vector |
.min |
function that will be used to calculate the minimum interval |
.max |
function that will be used to calculate the maximum interval |
a symbolic interval
sym.interval(c(1, 2, 4, 5)) sym.interval(1:10)sym.interval(c(1, 2, 4, 5)) sym.interval(1:10)
Compute a symbolic interval principal components curves
sym.interval.pc(sym.data, method = c('vertex', 'centers'), maxit, plot, scale, center)sym.interval.pc(sym.data, method = c('vertex', 'centers'), maxit, plot, scale, center)
sym.data |
Shoud be a symbolic data table read with the function read.sym.table(...) |
method |
It should be 'vertex' or 'centers'. |
maxit |
Maximum number of iterations. |
plot |
TRUE to plot immediately, FALSE if you do not want to plot. |
scale |
TRUE to standardize the data. |
center |
TRUE to center the data. |
prin.curve: This a symbolic data table with the interval principal components. As this is a symbolic data table we can apply over this table any other symbolic data analysis method (symbolic propagation).
cor.ps: This is the interval correlations between the original interval variables and the interval principal components, it can be use to plot the symbolic circle of correlations.
Jorge Arce.
Arce J. and Rodriguez O. (2015) 'Principal Curves and Surfaces to Interval Valued Variables'. The 5th Workshop on Symbolic Data Analysis, SDA2015, Orleans, France, November.
Hastie,T. (1984). Principal Curves and Surface. Ph.D Thesis Stanford University.
Hastie,T. & Weingessel,A. (2014). princurve - Fits a Principal Curve in Arbitrary Dimension.R package version 1.1–12 http://cran.r-project.org/web/packages/princurve/index.html.
Hastie,T. & Stuetzle, W. (1989). Principal Curves. Journal of the American Statistical Association, Vol. 84-406, 502–516.
Hastie, T., Tibshirani, R. & Friedman, J. (2008). The Elements of Statistical Learning; Data Mining, Inference and Prediction. Springer, New York.
sym.interval.pca
## Not run: data(oils) res.vertex.ps <- sym.interval.pc(oils, "vertex", 150, FALSE, FALSE, TRUE) class(res.vertex.ps$sym.prin.curve) <- c("sym.data.table") sym.scatterplot(res.vertex.ps$sym.prin.curve[, 1], res.vertex.ps$sym.prin.curve[, 2], labels = TRUE, col = "red", main = "PSC Oils Data" ) data(facedata) res.vertex.ps <- sym.interval.pc(facedata, "vertex", 150, FALSE, FALSE, TRUE) class(res.vertex.ps$sym.prin.curve) <- c("sym.data.table") sym.scatterplot(res.vertex.ps$sym.prin.curve[, 1], res.vertex.ps$sym.prin.curve[, 2], labels = TRUE, col = "red", main = "PSC Face Data" ) ## End(Not run)## Not run: data(oils) res.vertex.ps <- sym.interval.pc(oils, "vertex", 150, FALSE, FALSE, TRUE) class(res.vertex.ps$sym.prin.curve) <- c("sym.data.table") sym.scatterplot(res.vertex.ps$sym.prin.curve[, 1], res.vertex.ps$sym.prin.curve[, 2], labels = TRUE, col = "red", main = "PSC Oils Data" ) data(facedata) res.vertex.ps <- sym.interval.pc(facedata, "vertex", 150, FALSE, FALSE, TRUE) class(res.vertex.ps$sym.prin.curve) <- c("sym.data.table") sym.scatterplot(res.vertex.ps$sym.prin.curve[, 1], res.vertex.ps$sym.prin.curve[, 2], labels = TRUE, col = "red", main = "PSC Face Data" ) ## End(Not run)
Symbolic interval principal curves limits.
sym.interval.pc.limits(sym.data, prin.curve, num.vertex, lambda, var.ord)sym.interval.pc.limits(sym.data, prin.curve, num.vertex, lambda, var.ord)
sym.data |
Symbolic interval data table. |
prin.curve |
Principal curves. |
num.vertex |
Number of vertices of the hipercube. |
lambda |
Lambda. |
var.ord |
Order of the variables. |
Jorge Arce.
Arce J. and Rodriguez O. (2015) 'Principal Curves and Surfaces to Interval Valued Variables'. The 5th Workshop on Symbolic Data Analysis, SDA2015, Orleans, France, November.
Hastie,T. (1984). Principal Curves and Surface. Ph.D Thesis Stanford University.
Hastie,T. & Weingessel,A. (2014). princurve - Fits a Principal Curve in Arbitrary Dimension.R package version 1.1–12 http://cran.r-project.org/web/packages/princurve/index.html.
Hastie,T. & Stuetzle, W. (1989). Principal Curves. Journal of the American Statistical Association, Vol. 84-406, 502–516.
Hastie, T., Tibshirani, R. & Friedman, J. (2008). The Elements of Statistical Learning; Data Mining, Inference and Prediction. Springer, New York.
sym.interval.pc
This is a function is to carry out a k-means overs a interval symbolic data matrix.
