2 research outputs found
Matrix Approximation under Local Low-Rank Assumption
Matrix approximation is a common tool in machine learning for building
accurate prediction models for recommendation systems, text mining, and
computer vision. A prevalent assumption in constructing matrix approximations
is that the partially observed matrix is of low-rank. We propose a new matrix
approximation model where we assume instead that the matrix is only locally of
low-rank, leading to a representation of the observed matrix as a weighted sum
of low-rank matrices. We analyze the accuracy of the proposed local low-rank
modeling. Our experiments show improvements in prediction accuracy in
recommendation tasks.Comment: 3 pages, 2 figures, Workshop submission to the First International
Conference on Learning Representations (ICLR
Fast Rank Reduction for Non-negative Matrices via Mean Field Theory
We propose an efficient matrix rank reduction method for non-negative
matrices, whose time complexity is quadratic in the number of rows or columns
of a matrix. Our key insight is to formulate rank reduction as a mean-field
approximation by modeling matrices via a log-linear model on structured sample
space, which allows us to solve the rank reduction as convex optimization. The
highlight of this formulation is that the optimal solution that minimizes the
KL divergence from a given matrix can be analytically computed in a closed
form. We empirically show that our rank reduction method is faster than NMF and
its popular variant, lraNMF, while achieving competitive low rank approximation
error on synthetic and real-world datasets.Comment: 10 pages, 4 figure