A Unified Algorithmic Framework for Block-Structured Optimization Involving Big Data: With applications in machine learning and signal processing

This article presents a powerful algorithmic framework for big data optimization, called the block successive upper-bound minimization (BSUM). The BSUM includes as special cases many well-known methods for analyzing massive data sets, such as the block coordinate descent (BCD) method, the convex-concave procedure (CCCP) method, the block coordinate proximal gradient (BCPG) method, the nonnegative matrix factorization (NMF) method, the expectation maximization (EM) method, etc. In this article, various features and properties of the BSUM are discussed from the viewpoint of design flexibility, computational efficiency, parallel/distributed implementation, and the required communication overhead. Illustrative examples from networking, signal processing, and machine learning are presented to demonstrate the practical performance of the BSUM framework.

Introduction

With advances in sensor, communication, and storage technologies, data acquisition is now more ubiquitous than at any other time. This has made available big data sets in many areas of engineering, biological, social, and physical sciences. While the proper modeling and analysis of such data sets can yield valuable information for inference, estimation, tracking, learning, and decision making, their size and complexity present great challenges in algorithm design and implementation.