Quantum mechanics

Algorithm

Gaussian

Low-rank approximation

Pure mathematics

Materials science

Rank (graph theory)

Sparse matrix

Eigenvalues and eigenvectors

Computer science

Matrix (chemical analysis)

Tensor (intrinsic definition)

Physics

Mathematics

Politics

Political science

Artificial intelligence

Composite material

Representation (politics)

Combinatorics

Matrix completion

Matrix decomposition

Matrix approximation is a common tool in 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 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 over classical approaches for recommendation tasks.

Local Low-Rank Matrix Approximation