MPI-FAUN: An MPI-Based Framework for Alternating-Updating Nonnegative Matrix Factorization

TL;DR

MPI-FAUN is a high-performance, MPI-based parallel framework designed to efficiently solve large-scale non-negative matrix factorization problems by minimizing communication costs and supporting various algorithms.

Contribution

The paper introduces a flexible, scalable MPI-based framework for NMF that efficiently handles large datasets and supports multiple NMF algorithms, with proven communication cost minimization.

Findings

Demonstrates scalability on datasets with hundreds of millions to billions of entries.

Achieves significant performance improvements over baseline implementations.

Supports various NMF algorithms within a unified parallel framework.

Abstract

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors $W$ and $H$, for the given input matrix $A$, such that $A \approx W H$. NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient parallel algorithms to solve the problem for big data sets. The main contribution of this work is a new, high-performance parallel computational framework for a broad class of NMF algorithms that iteratively solves alternating non-negative least squares (NLS) subproblems for $W$ and $H$. It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). The framework is flexible and able to leverage a variety of NMF and NLS algorithms, including Multiplicative Update, Hierarchical Alternating Least Squares, and Block Principal Pivoting. Our implementation allows us to benchmark and compare different algorithms on massive dense and sparse data matrices of size that spans for few hundreds of millions to billions. We demonstrate the scalability of our algorithm and compare it with baseline implementations, showing significant performance improvements. The code and the datasets used for conducting the experiments are available online.