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Dimensionality reduction of the raw input variable space is an essential preprocessing step in the classification process. 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). 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; Estevez 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. A variety of linear feature extraction methods have been proposed. One well-known feature extraction methods may be principal component analysis (PCA) (Li et al., 2006). The purpose of PCA is to find an orthogonal set of projection vectors or principal components for feature extraction from given training data through maximizing the variance of the projected data with aim of optimal representing the data in terms of minimal reconstruction error. However, in its feature extraction for classification tasks, PCA does not sufficiently use class information associated with patterns and its maximization to the variance of the projected patterns might not necessarily be in favor of discrimination among classes, thus naturally it likely loses some useful discriminating information for classification. Linear discrimination analysis (LDA) is another popular linear dimensionally reduction algorithm for supervised feature extraction (Duda et al., 2001). LDA computes a linear transformation by maximizing the ratio of between-class distance to within-class distance, thereby achieving maximal discrimination. In LDA, a transformation matrix from an ndimensional feature space to a d-dimensional space is determined such that the Fisher criterion of between-class scatter over within-class scatter is maximized. LDA algorithm assumes the sample vectors of each class are generated from underlying multivariate

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