Maximization of Mutual Information for Supervised Linear Feature Extraction

Abstract

In this paper, we present a novel scheme for linear feature extraction in classification. The method is based on the maximization of the mutual information (MI) between the features extracted and the classes. The sum of the MI corresponding to each of the features is taken as an heuristic that approximates the MI of the whole output vector. Then, a component-by-component gradient-ascent method is proposed for the maximization of the MI, similar to the gradient-based entropy optimization used in independent component analysis (ICA). The simulation results show that not only is the method competitive when compared to existing supervised feature extraction methods in all cases studied, but it also remarkably outperform them when the data are characterized by strongly nonlinear boundaries between classes.

Pattern Representation in Feature Extraction and Classifier Design: Matrix Versus Vector

“…Feature extraction usually acts as a preprocessing stage for a certain purpose such as classification or approximation to the raw data, and is defined as the problem of extracting the most relevant information for the purpose from the raw data [17], [18], [19], [20], [29]. The classical vector-pattern-oriented feature extractions (VecFE) such as Principle Component Analysis (PCA) [22] and Linear Discriminant Analysis (LDA) [23] have been widely used in a variety of areas, but sometimes seem not effective due to their expensive computational cost and singularity problem.…”

Feature Extraction by Mutual Information Based on Minimal-Redundancy-Maximal-Relevance Criterion and Its Application to Classifying EEG Signal for Brain-Computer Interfaces

“…In general, it is desirable to keep the dimensionality of the input features as small as possible to reduce the computational cost of training a classifier as well as its complexity (Torkkola, 2003;Murillo & Rodriguez, 2007). Moreover, using large number of features, when the number of data is low, can cause degradation of the classification performance (Chow & Huang, 2005).…”

“…Moreover, using large number of features, when the number of data is low, can cause degradation of the classification performance (Chow & Huang, 2005). Reduction of the number of input features can be done by selecting useful features and discarding others (i.e., feature selection) (Battiti, 1994;Kwak & Choi, 2002;Peng et al, 2005;Estèvez et al, 2009;Sindhwani et al, 2004) or extracting new features containing maximal information about the class label from the original ones (i.e., feature extraction) (Torkkola, 2003;Hild II et al, 2006;Kwak, 2007;Murillo & Rodriguez, 2007). In this paper, we focus on feature selection methods.…”

“…To overcome the difficulties of MI estimation for feature extraction, Parzen window modeling was also employed to estimate the probability density function (Kwak, 2007). However, Parzen model may suffer from the "curse of dimensionality," which refers to the overfitting of the training data when their dimension is high (Murillo & Rodriguez, 2007). Due to this difficulty, some recent works on informationtheoretic learning have proposed the use of alternative measures for MI (Murillo & Rodriguez, 2007) by means of an entropy estimation method that has succeeded in independent component analysis (ICA).…”

“…However, Parzen model may suffer from the "curse of dimensionality," which refers to the overfitting of the training data when their dimension is high (Murillo & Rodriguez, 2007). Due to this difficulty, some recent works on informationtheoretic learning have proposed the use of alternative measures for MI (Murillo & Rodriguez, 2007) by means of an entropy estimation method that has succeeded in independent component analysis (ICA). The features are extracted one by one with maximal dependency to the target class.…”