A New Supervised Dimensionality Reduction Algorithm Using Linear Discriminant Analysis and Locality Preserving Projection

Linear discriminant analysis (LDA) is one of the most popular supervised dimensionality reduction (DR) techniques used in computer vision, machine learning, and pattern classification. However, LDA only captures global geometrical structure information of the data and ignores the geometrical variation of local data points of the same class. In this paper, a new supervised DR algorithm called local intraclass geometrical variation preserving LDA (LIPLDA) is proposed. More specifically, LIPLDA first casts LDA as a least squares problem, and then explicitly incorporates the local intraclass geometrical variation into the least squares formulation via regularization technique. We also show that the proposed algorithm can be extended to nonlinear DR scenarios by applying the kernel trick. Experimental results on four image databases demonstrate the effectiveness of our algorithm. Key-Words: dimensionality reduction, locality preserving projection, linear discriminant analysis, pattern classification