sym.kmeans(sym.data, k = 3, iter.max = 10, nstart = 1, algorithm = c('Hartigan-Wong', 'Lloyd', 'Forgy', 'MacQueen'))sym.kmeans(sym.data, k = 3, iter.max = 10, nstart = 1, algorithm = c('Hartigan-Wong', 'Lloyd', 'Forgy', 'MacQueen'))
sym.data |
Symbolic data table. |
k |
The number of clusters. |
iter.max |
Maximun number of iterations. |
nstart |
As in R kmeans function. |
algorithm |
The method to be use, as in kmeans R function. |
This function return the following information:
K-means clustering with 3 clusters of sizes 2, 2, 4
Cluster means:
GRA FRE IOD SAP
1 0.93300 -13.500 193.500 174.75
2 0.86300 30.500 54.500 195.25
3 0.91825 -6.375 95.375 191.50
Clustering vector:
L P Co S Ca O B H
1 1 3 3 3 3 2 2
Within cluster sum of squares by cluster:
[1] 876.625 246.125 941.875
(between_SS / total_SS = 92.0
Available components:
[1] 'cluster' 'centers' 'totss' 'withinss' 'tot.withinss' 'betweenss'
[7] 'size'
Oldemar Rodriguez Rojas
Carvalho F., Souza R.,Chavent M., and Lechevallier Y. (2006) Adaptive Hausdorff distances and dynamic clustering of symbolic interval data. Pattern Recognition Letters Volume 27, Issue 3, February 2006, Pages 167-179
sym.hclust
data(oils) sk <- sym.kmeans(oils, k = 3) sk$clusterdata(oils) sk <- sym.kmeans(oils, k = 3) sk$cluster
Symbolic k-Nearest Neighbor Regression
sym.knn( formula, sym.data, method = c("cm", "crm"), scale = TRUE, kmax = 20, kernel = "triangular" )sym.knn( formula, sym.data, method = c("cm", "crm"), scale = TRUE, kmax = 20, kernel = "triangular" )
formula |
a formula object. |
sym.data |
symbolc data.table |
method |
cm or crm |
scale |
logical, scale variable to have equal sd. |
kmax |
maximum number of k, if ks is not specified. |
kernel |
kernel to use. Possible choices are "rectangular" (which is standard unweighted knn), "triangular", "epanechnikov" (or beta(2,2)), "biweight" (or beta(3,3)), "triweight" (or beta(4,4)), "cos", "inv", "gaussian" and "optimal". |
Lima-Neto, E.A., De Carvalho, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis52, 1500-1515
Lima-Neto, E.A., De Carvalho, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347
Lima Neto, E.d.A., de Carvalho, F.d.A.T. Nonlinear regression applied to interval-valued data. Pattern Anal Applic 20, 809–824 (2017). https://doi.org/10.1007/s10044-016-0538-y
Rodriguez, O. (2018). Shrinkage linear regression for symbolic interval-valued variables.Journal MODULAD 2018, vol. Modulad 45, pp.19-38
To execute the Center Method (CR) and Center and Range Method (CRM) to Linear regression.
sym.lm(formula, sym.data, method = c('cm', 'crm'))sym.lm(formula, sym.data, method = c('cm', 'crm'))
formula |
An object of class 'formula' (or one that can be coerced to that class): a symbolic description of the model to be fitted. |
sym.data |
Should be a symbolic data table read with the function read.sym.table(...). |
method |
'cm' to Center Method and 'crm' to Center and Range Method. |
Models for lm are specified symbolically. A typical model has the form response ~ terms where response is the (numeric) response vector and terms is a series of terms which specifies a linear predictor for response. A terms specification of the form first + second indicates all the terms in first together with all the terms in second with duplicates removed. A specification of the form first:second indicates the set of terms obtained by taking the interactions of all terms in first with all terms in second. The specification first*second indicates the cross of first and second. This is the same as first + second + first:second.
sym.lm returns an object of class 'lm' or for multiple responses of class c('mlm', 'lm')
Oldemar Rodriguez Rojas
LIMA-NETO, E.A., DE CARVALHO, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis 52, 1500-1515.
LIMA-NETO, E.A., DE CARVALHO, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347.
data(int_prost_train) data(int_prost_test) res.cm <- sym.lm(lpsa ~ ., sym.data = int_prost_train, method = "cm") res.cmdata(int_prost_train) data(int_prost_test) res.cm <- sym.lm(lpsa ~ ., sym.data = int_prost_train, method = "cm") res.cm
This function executes a Multiple Correspondence Factor Analysis for variables of set type.
sym.mcfa(sym.data, pos.var)sym.mcfa(sym.data, pos.var)
sym.data |
A symbolic data table containing at least two set type variables. |
pos.var |
Column numbers in the symbolic data table that contain the set type variables. |
Jorge Arce
Arce J. and Rodriguez, O. (2018). Multiple Correspondence Analysis for Symbolic Multi–Valued Variables. On the Symbolic Data Analysis Workshop SDA 2018.
Benzecri, J.P. (1973). L' Analyse des Données. Tomo 2: L'Analyse des Correspondances. Dunod, Paris.
Castillo, W. and Rodriguez O. (1997). Algoritmo e implementacion del analisis factorial de correspondencias. Revista de Matematicas: Teoria y Aplicaciones, 24-31.
Takagi I. and Yadosiha H. (2011). Correspondence Analysis for symbolic contingency tables base on interval algebra. Elsevier Procedia Computer Science, 6, 352-357.
Rodriguez, O. (2007). Correspondence Analysis for Symbolic Multi–Valued Variables. CARME 2007 (Rotterdam, The Netherlands), http://www.carme-n.org/carme2007.
data("ex_mcfa1") sym.table <- classic.to.sym(ex_mcfa1, concept = suspect, hair = sym.set(hair), eyes = sym.set(eyes), region = sym.set(region) ) sym.tabledata("ex_mcfa1") sym.table <- classic.to.sym(ex_mcfa1, concept = suspect, hair = sym.set(hair), eyes = sym.set(eyes), region = sym.set(region) ) sym.table
Create an symbolic_modal type object
sym.modal(x = character())sym.modal(x = character())
x |
character vector |
a symbolic modal
sym.modal(factor(c("a", "b", "b", "l")))sym.modal(factor(c("a", "b", "b", "l")))
Symbolic neural networks regression
sym.nnet( formula, sym.data, method = c("cm", "crm"), hidden = c(10), threshold = 0.05, stepmax = 1e+05 )sym.nnet( formula, sym.data, method = c("cm", "crm"), hidden = c(10), threshold = 0.05, stepmax = 1e+05 )
formula |
a symbolic description of the model to be fitted. |
sym.data |
symbolic data.table |
method |
cm crm |
|
a vector of integers specifying the number of hidden neurons (vertices) in each layer. |
|
threshold |
a numeric value specifying the threshold for the partial derivatives of the error function as stopping criteria. |
stepmax |
the maximum steps for the training of the neural network. Reaching this maximum leads to a stop of the neural network's training process. |
Lima-Neto, E.A., De Carvalho, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis52, 1500-1515
Lima-Neto, E.A., De Carvalho, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347
Lima Neto, E.d.A., de Carvalho, F.d.A.T. Nonlinear regression applied to interval-valued data. Pattern Anal Applic 20, 809–824 (2017). https://doi.org/10.1007/s10044-016-0538-y
Rodriguez, O. (2018). Shrinkage linear regression for symbolic interval-valued variables.Journal MODULAD 2018, vol. Modulad 45, pp.19-38
Cazes, Chouakria, Diday and Schektman (1997) proposed the Centers and the Tops Methods to extend the well known principal components analysis method to a particular kind of symbolic objects characterized by multi–values variables of interval type.
