Online Matrix Factorization via Broyden Updates

TL;DR

This paper introduces an online matrix factorization algorithm that updates the factorization incrementally with each new data point, handling missing data and large datasets efficiently.

Contribution

It presents a novel online algorithm for matrix factorization using Broyden updates, extending to mini-batch processing and missing data handling.

Findings

Efficiently updates matrix factors with each new observation.

Performs well on real datasets compared to existing methods.

Handles missing data and large-scale datasets effectively.

Abstract

In this paper, we propose an online algorithm to compute matrix factorizations. Proposed algorithm updates the dictionary matrix and associated coefficients using a single observation at each time. The algorithm performs low-rank updates to dictionary matrix. We derive the algorithm by defining a simple objective function to minimize whenever an observation is arrived. We extend the algorithm further for handling missing data. We also provide a mini-batch extension which enables to compute the matrix factorization on big datasets. We demonstrate the efficiency of our algorithm on a real dataset and give comparisons with well-known algorithms such as stochastic gradient matrix factorization and nonnegative matrix factorization (NMF).