Pseudo-inverse Locality Preserving Projections

This paper proposes a novel algorithm, named pseudo-inverse locality preserving projections (PLPP), for dimensionality reduction involving undersampled problems. This algorithm considers the matrix singularity caused by undersampled problems by substituting the Moore-Penrose pseudo-inverse for the inverse of the matrix. Under the pseudo-inverse form eigenequation, the optimal locality preserving projections can be found by using the simultaneous diagonalization of three matrices technique, which intuitively solves the generalized eigenvalue decomposition problem. Theoretical analysis shows the flexible time complexity and better locality preserving power of PLPP. We compare the proposed PLPP with PCA, PCA+LDA, PCA+LPP on ORL face database and 20-Newsgroups text data sets. Experimental results show the effectiveness of the proposed algorithm.