sym.pca(sym.data, ...) ## S3 method for class 'symbolic_tbl' sym.pca( sym.data, method = c("classic", "tops", "centers", "principal.curves", "optimized.distance", "optimized.variance"), ... )sym.pca(sym.data, ...) ## S3 method for class 'symbolic_tbl' sym.pca( sym.data, method = c("classic", "tops", "centers", "principal.curves", "optimized.distance", "optimized.variance"), ... )
sym.data |
Shoud be a symbolic data table |
... |
further arguments passed to or from other methods. |
method |
It is use so select the method, 'classic' execute a classical principal component analysis over the centers of the intervals, 'tops' to use the vertices algorithm and 'centers' to use the centers algorithm. |
Sym.Components: This a symbolic data table with the interval principal components. As this is a symbolic data table we can apply over this table any other symbolic data analysis method (symbolic propagation).
Sym.Prin.Correlations: This is the interval correlations between the original interval variables and the interval principal components, it can be use to plot the symbolic circle of correlations.
Oldemar Rodriguez Rojas
Bock H-H. and Diday E. (eds.) (2000). Analysis of Symbolic Data. Exploratory methods for extracting statistical information from complex data. Springer, Germany.
Cazes P., Chouakria A., Diday E. et Schektman Y. (1997). Extension de l'analyse en composantes principales a des donnees de type intervalle, Rev. Statistique Appliquee, Vol. XLV Num. 3 pag. 5-24, France.
Chouakria A. (1998) Extension des methodes d'analysis factorialle a des donnees de type intervalle, Ph.D. Thesis, Paris IX Dauphine University.
Makosso-Kallyth S. and Diday E. (2012). Adaptation of interval PCA to symbolic histogram variables, Advances in Data Analysis and Classification July, Volume 6, Issue 2, pp 147-159.
Rodriguez, O. (2000). Classification et Modeles Lineaires en Analyse des Donnees Symboliques. Ph.D. Thesis, Paris IX-Dauphine University.
sym.histogram.pca
## Not run: data(oils) res <- sym.pca(oils, "centers") sym.scatterplot(res$Sym.Components[, 1], res$Sym.Components[, 1], labels = TRUE, col = "red", main = "PCA Oils Data" ) sym.scatterplot3d(res$Sym.Components[, 1], res$Sym.Components[, 2], res$Sym.Components[, 3], color = "blue", main = "PCA Oils Data" ) sym.scatterplot.ggplot(res$Sym.Components[, 1], res$Sym.Components[, 2], labels = TRUE ) sym.circle.plot(res$Sym.Prin.Correlations) res <- sym.pca(oils, "classic") plot(res, choix = "ind") plot(res, choix = "var") data(lynne2) res <- sym.pca(lynne2, "centers") sym.scatterplot(res$Sym.Components[, 1], res$Sym.Components[, 2], labels = TRUE, col = "red", main = "PCA Lynne Data" ) sym.scatterplot3d(res$Sym.Components[, 1], res$Sym.Components[, 2], res$Sym.Components[, 3], color = "blue", main = "PCA Lynne Data" ) sym.scatterplot.ggplot(res$Sym.Components[, 1], res$Sym.Components[, 2], labels = TRUE ) sym.circle.plot(res$Sym.Prin.Correlations) data(StudentsGrades) st <- StudentsGrades s.pca <- sym.pca(st) plot(s.pca, choix = "ind") plot(s.pca, choix = "var") ## End(Not run)## Not run: data(oils) res <- sym.pca(oils, "centers") sym.scatterplot(res$Sym.Components[, 1], res$Sym.Components[, 1], labels = TRUE, col = "red", main = "PCA Oils Data" ) sym.scatterplot3d(res$Sym.Components[, 1], res$Sym.Components[, 2], res$Sym.Components[, 3], color = "blue", main = "PCA Oils Data" ) sym.scatterplot.ggplot(res$Sym.Components[, 1], res$Sym.Components[, 2], labels = TRUE ) sym.circle.plot(res$Sym.Prin.Correlations) res <- sym.pca(oils, "classic") plot(res, choix = "ind") plot(res, choix = "var") data(lynne2) res <- sym.pca(lynne2, "centers") sym.scatterplot(res$Sym.Components[, 1], res$Sym.Components[, 2], labels = TRUE, col = "red", main = "PCA Lynne Data" ) sym.scatterplot3d(res$Sym.Components[, 1], res$Sym.Components[, 2], res$Sym.Components[, 3], color = "blue", main = "PCA Lynne Data" ) sym.scatterplot.ggplot(res$Sym.Components[, 1], res$Sym.Components[, 2], labels = TRUE ) sym.circle.plot(res$Sym.Prin.Correlations) data(StudentsGrades) st <- StudentsGrades s.pca <- sym.pca(st) plot(s.pca, choix = "ind") plot(s.pca, choix = "var") ## End(Not run)
To execute predict method the Center Method (CR) and Center and Range Method (CRM) to Linear regression.
