Accelerated Parallel and Distributed Algorithm using Limited Internal Memory for Nonnegative Matrix Factorization

TL;DR

This paper introduces a novel accelerated parallel and distributed algorithm for nonnegative matrix factorization that efficiently handles large datasets with limited internal memory, achieving faster convergence and better performance than existing methods.

Contribution

It proposes a flexible accelerated NMF algorithm combining anti-lopsided and block coordinate descent techniques, optimized for parallel, distributed environments with limited memory.

Findings

Achieves linear convergence rate of .5 in optimizing factor matrices.

Effectively exploits data sparseness for large datasets.

Outperforms 7 state-of-the-art methods in convergence, optimality, and iteration count.

Abstract

Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation. For large datasets, NMF performance depends on some major issues: fast algorithms, fully parallel distributed feasibility and limited internal memory. This research aims to design a fast fully parallel and distributed algorithm using limited internal memory to reach high NMF performance for large datasets. In particular, we propose a flexible accelerated algorithm for NMF with all its $L_1$ $L_2$ regularized variants based on full decomposition, which is a combination of an anti-lopsided algorithm and a fast block coordinate descent algorithm. The proposed algorithm takes advantages of both these algorithms to achieve a linear convergence rate of $\mathcal{O}(1-\frac{1}{||Q||_2})^k$ in optimizing each factor matrix when fixing the other factor one in the sub-space of passive variables, where $r$ is the number of latent components; where $\sqrt{r} \leq ||Q||_2 \leq r$. In addition, the algorithm can exploit the data sparseness to run on large datasets with limited internal memory of machines. Furthermore, our experimental results are highly competitive with 7 state-of-the-art methods about three significant aspects of convergence, optimality and average of the iteration number. Therefore, the proposed algorithm is superior to fast block coordinate descent methods and accelerated methods.