Distributed Bayesian Matrix Decomposition for Big Data Mining and Clustering
This work addresses the problem of big data mining and clustering for applications with distributed data storage, though it is incremental as it builds on existing distributed computing strategies.
The paper tackles the inefficiency of processing big data with matrix decomposition in a single machine by proposing a distributed Bayesian matrix decomposition model (DBMD) that scales well and handles heterogeneous noise, achieving superior or competitive performance in real-world experiments.
Matrix decomposition is one of the fundamental tools to discover knowledge from big data generated by modern applications. However, it is still inefficient or infeasible to process very big data using such a method in a single machine. Moreover, big data are often distributedly collected and stored on different machines. Thus, such data generally bear strong heterogeneous noise. It is essential and useful to develop distributed matrix decomposition for big data analytics. Such a method should scale up well, model the heterogeneous noise, and address the communication issue in a distributed system. To this end, we propose a distributed Bayesian matrix decomposition model (DBMD) for big data mining and clustering. Specifically, we adopt three strategies to implement the distributed computing including 1) the accelerated gradient descent, 2) the alternating direction method of multipliers (ADMM), and 3) the statistical inference. We investigate the theoretical convergence behaviors of these algorithms. To address the heterogeneity of the noise, we propose an optimal plug-in weighted average that reduces the variance of the estimation. Synthetic experiments validate our theoretical results, and real-world experiments show that our algorithms scale up well to big data and achieves superior or competing performance compared to other distributed methods.