sym.predict(model, ...) ## S3 method for class 'symbolic_lm_cm' sym.predict(model, new.sym.data, ...) ## S3 method for class 'symbolic_lm_crm' sym.predict(model, new.sym.data, ...) ## S3 method for class 'symbolic_glm_cm' sym.predict(model, new.sym.data, response, ...) ## S3 method for class 'symbolic_glm_crm' sym.predict(model, new.sym.data, response, ...)sym.predict(model, ...) ## S3 method for class 'symbolic_lm_cm' sym.predict(model, new.sym.data, ...) ## S3 method for class 'symbolic_lm_crm' sym.predict(model, new.sym.data, ...) ## S3 method for class 'symbolic_glm_cm' sym.predict(model, new.sym.data, response, ...) ## S3 method for class 'symbolic_glm_crm' sym.predict(model, new.sym.data, response, ...)
model |
The output of lm method. |
... |
additional arguments affecting the predictions produced. |
new.sym.data |
Should be a symbolic data table read with the function read.sym.table(...). |
response |
The number of the column where is the response variable in the interval data table. |
sym.predict produces a vector of predictions or a matrix of predictions and bounds with column names fit, lwr, and upr if interval is set. For type = 'terms' this is a matrix with a column per term and may have an attribute 'constant'
Oldemar Rodriguez Rojas
LIMA-NETO, E.A., DE CARVALHO, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis 52, 1500-1515.
LIMA-NETO, E.A., DE CARVALHO, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347.
sym.glm
data(int_prost_train) data(int_prost_test) model <- sym.lm(lpsa ~ ., sym.data = int_prost_train, method = "cm") pred.cm <- sym.predict(model, int_prost_test) pred.cmdata(int_prost_train) data(int_prost_test) model <- sym.lm(lpsa ~ ., sym.data = int_prost_train, method = "cm") pred.cm <- sym.predict(model, int_prost_test) pred.cm
Predict model_gbm_cm model
## S3 method for class 'symbolic_gbm_cm' sym.predict(model, new.sym.data, n.trees = 500, ...)## S3 method for class 'symbolic_gbm_cm' sym.predict(model, new.sym.data, n.trees = 500, ...)
model |
model |
new.sym.data |
new data |
n.trees |
Integer specifying the total number of trees to fit. This is equivalent to the number of iterations and the number of basis functions in the additive expansion. Default is 100. |
... |
optional parameters |
Lima-Neto, E.A., De Carvalho, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis52, 1500-1515
Lima-Neto, E.A., De Carvalho, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347
Lima Neto, E.d.A., de Carvalho, F.d.A.T. Nonlinear regression applied to interval-valued data. Pattern Anal Applic 20, 809–824 (2017). https://doi.org/10.1007/s10044-016-0538-y
Rodriguez, O. (2018). Shrinkage linear regression for symbolic interval-valued variables.Journal MODULAD 2018, vol. Modulad 45, pp.19-38
Predict model_gbm_crm model
## S3 method for class 'symbolic_gbm_crm' sym.predict(model, new.sym.data, n.trees = 500, ...)## S3 method for class 'symbolic_gbm_crm' sym.predict(model, new.sym.data, n.trees = 500, ...)
model |
model |
new.sym.data |
new data |
n.trees |
Integer specifying the total number of trees to fit. This is equivalent to the number of iterations and the number of basis functions in the additive expansion. Default is 100. |
... |
optional parameters |
Lima-Neto, E.A., De Carvalho, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis52, 1500-1515
Lima-Neto, E.A., De Carvalho, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347
Lima Neto, E.d.A., de Carvalho, F.d.A.T. Nonlinear regression applied to interval-valued data. Pattern Anal Applic 20, 809–824 (2017). https://doi.org/10.1007/s10044-016-0538-y
Rodriguez, O. (2018). Shrinkage linear regression for symbolic interval-valued variables.Journal MODULAD 2018, vol. Modulad 45, pp.19-38
Predict model_knn_cm model
## S3 method for class 'symbolic_knn_cm' sym.predict(model, new.sym.data, ...)## S3 method for class 'symbolic_knn_cm' sym.predict(model, new.sym.data, ...)
model |
model |
new.sym.data |
new data |
... |
optional parameters |
Lima-Neto, E.A., De Carvalho, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis52, 1500-1515
Lima-Neto, E.A., De Carvalho, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347
Lima Neto, E.d.A., de Carvalho, F.d.A.T. Nonlinear regression applied to interval-valued data. Pattern Anal Applic 20, 809–824 (2017). https://doi.org/10.1007/s10044-016-0538-y
Rodriguez, O. (2018). Shrinkage linear regression for symbolic interval-valued variables.Journal MODULAD 2018, vol. Modulad 45, pp.19-38
Predict model_knn_crm model
## S3 method for class 'symbolic_knn_crm' sym.predict(model, new.sym.data, ...)## S3 method for class 'symbolic_knn_crm' sym.predict(model, new.sym.data, ...)
model |
model |
new.sym.data |
new data |
... |
optional parameters |
Lima-Neto, E.A., De Carvalho, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis52, 1500-1515
Lima-Neto, E.A., De Carvalho, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347
Lima Neto, E.d.A., de Carvalho, F.d.A.T. Nonlinear regression applied to interval-valued data. Pattern Anal Applic 20, 809–824 (2017). https://doi.org/10.1007/s10044-016-0538-y
Rodriguez, O. (2018). Shrinkage linear regression for symbolic interval-valued variables.Journal MODULAD 2018, vol. Modulad 45, pp.19-38
Predict nnet_cm model
## S3 method for class 'symbolic_nnet_cm' sym.predict(model, new.sym.data, ...)## S3 method for class 'symbolic_nnet_cm' sym.predict(model, new.sym.data, ...)
