eegAnalysis (version 0.0)

featureSelection: Feature Selection Algorithm

Description

This algorithm allows the user to use his own features. Thus, the featureSelection function selects the best set of the features among the features given by the user. It can be used to select features of any number of classes.

Usage

featureSelection(features, classes.Id, alpha = 0.05, alphaCorr = 0.05, 
minAcc = 0.7, fast = FALSE, testProp = 0.2)

Arguments

features

is the data set containing the features. The data frame must be organized as follows: each row represents a different feature, and each columns represents each replication of that feature for each class in the study.

classes.Id

is a vector with length equal to the number of columns of data. Thus, each value in the vector identifies the class ID of each column. For example, let classes.Id = c(rep(1,5),rep(2,5)), this means that the first 5 columns of data represents the class with ID 1 and the columns 6 to 10 represent the class with ID 2.

alpha

a vector with the significance level for each FDR test to be performed. It has to be a number between 0 and 1. The closer to zero, the less features tend to be selected. See details.

alphaCorr

significance level for the correlation test. It has to be a number between 0 and 1. The closer to zero, the less features tend to be selected. See details.

minAcc

minimum accuracy to be achieved by the SVM test. It has to be a number between 0 and 1. The closer to one, the less features tend to be selected. See details.

fast

If FALSE it uses the SVM implementation of the e1071 package. If TRUE the algorithm uses another implementation optimized for the one dimensional case that tends to be much faster, but it may not converge in some cases.

testProp

the proportion of replicates of each class used in the test phase of the SVM test. See details.

Value

Selected

A vector with the number of the features selected. In other words, each number in this vector represents the number of the row selected from the original data set.

FDRscore

A vector that represents the score of each selected feature in the FDR test. It is a value between 0 and 1. The closer to 1, the better is the selected feature in terms of this test.

SVMscore

A vector that represents the score of each selected feature in the SVM test. It is a value between 0 and 1. The closer to 1, the better is the selected feature in terms of this test.

Details

The feature selector is a statistical algorithm that performs several tests to select the best set of features to classify a new data set in the future. The feature selection is performed the following steps:

1- The training set is divided in two sets. The number of replicates (samples, recordings) of each class in each set is defined by the parameter testProp.

2- A analysis of variance is evaluated and a false discovery rate (FDR) test, with significance level given by the parameter alpha, is performed to select the features with the greatest differences between classes means.

3- For each feature selected, a SVM classifier is trained individually for the first group of replicates defined randomly by the parameter testProp.

4- The features are extracted from the second group of replicates and classified. The features with a correct classification rate of at least minAcc (parameter) are selected.

5- A correlation test is performed to eliminate redundant features with significance level given by alphaCorr.

References

Hastie, T., Tibshirani, R., Friedman, J. (2009) The Elements of Statistical Learning: Data Mining, Inference, and Prediction. 2nd ed. Stanford: Springer.

Coutinho, M. (2013) Selecting features for EEG classification and constructions of Brain-Machine Interfaces. Universidade de Brasilia (UnB), Master dissertation.

Examples

library(eegAnalysis)

### Simulating some features

# number of features
n.features = 150
# number of replications of class A
n.classA = 200
# number of replications of class B
n.classB = 250

# initializing the features data frame
features<-mat.or.vec(n.features,n.classA+n.classB)
# initializing the classes.ID vector
classes.Id<-c(rep(0,n.classA),rep(1,n.classB))


# simulating the features with the normal distribution
# note that the higher the number of the row, the higher 
# is the gap between the means of the simulated normal distribution
for(i in 1:n.features)
{
  features[i,]<-c(rnorm(n.classA,1,1),rnorm(n.classB,1+i/200,1))
}

### Selecting the features and comparing the speed changing the fast parameter
### NOTE: there may be differences between the selected features due to some 
### randomness present in the algorithm.
system.time({
  feat<-featureSelection(features, classes.Id, alpha = 0.05, alphaCorr = 0.05, 
                         minAcc = 0.65, fast = FALSE, testProp = 0.2)
})
system.time({
  fastFeat<-featureSelection(features, classes.Id, alpha = 0.05, alphaCorr = 0.05, 
                             minAcc = 0.65, fast = TRUE, testProp = 0.2)
})


### Reducing the initial data frame to the selected features
names(fastFeat)
SelectedFeatures <- features[fastFeat$Selected,]