INTERNATIONAL JOURNAL OF ADVANCE RESEARCH
IN MULTIDISCIPLINARY

The need for the analysis of data patterns and structures has increased significantly since a while ago. Research into network topology is common in many disciplines, including sociology, biology, and computer science. In my research, I focus on graph-based models and sparse optimization strategies for analyzing networks with data with several dimensions. Our research here focuses on a single facet of networks called “clustering” the process of dividing a network into related groups. These webs of relationships may stand in for social units, functional modules, or even individual visual pieces. Both theoretical research and numerical simulation are part of my job description. We start by taking a look at a number of image and social network datasets through the lens of a quality parameter known as “modularity,” which is widely used in network research for data clustering. We next examine the modularity function from a new angle, redefining it as an optimization issue for the energy functional with a total variation term and an L2 gradient. balancing term (as a joint effort with my colleagues).