model |
model |
new.sym.data |
new data |
... |
optional parameters |
Lima-Neto, E.A., De Carvalho, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis52, 1500-1515
Lima-Neto, E.A., De Carvalho, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347
Lima Neto, E.d.A., de Carvalho, F.d.A.T. Nonlinear regression applied to interval-valued data. Pattern Anal Applic 20, 809–824 (2017). https://doi.org/10.1007/s10044-016-0538-y
Rodriguez, O. (2018). Shrinkage linear regression for symbolic interval-valued variables.Journal MODULAD 2018, vol. Modulad 45, pp.19-38
Predict nnet_crm model
## S3 method for class 'symbolic_nnet_crm' sym.predict(model, new.sym.data, ...)## S3 method for class 'symbolic_nnet_crm' sym.predict(model, new.sym.data, ...)
model |
model |
new.sym.data |
new data |
... |
optional parameters |
Lima-Neto, E.A., De Carvalho, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis52, 1500-1515
Lima-Neto, E.A., De Carvalho, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347
Lima Neto, E.d.A., de Carvalho, F.d.A.T. Nonlinear regression applied to interval-valued data. Pattern Anal Applic 20, 809–824 (2017). https://doi.org/10.1007/s10044-016-0538-y
Rodriguez, O. (2018). Shrinkage linear regression for symbolic interval-valued variables.Journal MODULAD 2018, vol. Modulad 45, pp.19-38
Predict rf_cm model
## S3 method for class 'symbolic_rf_cm' sym.predict(model, new.sym.data, ...)## S3 method for class 'symbolic_rf_cm' sym.predict(model, new.sym.data, ...)
model |
model |
new.sym.data |
new data |
... |
optional parameters |
Lima-Neto, E.A., De Carvalho, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis52, 1500-1515
Lima-Neto, E.A., De Carvalho, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347
Lima Neto, E.d.A., de Carvalho, F.d.A.T. Nonlinear regression applied to interval-valued data. Pattern Anal Applic 20, 809–824 (2017). https://doi.org/10.1007/s10044-016-0538-y
Rodriguez, O. (2018). Shrinkage linear regression for symbolic interval-valued variables.Journal MODULAD 2018, vol. Modulad 45, pp.19-38
Predict rf_crm model
## S3 method for class 'symbolic_rf_crm' sym.predict(model, new.sym.data, ...)## S3 method for class 'symbolic_rf_crm' sym.predict(model, new.sym.data, ...)
model |
model |
new.sym.data |
new data |
... |
optional parameters |
Lima-Neto, E.A., De Carvalho, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis52, 1500-1515
Lima-Neto, E.A., De Carvalho, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347
Lima Neto, E.d.A., de Carvalho, F.d.A.T. Nonlinear regression applied to interval-valued data. Pattern Anal Applic 20, 809–824 (2017). https://doi.org/10.1007/s10044-016-0538-y
Rodriguez, O. (2018). Shrinkage linear regression for symbolic interval-valued variables.Journal MODULAD 2018, vol. Modulad 45, pp.19-38
Predict rt_cm model
## S3 method for class 'symbolic_rt_cm' sym.predict(model, new.sym.data, ...)## S3 method for class 'symbolic_rt_cm' sym.predict(model, new.sym.data, ...)
model |
a model_rt_crm object |
new.sym.data |
new data |
... |
arguments to predict.rpart |
Lima-Neto, E.A., De Carvalho, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis52, 1500-1515
Lima-Neto, E.A., De Carvalho, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347
Lima Neto, E.d.A., de Carvalho, F.d.A.T. Nonlinear regression applied to interval-valued data. Pattern Anal Applic 20, 809–824 (2017). https://doi.org/10.1007/s10044-016-0538-y
Rodriguez, O. (2018). Shrinkage linear regression for symbolic interval-valued variables.Journal MODULAD 2018, vol. Modulad 45, pp.19-38
Predict rt_crm model
## S3 method for class 'symbolic_rt_crm' sym.predict(model, new.sym.data, ...)## S3 method for class 'symbolic_rt_crm' sym.predict(model, new.sym.data, ...)
model |
a model_rt_crm object |
new.sym.data |
new data |
... |
optional parameters |
Lima-Neto, E.A., De Carvalho, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis52, 1500-1515
Lima-Neto, E.A., De Carvalho, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347
Lima Neto, E.d.A., de Carvalho, F.d.A.T. Nonlinear regression applied to interval-valued data. Pattern Anal Applic 20, 809–824 (2017). https://doi.org/10.1007/s10044-016-0538-y
Rodriguez, O. (2018). Shrinkage linear regression for symbolic interval-valued variables.Journal MODULAD 2018, vol. Modulad 45, pp.19-38
Predict model_svm_cm model
## S3 method for class 'symbolic_svm_cm' sym.predict(model, new.sym.data, ...)## S3 method for class 'symbolic_svm_cm' sym.predict(model, new.sym.data, ...)
model |
model |
new.sym.data |
new data |
... |
optional parameters |
Lima-Neto, E.A., De Carvalho, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis52, 1500-1515
Lima-Neto, E.A., De Carvalho, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347
Lima Neto, E.d.A., de Carvalho, F.d.A.T. Nonlinear regression applied to interval-valued data. Pattern Anal Applic 20, 809–824 (2017). https://doi.org/10.1007/s10044-016-0538-y
Rodriguez, O. (2018). Shrinkage linear regression for symbolic interval-valued variables.Journal MODULAD 2018, vol. Modulad 45, pp.19-38
Predict model_svm_crm model
## S3 method for class 'symbolic_svm_crm' sym.predict(model, new.sym.data, ...)## S3 method for class 'symbolic_svm_crm' sym.predict(model, new.sym.data, ...)
