Package 'FADA'

Title: Variable Selection for Supervised Classification in High Dimension
Description: The functions provided in the FADA (Factor Adjusted Discriminant Analysis) package aim at performing supervised classification of high-dimensional and correlated profiles. The procedure combines a decorrelation step based on a factor modeling of the dependence among covariates and a classification method. The available methods are Lasso regularized logistic model (see Friedman et al. (2010)), sparse linear discriminant analysis (see Clemmensen et al. (2011)), shrinkage linear and diagonal discriminant analysis (see M. Ahdesmaki et al. (2010)). More methods of classification can be used on the decorrelated data provided by the package FADA.
Authors: Emeline Perthame (Institut Pasteur, Paris, France), Chloe Friguet (Universite de Bretagne Sud, Vannes, France) and David Causeur (Agrocampus Ouest, Rennes, France)
Maintainer: David Causeur <[email protected]>
License: GPL (>= 2)
Version: 1.3.5
Built: 2025-02-10 03:13:07 UTC
Source: https://github.com/cran/FADA

Help Index

Variable selection for supervised classification in high dimension

Description

The functions provided in the FADA (Factor Adjusted Discriminant Analysis) package aim at performing supervised classification of high-dimensional and correlated profiles. The procedure combines a decorrelation step based on a factor modeling of the dependence among covariates and a classification method. The available methods are Lasso regularized logistic model (see Friedman et al. (2010)), sparse linear discriminant analysis (see Clemmensen et al. (2011)), shrinkage linear and diagonal discriminant analysis (see M. Ahdesmaki et al. (2010)). More methods of classification can be used on the decorrelated data provided by the package FADA.

Details

Package: FADA
Type: Package
Version: 1.2
Date: 2014-10-08
License: GPL (>= 2)

The functions available in this package are used in this order:

  • Step 1: Decorrelation of the training dataset using a factor model of the covariance by the decorrelate.train function. The number of factors of the model can be estimated or forced.

  • Step 2: If needed, decorrelation of the testing dataset by using the decorrelate.test function and the estimated factor model parameters provided by decorrelate.train.

  • Step 3: Estimation of a supervised classification model using the decorrelated training dataset by the FADA function. One can choose among several classification methods (more details in the manual of FADA function).

  • Step 4: If needed, computation of the error rate by the FADA function, either using a supplementary test dataset or by K-fold cross-validation.

Author(s)

Emeline Perthame (Agrocampus Ouest, Rennes, France), Chloe Friguet (Universite de Bretagne Sud, Vannes, France) and David Causeur (Agrocampus Ouest, Rennes, France)

Maintainer: David Causeur, http://math.agrocampus-ouest.fr/infoglueDeliverLive/membres/david.causeur, mailto: [email protected]

References

Ahdesmaki, M. and Strimmer, K. (2010), Feature selection in omics prediction problems using cat scores and false non-discovery rate control. Annals of Applied Statistics, 4, 503-519.

Clemmensen, L., Hastie, T. and Witten, D. and Ersboll, B. (2011), Sparse discriminant analysis. Technometrics, 53(4), 406-413.

Friedman, J., Hastie, T. and Tibshirani, R. (2010), Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33, 1-22.

Friguet, C., Kloareg, M. and Causeur, D. (2009), A factor model approach to multiple testing under dependence. Journal of the American Statistical Association, 104:488, 1406-1415.

Perthame, E., Friguet, C. and Causeur, D. (2015), Stability of feature selection in classification issues for high-dimensional correlated data, Statistics and Computing.

Examples

### Not run 
 ### example of an entire analysis with FADA package if a testing data set is available
 ### loading data
 # data(data.train)
 # data(data.test)
 
 # dim(data.train$x) # 30 250
 # dim(data.test$x) # 1000 250

 ### decorrelation of the training data set
 # res = decorrelate.train(data.train) # Optimal number of factors is 3
 ### decorrelation of the testing data set afterward
 # res2 = decorrelate.test(res,data.test)

 ### classification step with sda, using local false discovery rate for variable selection
 ### linear discriminant analysis
 # FADA.LDA = FADA(res2,method="sda",sda.method="lfdr")
 
 ### diagonal discriminant analysis 
 # FADA.DDA =  FADA(res2, method="sda",sda.method="lfdr",diagonal=TRUE)


### example of an entire analysis with FADA package if no testing data set is available
 ### loading data
 
 ### decorrelation step
 # res = decorrelate.train(data.train) # Optimal number of factors is 3
 
 ### classification step with sda, using local false discovery rate for variable selection
 ### linear discriminant analysis, error rate is computed by 10-fold CV (20 replications of the CV)
 # FADA.LDA = FADA(res,method="sda",sda.method="lfdr")

Test dataset simulated with the same distribution as the training dataset data.train.

