Ranking, Clustering, and Data Visualization Methods for Revealing Network Structur

When presented with data, often the objective is to identify an emergent pattern or structure that governs how the data was generated. My research focuses on methods for inferring this global structure depending on the nature of the data collected. Determining a competitive society's global hierarchical structure has long been of interest in many disciplines, including evolutionary biology, social sciences, and even sports. In Chapter 1, an algorithm for revealing a competitive society's hierarchical structure is introduced and is used to analyze two networks on a society of rhesus macaques. In Chapter 2, I explore how the understanding of a society's structure gives great insight as to its fragility and receptiveness to mimicking. I also discuss unsupervised learning algorithms and data visualization techniques for discovering the structure within non-competitive matrix data. In Chapter 3, I offer a method for identifying robust near-optimal solutions to two classical combinatorial optimization problems by determining the block structure within the problems' respective cost matrices. I take a similar approach in Chapter 4 to find the block structure in an e-sport's box scores. This information is used to determine which player skills lead more often to a team's success in various settings. Finally, in Chapter 5, these algorithms are applied to reveal what facets of a baseball pitcher's repertoire may contribute positively or negatively to his effectiveness. Such structure in matrix data is most clearly displayed using heatmaps throughout the final three chapters, demonstrating that global structure can often be discovered if it is simply visualized in a constructive manner.