model |
model |
new.sym.data |
new data |
... |
optional parameters |
Lima-Neto, E.A., De Carvalho, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis52, 1500-1515
Lima-Neto, E.A., De Carvalho, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347
Lima Neto, E.d.A., de Carvalho, F.d.A.T. Nonlinear regression applied to interval-valued data. Pattern Anal Applic 20, 809–824 (2017). https://doi.org/10.1007/s10044-016-0538-y
Rodriguez, O. (2018). Shrinkage linear regression for symbolic interval-valued variables.Journal MODULAD 2018, vol. Modulad 45, pp.19-38
Symbolic Regression with Random Forest
sym.rf(formula, sym.data, method = c("cm", "crm"), ntree = 500)sym.rf(formula, sym.data, method = c("cm", "crm"), ntree = 500)
formula |
a formula, with a response but no interaction terms. If this a a data frame, that is taken as the model frame (see model.frame). |
sym.data |
symbolic data table |
method |
cm crm |
ntree |
Number of trees to grow. This should not be set to too small a number, to ensure that every input row gets predicted at least a few times. |
Lima-Neto, E.A., De Carvalho, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis52, 1500-1515
Lima-Neto, E.A., De Carvalho, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347
Lima Neto, E.d.A., de Carvalho, F.d.A.T. Nonlinear regression applied to interval-valued data. Pattern Anal Applic 20, 809–824 (2017). https://doi.org/10.1007/s10044-016-0538-y
Rodriguez, O. (2018). Shrinkage linear regression for symbolic interval-valued variables.Journal MODULAD 2018, vol. Modulad 45, pp.19-38
Symbolic Regression Trees
sym.rt( formula, sym.data, method = c("cm", "crm"), minsplit = 20, maxdepth = 10 )sym.rt( formula, sym.data, method = c("cm", "crm"), minsplit = 20, maxdepth = 10 )
formula |
a formula, with a response but no interaction terms. If this a a data frame, that is taken as the model frame (see model.frame). |
sym.data |
a symbolic data table |
method |
cm crm |
minsplit |
the minimum number of observations that must exist in a node in order for a split to be attempted. |
maxdepth |
Set the maximum depth of any node of the final tree, with the root node counted as depth 0. Values greater than 30 rpart will give nonsense results on 32-bit machines. |
Lima-Neto, E.A., De Carvalho, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis52, 1500-1515
Lima-Neto, E.A., De Carvalho, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347
Lima Neto, E.d.A., de Carvalho, F.d.A.T. Nonlinear regression applied to interval-valued data. Pattern Anal Applic 20, 809–824 (2017). https://doi.org/10.1007/s10044-016-0538-y
Rodriguez, O. (2018). Shrinkage linear regression for symbolic interval-valued variables.Journal MODULAD 2018, vol. Modulad 45, pp.19-38
This function could be use to plot two symbolic variables in a X-Y plane.
sym.scatterplot(sym.var.x, sym.var.y, labels = FALSE, ...)sym.scatterplot(sym.var.x, sym.var.y, labels = FALSE, ...)
sym.var.x |
First symbolic variable |
sym.var.y |
Second symbolic variable. |
labels |
As in R plot function. |
... |
As in R plot function. |
Return a graphics.
Oldemar Rodriguez Rojas
Bock H-H. and Diday E. (eds.) (2000). Analysis of Symbolic Data. Exploratory methods for extracting statistical information from complex data. Springer, Germany.
Rodriguez, O. (2000). Classification et Modeles Lineaires en Analyse des Donnees Symboliques. Ph.D. Thesis, Paris IX-Dauphine University.
sym.scatterplot3d
## Not run: data(example3) sym.data <- example3 sym.scatterplot(sym.data[, 3], sym.data[, 7], col = "blue", main = "Main Title") sym.scatterplot(sym.data[, 1], sym.data[, 4], labels = TRUE, col = "blue", main = "Main Title" ) sym.scatterplot(sym.data[, 2], sym.data[, 6], labels = TRUE, col = "red", main = "Main Title", lwd = 3 ) data(oils) sym.scatterplot(oils[, 2], oils[, 3], labels = TRUE, col = "red", main = "Oils Data" ) data(lynne1) sym.scatterplot(lynne1[, 2], lynne1[, 1], labels = TRUE, col = "red", main = "Lynne Data" ) ## End(Not run)## Not run: data(example3) sym.data <- example3 sym.scatterplot(sym.data[, 3], sym.data[, 7], col = "blue", main = "Main Title") sym.scatterplot(sym.data[, 1], sym.data[, 4], labels = TRUE, col = "blue", main = "Main Title" ) sym.scatterplot(sym.data[, 2], sym.data[, 6], labels = TRUE, col = "red", main = "Main Title", lwd = 3 ) data(oils) sym.scatterplot(oils[, 2], oils[, 3], labels = TRUE, col = "red", main = "Oils Data" ) data(lynne1) sym.scatterplot(lynne1[, 2], lynne1[, 1], labels = TRUE, col = "red", main = "Lynne Data" ) ## End(Not run)
Create an symbolic_set type object
sym.set(x = NA)sym.set(x = NA)
x |
character vector |
a symbolic set
sym.set(factor(c("a", "b", "b", "l")))sym.set(factor(c("a", "b", "b", "l")))
Symbolic Support Vector Machines Regression
sym.svm( formula, sym.data, method = c("cm", "crm"), scale = TRUE, kernel = "radial" )sym.svm( formula, sym.data, method = c("cm", "crm"), scale = TRUE, kernel = "radial" )
formula |
a symbolic description of the model to be fit. |
sym.data |
symbolic data.table |
method |
method |
scale |
A logical vector indicating the variables to be scaled. If scale is of length 1, the value is recycled as many times as needed. Per default, data are scaled internally (both x and y variables) to zero mean and unit variance. The center and scale values are returned and used for later predictions. |
kernel |
the kernel used in training and predicting. You might consider changing some of the following parameters, depending on the kernel type. |
Lima-Neto, E.A., De Carvalho, F.A.T., (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis52, 1500-1515
Lima-Neto, E.A., De Carvalho, F.A.T., (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis 54, 333-347
Lima Neto, E.d.A., de Carvalho, F.d.A.T. Nonlinear regression applied to interval-valued data. Pattern Anal Applic 20, 809–824 (2017). https://doi.org/10.1007/s10044-016-0538-y
Rodriguez, O. (2018). Shrinkage linear regression for symbolic interval-valued variables.Journal MODULAD 2018, vol. Modulad 45, pp.19-38
This function applies the UMAP algorithm to a symbolic data table.