Description

The test dataset has the same list structure as the training dataset dta. Only the numbers of rows of the x component and length of the y component are different since the test sample size is 1000.

Usage

data(data.test)

Format

List with 2 components: x, the 1000x250 matrix of simulated explanatory variables and y, the 1000x1 grouping variable (coded 1 and 2).

Examples

data(data.test)
dim(data.test$x) # 1000 250
data.test$y # 2 levels

Training data

Description

Simulated training dataset. The x component is a matrix of explanatory variables, with 30 rows and 250 columns. Each row is simulated according to a multinormal distribution which mean depends on a group membership given by the y component. The variance matrix is the same within each group.

Usage

data(data.train)

Format

A list with 2 components. x is a 30x250 matrix of simulated explanatory variables. y is a 30x1 grouping variable (coded 1 and 2).

Examples

data(data.train)
dim(data.train$x) # 30 250
data.train$y # 2 levels
hist(cor(data.train$x[data.train$y==1,])) # high dependence 
hist(cor(data.train$x[data.train$y==2,]))

Factor Adjusted Discriminant Analysis 2: Decorrelation of a testing data set after running the decorrelate.train function on a training data set

Description

This function decorrelates the test dataset by adjusting data for the effects of latent factors of dependence, after running the decorrelate.train function on a training data set.

Usage

decorrelate.test(faobject,data.test)

Arguments

faobject

An object returned by function decorrelate.train.
data.test

A list containing the testing dataset, with the following component: x is a n x p matrix of explanatory variables, where n stands for the testing sample size and p for the number of explanatory variables.

Value

Returns a list with the following elements:

meanclass

Group means estimated after iterative decorrelation
fa.training

Decorrelated training data
fa.testing

Decorrelated testing data
Psi

Estimation of the factor model parameters: specific variance
B

Estimation of the factor model parameters: loadings
factors.training

Scores of the trainings individuals on the factors
factors.testing

Scores of the testing individuals on the factors
groups

Recall of group variable of training data
proba.training

Internal value (estimation of individual probabilities for the training dataset)
proba.testing

Internal value (estimation of individual probabilities for the testing dataset)
mod.decorrelate.test

Internal value (classification model)

Author(s)

Emeline Perthame, Chloe Friguet and David Causeur

References

Friedman, J., Hastie, T. and Tibshirani, R. (2010), Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33, 1-22.

Friguet, C., Kloareg, M. and Causeur, D. (2009), A factor model approach to multiple testing under dependence. Journal of the American Statistical Association, 104:488, 1406-1415.

Perthame, E., Friguet, C. and Causeur, D. (2015), Stability of feature selection in classification issues for high-dimensional correlated data, Statistics and Computing.

See Also

FADA-package FADA glmnet-package

Examples

data(data.train)
data(data.test)
fa = decorrelate.train(data.train)
fa2 = decorrelate.test(fa,data.test)
names(fa2)

Factor Adjusted Discriminant Analysis 1: Decorrelation of the training data

Description

This function decorrelates the training dataset by adjusting data for the effects of latent factors of dependence.

Usage

decorrelate.train(data.train, nbf = NULL, maxnbfactors=12, diagnostic.plot = FALSE, 
min.err = 0.001, verbose = TRUE,EM = TRUE, maxiter = 15,...)

Arguments

data.train

A list containing the training dataset with the following components: x is the n x p matrix of explanatory variables, where n stands for the training sample size and p for the number of explanatory variables ; y is a numeric vector giving the group of each individual numbered from 1 to K.
nbf

Number of factors. If nbf = NULL, the number of factors is estimated. nbf can also be set to a positive integer value. If nbf = 0, the data are not factor-adjusted.
maxnbfactors

The maximum number of factors. Default is maxnbfactors=12.
diagnostic.plot

If diagnostic.plot =TRUE, the values of the variance inflation criterion are plotted for each number of factors. Default is diagnostic.plot =FALSE. This option might be helpful to manually determine the optimal number of factors.
min.err

Threshold of convergence of the algorithm criterion. Default is min.err=0.001.
verbose

Print out number of factors and values of the objective criterion along the iterations. Default is TRUE.
EM

The method used to estimate the parameters of the factor model. If EM=TRUE, parameters are estimated by an EM algorithm. Setting EM=TRUE is recommended when the number of covariates exceeds the number of observations. If EM=FALSE, the parameters are estimated by maximum-likelihood using factanal. Default is EM=TRUE
maxiter

Maximum number of iterations for estimation of the factor model.
...

Other arguments that can be passed in the cv.glmnet and glmnet functions from glmnet package. These functions are used to estimate individual group probabilities. Modifying these parameters should not affect the decorrelation procedure. However, the argument nfolds in cv.glmnet is set to 10 by default and should be reduced (minimum 3) for large datasets, in order to decrease the computation time of decorrelation.train.

