Learning nonnegative matrix factorizations from compressed data

TL;DR

This paper introduces a scalable framework for nonnegative matrix factorization directly from compressed data, enabling efficient data analysis with minimal access to original data.

Contribution

It develops a theoretically supported approach to recover nonnegative low-rank factors from compressed measurements using randomized sketching methods.

Findings

Effective recovery of nonnegative factors from compressed data

Compatibility with various algorithms including multiplicative updates

Validated performance on real-world datasets

Abstract

We propose a flexible and theoretically supported framework for scalable nonnegative matrix factorization. The goal is to find nonnegative low-rank components directly from compressed measurements, accessing the original data only once or twice. We consider compression through randomized sketching methods that can be adapted to the data, or can be oblivious. We formulate optimization problems that only depend on the compressed data, but which can recover a nonnegative factorization which closely approximates the original matrix. The defined problems can be approached with a variety of algorithms, and in particular, we discuss variations of the popular multiplicative updates method for these compressed problems. We demonstrate the success of our approaches empirically and validate their performance in real-world applications.