International Journal of Advanced Science and Technology Vol. 29, No. 05, (2020), pp. 862-868 862 ISSN: 2005-4238 IJAST Copyright ⓒ 2020 SERSC A SYSTEMATIC REVIEW OF GRAPH SIGNAL PROCESSING Nagaraju Sonti * , Dr.P.Venkatappa Reddy ** * Research Scholar, ** Associate Professor Dept. of ECE, Vignan’s Foundation for Science, Techology & Research, Guntur, India, Abstract Graph signal processing(GSP) is a representation of data in graphical format with directed or undirected vertices. In many applications such as big data networks, economic and social networks analysis signals with graph is relevant. Harmonic analysis for processing the signals with spectral and algebric graphical thereotical concepts are merged and analyzed with respect to signal processing schemes on graphs. In this work, main challenges of GSP are discussed with Graph Spectral Domains (GSD) and when processing the signals on graph. The information is extracted efficiently from the high- dimensional data by using operators of signals on graph and transformation of graph on signal are highlighted in this work. Finally, a brief discussion of open issues of GSP are reviewed. Keywords—Big Data, Graph Signal Processing, High-Dimensional data, Irregular graph, Spectral Graph. 1. INTRODUCTION In recent years, GSP is an active research area because graph provides many advanced solutions in various applications. In many practical cases, signal domain is unable to define a collection of points in space on regular grid or a set of equidistant instants in time. In some cases, the data domains are not related to time or space and it is irregular which can be solved by graph. According to fundamental properties of data, graph exploits the relevant relations among the data. Graph consists of both vertices and edges, where the data values are defined/sensed in vertices and edges connect these vertices [1]. For efficient application of GSP approach, defining the appropriate graph structure is very important, because GSP is more useful in many applications such as biological, technological, social networks and even in classical SP (CSP). The signals are analyzed and processed in the spectral domain, which leads to many simple and effective algorithms in CSP and now it extends to graph signals also. To represent graphs in spectral domain authors in [2] proposed Laplacian spectral decomposition or adjacency matrix. In statistical learning problems, the representation of similar data points is well known to its Weighted graphs for many applications includes automatic text classification and machine vision [3]. GSP defines the correlation between data samples are effectively captured in time and space by inserting the signal structure onto the graph, which leads to scalable and flexible approach to many SP problems. When training periods are short and unable to build an efficient class model in data classification problem, GSP gives a solution for it [4]. Due to the large signal values with more number of vertices compressive sensing and subsampling problems were occured in GSP. The above mentioned problems are much related to the possibility of reconstruction of minimum number of measurements (samples of