Big Data Analytics Using Graph Signal Processing

Abstract

The networks are fundamental to our modern world and they appear throughout science and society. Access to a massive amount of data presents a unique opportunity to the researcher’s community. As networks grow in size the complexity increases and our ability to analyze them using the current state of the art is at severe risk of failing to keep pace. Therefore, this paper initiates a discussion on graph signal processing for large-scale data analysis. We first provide a comprehensive overview of core ideas in Graph signal processing (GSP) and their connection to conventional digital signal processing (DSP). We then summarize recent developments in developing basic GSP tools, including methods for graph filtering or graph learning, graph signal, graph Fourier transform (GFT), spectrum, graph frequency, etc. Graph filtering is a basic task that allows for isolating the contribution of individual frequencies and therefore enables the removal of noise. We then consider a graph filter as a model that helps to extend the application of GSP methods to large datasets. To show the suitability and the effeteness, we first created a noisy graph signal and then applied it to the filter. After several rounds of simulation results. We see that the filtered signal appears to be smoother and is closer to the original noise-free distance-based signal. By using this example application, we thoroughly demonstrated that graph filtration is efficient for big data analytics.