Value

Returns a list with the following elements:

meanclass

Group means estimated after iterative decorrelation
fa.training

Decorrelated training data
Psi

Estimation of the factor model parameters: specific variance
B

Estimation of the factor model parameters: loadings
factors.training

Scores of the trainings individuals on the factors
groups

Recall of group variable of training data
proba.training

Internal value (estimation of individual probabilities for the training dataset)

Author(s)

Emeline Perthame, Chloe Friguet and David Causeur

References

Friedman, J., Hastie, T. and Tibshirani, R. (2010), Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33, 1-22.

Friguet, C., Kloareg, M. and Causeur, D. (2009), A factor model approach to multiple testing under dependence. Journal of the American Statistical Association, 104:488, 1406-1415.

Perthame, E., Friguet, C. and Causeur, D. (2015), Stability of feature selection in classification issues for high-dimensional correlated data, Statistics and Computing.

See Also

FADA-package FADA glmnet-package factanal

Examples

data(data.train)

res0 = decorrelate.train(data.train,nbf=3) #  when the number of factors is forced

res1 = decorrelate.train(data.train) #  when the optimal number of factors is unknown

Factor Adjusted Discriminant Analysis 3-4 : Supervised classification on decorrelated data

Description

This function performs supervised classification on factor-adjusted data.

Usage

FADA(faobject, K=10,B=20, nbf.cv = NULL,method = c("glmnet", 
    "sda", "sparseLDA"), sda.method = c("lfdr", "HC"), alpha=0.1, ...)

Arguments

faobject

An object returned by function decorrelate.train or decorrelate.test.
K

Number of folds to estimate classification error rate, only when no testing data is provided. Default is K=10.
B

Number of replications of the cross-validation. Default is B=20.
nbf.cv

Number of factors for cross validation to compute error rate, only when no testing data is provided. By default, nbf = NULL and the number of factors is estimated for each fold of the cross validation. nbf can also be set to a positive integer value. If nbf = 0, the data are not factor-adjusted.
method

The method used to perform supervised classification model. 3 options are available. If method = "glmnet", a Lasso penalized logistic regression is performed using glmnet R package. If method = "sda", a LDA or DDA (see diagonal argument) is performed using Shrinkage Discriminant Analysis using sda R package. If method = "sparseLDA", a Lasso penalized LDA is performed using SparseLDA R package.
sda.method

The method used for variable selection, only if method="sda". If sda.method="lfdr", variables are selected through CAT scores and False Non Discovery Rate control. If sda.method="HC", the variable selection method is Higher Cristicism Thresholding.
alpha

The proportion of the HC objective to be observed, only if method="sda" and sda.method="HC". Default is 0.1.
...

Some arguments to tune the classification method. See the documentation of the chosen method (glmnet, sda or sda) for more informations about these parameters.

Value

Returns a list with the following elements:

method

Recall of the classification method
selected

A vector containing index of the selected variables
proba.train

A matrix containing predicted group frequencies of training data.
proba.test

A matrix containing predicted group frequencies of testing data, if a testing data set has been provided
predict.test

A matrix containing predicted classes of testing data, if a testing data set has been provided
cv.error

A numeric value containing the average classification error, computed by cross validation, if no testing data set has been provided
cv.error.se

A numeric value containing the standard error of the classification error, computed by cross validation, if no testing data set has been provided
mod

The classification model performed. The class of this element is the class of a model returned by the chosen method. See the documentation of the chosen method for more details.

Author(s)

Emeline Perthame, Chloe Friguet and David Causeur

References

Ahdesmaki, M. and Strimmer, K. (2010), Feature selection in omics prediction problems using cat scores and false non-discovery rate control. Annals of Applied Statistics, 4, 503-519.

Clemmensen, L., Hastie, T. and Witten, D. and Ersboll, B. (2011), Sparse discriminant analysis. Technometrics, 53(4), 406-413.

Friedman, J., Hastie, T. and Tibshirani, R. (2010), Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33, 1-22.

Friguet, C., Kloareg, M. and Causeur, D. (2009), A factor model approach to multiple testing under dependence. Journal of the American Statistical Association, 104:488, 1406-1415.

Perthame, E., Friguet, C. and Causeur, D. (2015), Stability of feature selection in classification issues for high-dimensional correlated data, Statistics and Computing.

See Also

FADA, decorrelate.train, decorrelate.test, sda, sda-package, glmnet-package

Examples

data(data.train)
data(data.test)

# When testing data set is provided
res = decorrelate.train(data.train)
res2 = decorrelate.test(res, data.test)
classif = FADA(res2,method="sda",sda.method="lfdr")

### Not run 
# When no testing data set is provided
# Classification error rate is computed by a K-fold cross validation.
# res = decorrelate.train(data.train)
# classif = FADA(res, method="sda",sda.method="lfdr")