Nonlinear parsimonious feature selection (NPFS)

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Table of contents

1 State of the art 
2 Sparse classification methods 
2.1 Support Vector Machine (SVM)
2.1.1 L2 nonlinear
2.1.2 Recursive Feature Elimination (RFE)
2.1.3 L1 linear
2.1.4 Projection in a polynomial space of degree d
2.2 Nonlinear parsimonious feature selection (NPFS)
2.2.1 Gaussian mixture model (GMM)
2.2.2 k-fold cross-validation
2.2.3 Updating the model
2.2.4 Marginalization of Gaussian distribution
2.2.5 Leave-one-out cross-validation
3 Experimental results 
3.1 Data set
3.2 Results on synthetic data set
3.3 Results on real data set
3.3.1 Accuracy
3.3.2 Selected features
3.3.3 Computation time
3.3.4 Classification maps
4 Leave-One-Out Cross-Validation versus k-fold Cross-Validation 
4.1 Accuracy
4.2 Selected features
4.3 Computation time
A Data resizing 
A.1 No rescale
A.2 Rescale between 0 and 1
A.3 Rescale between 􀀀1 and 1
A.4 Standardize
A.5 Effect of the resizing
B Simple forward feature selection 
B.1 Notations
B.2 Estimators
B.2.1 Proportion
B.2.2 Mean vector
B.2.3 Covariance matrix
B.2.4 Decision rule
B.3 Updating formulas
B.3.1 Proportion
B.3.2 Mean estimation
B.3.3 Covariance matrix estimation
B.4 LOOCV algorithm
C Figures