On sparse linear discriminant analysis algorithm for high-dimensional data classification

In this paper, we present a sparse linear discriminant analysis (LDA) algorithm for high-dimensional objects in subspaces. In high dimensional data, groups of objects often exist in subspaces rather than in the entire space. For example, in text data classification, groups of documents of different types are categorized by different subsets of terms. The terms for one group may not occur in the samples of other groups. In the new algorithm, we consider a LDA to calculate a weight for each dimension and use the weight values to identify the subsets of important dimensions in the discriminant vectors that categorize different groups. This is achieved by including the weight sparsity term in the objective function that is minimized in the LDA. We develop an iterative algorithm for computing such sparse and orthogonal vectors in the LDA. Experiments on real data sets have shown that the new algorithm can generate better classification results and identify relevant dimensions.