Generalized low rank approximations of matrices

The problem of computing low rank approximations of matrices is considered. The novel aspect of our approach is that the low rank approximations are on a collection of matrices. We formulate this as an optimization problem, which aims to minimize the reconstruction (approximation) error. To the best of our knowledge, the optimization problem proposed in this paper does not admit a closed form solution in general. We thus derive an iterative algorithm, namely GLRAM, which stands for the Generalized Low Rank Approximations of Matrices. GLRAM reduces the reconstruction error sequentially, and the resulting approximation is thus improved during successive iterations. Experimental results show that the algorithm converges rapidly. We conduct extensive experiments on image data to evaluate the effectiveness of the proposed algorithm and compare the computed low rank approximations with those obtained from traditional Singular Value Decomposition (SVD) based method, in terms of the reconstru...

• Type: Conference
• Year: 2004
• Where: ICML
• Authors: Jieping Ye
• Keywords: Computed Low Rank, ICML 2004, Low Rank Approximations, Machine Learning, Reconstruction Error