Linear dimensionality reduction using relevance weighted LDA

The linear discriminant analysis (LDA) is one of the most traditional linear dimensionality reduction methods. This paper incorporates the inter-class relationships as relevance weights into the estimation of the overall within-class scatter matrix in order to improve the performance of the basic LDA method and some of its improved variants. We demonstrate that in some specific situations the standard multi-class LDA almost totally fails to find a discriminative subspace if the proposed relevance weights are not incorporated. In order to estimate the relevance weights of individual within-class scatter matrices, we propose several methods of which one employs the evolution strategies.