Matrix Approximation under Local Low-Rank Assumption
This work addresses matrix approximation for recommendation systems, text mining, and computer vision, but appears incremental as it modifies an existing assumption rather than introducing a fundamentally new approach.
The paper tackled the problem of matrix approximation by proposing a local low-rank assumption instead of the traditional global low-rank one, representing the matrix as a weighted sum of low-rank matrices, and experiments showed improvements in prediction accuracy for recommendation tasks.
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.