Year: 2018
Type: preprint
Abstract: In this work, we deal with rank-constrained integer least-squares optimization problems arising in low-rank matrix factorization related applications. We propose a solution for constrained integer least-squares problem subject to equality, sparsity, and rank constraints. The algorithm combines the Fincke-Pohst enumeration (or sphere decoding algorithm) with rank constraints and sparse solutions of Diophantine equations to arrive at an optimal solution. The proposed approach consists of two steps as follows: (i) find the solution set for Diophantine equations arising from the linear and sparsity constraints, (ii) find the matrix which minimizes the integer least-squares objective and satisfying the rank constraints using the solution set obtained in the step 1. The proposed algorithm is illustrated using a simple example. Then, we perform experiments to study the computational aspects of different steps of the proposed algorithm.
Source: arXiv (Cornell University)
Authors: Ayyar, Arun, Bhatt, Nirav
Institution: Indian Institute of Technology Madras
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2898749241