A two-dimensional decomposition approach for matrix completion through gossip

TL;DR

This paper introduces a decentralized, gossip-based method for matrix completion that decomposes a matrix into grid blocks, enabling scalable and server-free low-rank matrix factorization.

Contribution

It proposes a novel two-dimensional decomposition approach using gossip communication, eliminating the need for a central server in matrix completion tasks.

Findings

Performs well on synthetic datasets

Effective on real datasets

Scalable and decentralized approach

Abstract

Factoring a matrix into two low rank matrices is at the heart of many problems. The problem of matrix completion especially uses it to decompose a sparse matrix into two non sparse, low rank matrices which can then be used to predict unknown entries of the original matrix. We present a scalable and decentralized approach in which instead of learning two factors for the original input matrix, we decompose the original matrix into a grid blocks, each of whose factors can be individually learned just by communicating (gossiping) with neighboring blocks. This eliminates any need for a central server. We show that our algorithm performs well on both synthetic and real datasets.