Big Data Analysis with Signal Processing on Graphs
Aliaksei Sandryhaila, M F Moura Jose · IEEE Signal Processing Magazine · 2014
Analysis and processing of very large datasets, or Big Data, poses a significant challenge. Massive datasets are collected and studied in numerous domains, from engineering sciences to social networks, biomolecular research, commerce and security. Extracting valuable information from Big Data requires innovative approaches that efficiently process large amounts of data as well as handle and, moreover, utilize their structure. This article discusses a paradigm for large-scale data analysis based on the discrete signal processing on graphs (DSPG). DSPG extends signal processing concepts and methodologies from the classical signal processing theory to data indexed by general graphs. Big Data analysis presents several challenges to DSPG, in particular, in filtering and frequency analysis of very large datasets. We review fundamental concepts of DSPG, including graph signals and graph filters, graph Fourier transform, graph frequency and spectrum ordering, and compare them with their counterparts from the classical signal processing theory. We then consider product graphs as a graph model that helps extend the application of DSPG methods to large datasets through efficient implementation based on parallelization and vectorization. We relate the presented framework to existing methods for large-scale data processing and illustrate it with an application to data compression.