Sparse Fisher's Linear Discriminant Analysis

Fisher's linear discriminant analysis (LDA) is traditionally used in statistics and pattern recognition to linearly-project high-dimensional observations from two or more classes onto a low-dimensional feature space before classification. The computational complexity of the linear feature extraction method increases linearly with dimensionality of the observation samples. For high-dimensional signals, high computational cost can render the method unsuitable for implementation in real time. In this paper, we propose sparse Fisher's linear discriminant analysis, which allows one to search for low-dimensional subspaces, spanned by sparse discriminant vectors, in the high-dimensional space of observation samples from two classes. The sparsity constraints on the space of potential discriminant feature vectors are enforced using the sparse matrix transform (SMT) framework, proposed recently for regularized covariance estimation. Classical Fisher's LDA is a special case of sparse Fisher's LDA when the sparsity constraints on the feature vectors in the estimation algorithm are fully relaxed. The number of non-zero components in a discriminant direction estimated using our proposed discriminant analysis technique is tunable; this feature can be used to control the compromise between computational complexity and accuracy of the eventual classification algorithm. The experimental results discussed in the manuscript demonstrate the effectiveness of the new method for low-complexity data-classification applications.