sym.umap(sym.data, ...) ## S3 method for class 'symbolic_tbl' sym.umap( sym.data = NULL, config = umap::umap.defaults, method = c("naive", "umap-learn"), preserve.seed = TRUE, ... )sym.umap(sym.data, ...) ## S3 method for class 'symbolic_tbl' sym.umap( sym.data = NULL, config = umap::umap.defaults, method = c("naive", "umap-learn"), preserve.seed = TRUE, ... )
sym.data |
symbolic data table |
... |
list of settings; values overwrite defaults from config; see documentation of umap.default for details about available settings |
config |
object of class umap.config |
method |
character, implementation. Available methods are 'naive' (an implementation written in pure R) and 'umap-learn' (requires python package 'umap-learn') |
preserve.seed |
logical, leave TRUE to insulate external code from randomness within the umap algorithms; set FALSE to allow randomness used in umap algorithms to alter the external random-number generator |
This function get a symbolic variable from a symbolic data table.
sym.var(sym.data, number.sym.var)sym.var(sym.data, number.sym.var)
sym.data |
The symbolic data table |
number.sym.var |
The number of the column for the variable (feature) that we want to get. |
Return a symbolic data variable with the following structure:
$N
[1] 7
$var.name
[1] 'F6'
$var.type
[1] '$I'
$obj.names
[1] 'Case1' 'Case2' 'Case3' 'Case4' 'Case5' 'Case6' 'Case7'
$var.data.vector
F6 F6.1
Case1 0.00 90.00
Case2 -90.00 98.00
Case3 65.00 90.00
Case4 45.00 89.00
Case5 20.00 40.00
Case6 5.00 8.00
Case7 3.14 6.76
Oldemar Rodriguez Rojas
Billard L. and Diday E. (2006). Symbolic data analysis: Conceptual statistics and data mining. Wiley, Chichester.
Bock H-H. and Diday E. (eds.) (2000). Analysis of Symbolic Data. Exploratory methods for extracting statistical information from complex data. Springer, Germany.
sym.obj
Us crime classic data table that can be used to generate symbolic data tables.
data(USCrime)data(USCrime)
An object of class data.frame with 1994 rows and 103 columns.
http://archive.ics.uci.edu/ml/
HASTIE, T., TIBSHIRANI, R. and FRIEDMAN, J. (2008). The Elements of Statistical Learning: Data Mining, Inference and Prediction. New York: Springer.
## Not run: data(USCrime) us.crime <- USCrime dim(us.crime) head(us.crime) summary(us.crime) names(us.crime) nrow(us.crime) result <- classic.to.sym(us.crime, concept = "state", variables = c(NumInShelters, NumImmig), variables.types = c( NumInShelters = type.histogram(), NumImmig = type.histogram() ) ) result ## End(Not run)## Not run: data(USCrime) us.crime <- USCrime dim(us.crime) head(us.crime) summary(us.crime) names(us.crime) nrow(us.crime) result <- classic.to.sym(us.crime, concept = "state", variables = c(NumInShelters, NumImmig), variables.types = c( NumInShelters = type.histogram(), NumImmig = type.histogram() ) ) result ## End(Not run)
Us crime classic data table genetated from uscrime data.
data(uscrime_int)data(uscrime_int)
An object of class symbolic_tbl (inherits from tbl_df, tbl, data.frame) with 46 rows and 102 columns.
Rodriguez O. (2013). A generalization of Centre and Range method for fitting a linear regression model to symbolic interval data using Ridge Regression, Lasso and Elastic Net methods. The IFCS2013 conference of the International Federation of Classification Societies, Tilburg University Holland.
data(uscrime_int) car.data <- uscrime_int res.cm.lasso <- sym.glm( sym.data = car.data, response = 102, method = "cm", alpha = 1, nfolds = 10, grouped = TRUE ) plot(res.cm.lasso) plot(res.cm.lasso$glmnet.fit, "norm", label = TRUE) plot(res.cm.lasso$glmnet.fit, "lambda", label = TRUE) pred.cm.lasso <- sym.predict(res.cm.lasso, response = 102, car.data) RMSE.L(car.data$ViolentCrimesPerPop, pred.cm.lasso) RMSE.U(car.data$ViolentCrimesPerPop, pred.cm.lasso) R2.L(car.data$ViolentCrimesPerPop, pred.cm.lasso) R2.U(car.data$ViolentCrimesPerPop, pred.cm.lasso) deter.coefficient(car.data$ViolentCrimesPerPop, pred.cm.lasso)data(uscrime_int) car.data <- uscrime_int res.cm.lasso <- sym.glm( sym.data = car.data, response = 102, method = "cm", alpha = 1, nfolds = 10, grouped = TRUE ) plot(res.cm.lasso) plot(res.cm.lasso$glmnet.fit, "norm", label = TRUE) plot(res.cm.lasso$glmnet.fit, "lambda", label = TRUE) pred.cm.lasso <- sym.predict(res.cm.lasso, response = 102, car.data) RMSE.L(car.data$ViolentCrimesPerPop, pred.cm.lasso) RMSE.U(car.data$ViolentCrimesPerPop, pred.cm.lasso) R2.L(car.data$ViolentCrimesPerPop, pred.cm.lasso) R2.U(car.data$ViolentCrimesPerPop, pred.cm.lasso) deter.coefficient(car.data$ViolentCrimesPerPop, pred.cm.lasso)
Us crime classic data table genetated from uscrime data.
data(uscrime_int)data(uscrime_int)
An object of class symbolic_tbl (inherits from tbl_df, tbl, data.frame) with 46 rows and 102 columns.
