Compressed Factorization: Fast and Accurate Low-Rank Factorization of Compressively-Sensed Data

TL;DR

This paper introduces a method for performing low-rank matrix and tensor factorizations directly on compressively-sensed data, enabling efficient and accurate recovery of original factors with theoretical guarantees.

Contribution

It proposes a novel approach of factorizing compressed data first and then reconstructing original factors, with proven conditions for successful recovery in matrix and tensor cases.

Findings

The method accurately recovers original factors from compressed data.

Theoretical guarantees are established for the recovery process.

Practical experiments demonstrate effectiveness on real-world datasets.

Abstract

What learning algorithms can be run directly on compressively-sensed data? In this work, we consider the question of accurately and efficiently computing low-rank matrix or tensor factorizations given data compressed via random projections. We examine the approach of first performing factorization in the compressed domain, and then reconstructing the original high-dimensional factors from the recovered (compressed) factors. In both the matrix and tensor settings, we establish conditions under which this natural approach will provably recover the original factors. While it is well-known that random projections preserve a number of geometric properties of a dataset, our work can be viewed as showing that they can also preserve certain solutions of non-convex, NP-Hard problems like non-negative matrix factorization. We support these theoretical results with experiments on synthetic data and demonstrate the practical applicability of compressed factorization on real-world gene expression and EEG time series datasets.