Normalized dimensionality reduction using nonnegative matrix factorization

Abstract

In this paper, we propose an iterative normalized compression method for dimensionality reduction using non-negative matrix factorization (NCMF). To factorize the instance matrix X into C×M, an objective function is defined to impose the normalization constraints to the basis matrix C and the coefficient matrix M. We argue that in many applications, instances are often normalized in one way or the other. By integrating data normalization constraints into the objective function and transposing the instance matrix, one can directly discover relations among different dimensions and devise effective and efficient procedure for matrix factorization. In the paper, we assume that feature dimensions in instance matrix are normalized, and propose an iterative solution NCMF to achieve rapid matrix factorization for dimensionality reduction. As a result, the basis matrix can be viewed as a compression matrix and the coefficient matrix becomes a mapping matrix. NCMF is simple, effective, and only needs to initialize the mapping matrix. Experimental comparisons on text, biological and image data demonstrate that NCMF gains 21.02% computational time reduction, 39.60% sparsity improvement for mapping matrix, and 8.59% clustering accuracy improvement. © 2010 Elsevier B.V.