Rodriguez O. (2013). A generalization of Centre and Range method for fitting a linear regression model to symbolic interval data using Ridge Regression, Lasso and Elastic Net methods. The IFCS2013 conference of the International Federation of Classification Societies, Tilburg University Holland.
Compute the symbolic variance.
var(x, ...) ## Default S3 method: var(x, y = NULL, na.rm = FALSE, use, ...) ## S3 method for class 'symbolic_interval' var(x, method = c("centers", "interval", "billard"), na.rm = FALSE, ...) ## S3 method for class 'symbolic_tbl' var(x, ...)var(x, ...) ## Default S3 method: var(x, y = NULL, na.rm = FALSE, use, ...) ## S3 method for class 'symbolic_interval' var(x, method = c("centers", "interval", "billard"), na.rm = FALSE, ...) ## S3 method for class 'symbolic_tbl' var(x, ...)
x |
A symbolic interval. |
... |
As in R median function. |
y |
NULL (default) or a vector, matrix or data frame with compatible dimensions to x. The default is equivalent to y = x (but more efficient). |
na.rm |
logical. Should missing values be removed? |
use |
an optional character string giving a method for computing covariances in the presence of missing values. This must be (an abbreviation of) one of the strings 'everything', 'all.obs', 'complete.obs', 'na.or.complete', or 'pairwise.complete.obs'. |
method |
The method to be use. |
Oldemar Rodriguez Rojas
Billard L. and Diday E. (2006). Symbolic data analysis: Conceptual statistics and data mining. Wiley, Chichester.
Rodriguez, O. (2000). Classification et Modeles Lineaires en Analyse des Donnees Symboliques. Ph.D. Thesis, Paris IX-Dauphine University.
Variance of the principal curve
variance.princ.curve(data,curve)variance.princ.curve(data,curve)
data |
Classic data table. |
curve |
The principal curve. |
The variance of the principal curve.
Jorge Arce.
Arce J. and Rodriguez O. (2015) 'Principal Curves and Surfaces to Interval Valued Variables'. The 5th Workshop on Symbolic Data Analysis, SDA2015, Orleans, France, November.
Hastie,T. (1984). Principal Curves and Surface. Ph.D Thesis Stanford University.
Hastie,T. & Weingessel,A. (2014). princurve - Fits a Principal Curve in Arbitrary Dimension.R package version 1.1–12 http://cran.r-project.org/web/packages/princurve/index.html.
Hastie,T. & Stuetzle, W. (1989). Principal Curves. Journal of the American Statistical Association, Vol. 84-406, 502–516.
Hastie, T., Tibshirani, R. & Friedman, J. (2008). The Elements of Statistical Learning; Data Mining, Inference and Prediction. Springer, New York.
sym.interval.pc
Vertex of the intervals
vertex.interval(sym.data)vertex.interval(sym.data)
sym.data |
Symbolic interval data table. |
Vertices of the intervals.
Jorge Arce.
Arce J. and Rodriguez O. (2015) 'Principal Curves and Surfaces to Interval Valued Variables'. The 5th Workshop on Symbolic Data Analysis, SDA2015, Orleans, France, November.
Hastie,T. (1984). Principal Curves and Surface. Ph.D Thesis Stanford University.
Hastie,T. & Weingessel,A. (2014). princurve - Fits a Principal Curve in Arbitrary Dimension.R package version 1.1–12 http://cran.r-project.org/web/packages/princurve/index.html.
Hastie,T. & Stuetzle, W. (1989). Principal Curves. Journal of the American Statistical Association, Vol. 84-406, 502–516.
Hastie, T., Tibshirani, R. & Friedman, J. (2008). The Elements of Statistical Learning; Data Mining, Inference and Prediction. Springer, New York.
sym.interval.pc
Symbolic data matrix with all the variables of interval type.
data(VeterinaryData)data(VeterinaryData)
$I Height Height $I Weight Weight
1 $I 120.0 180.0 $I 222.2 354.0
2 $I 158.0 160.0 $I 322.0 355.0
3 $I 175.0 185.0 $I 117.2 152.0
4 $I 37.9 62.9 $I 22.2 35.0
5 $I 25.8 39.6 $I 15.0 36.2
6 $I 22.8 58.6 $I 15.0 51.8
7 $I 22.0 45.0 $I 0.8 11.0
8 $I 18.0 53.0 $I 0.4 2.5
9 $I 40.3 55.8 $I 2.1 4.5
10 $I 38.4 72.4 $I 2.5 6.1
Billard L. and Diday E. (2006). Symbolic data analysis: Conceptual statistics and data mining. Wiley, Chichester.
data(VeterinaryData) VeterinaryDatadata(VeterinaryData) VeterinaryData
This function write (save) a symbolic data table from a CSV data file.
write.sym.table(sym.data, file, sep, dec, row.names = NULL, col.names = NULL)write.sym.table(sym.data, file, sep, dec, row.names = NULL, col.names = NULL)
sym.data |
Symbolic data table |
file |
The name of the CSV file. |
sep |
As in R function read.table |
dec |
As in R function read.table |
row.names |
As in R function read.table |
col.names |
As in R function read.table |
Write in CSV file the symbolic data table.
Oldemar Rodriguez Rojas
Bock H-H. and Diday E. (eds.) (2000). Analysis of Symbolic Data. Exploratory methods for extracting statistical information from complex data. Springer, Germany.
read.sym.table
## Not run: data(example1) write.sym.table(example1, file = "temp4.csv", sep = "|", dec = ".", row.names = TRUE, col.names = TRUE) ex1 <- read.sym.table("temp4.csv", header = TRUE, sep = "|", dec = ".", row.names = 1) ## End(Not run)## Not run: data(example1) write.sym.table(example1, file = "temp4.csv", sep = "|", dec = ".", row.names = TRUE, col.names = TRUE) ex1 <- read.sym.table("temp4.csv", header = TRUE, sep = "|", dec = ".", row.names = 1) ## End(Not run)