Data Analysis Using Representation Theory and Clustering Algorithms

Abstract

This work aims to expand the knowledge of the area of data analysis through both persistence homology, as well as representations of directed graphs. To be specific, we looked for how we can analyze homology cluster groups using agglomerative Hierarchical Clustering algorithms and methods. Additionally, the Wine data, which is offered in R studio, was analyzed using various cluster algorithms such as Hierarchical Clustering, K-Means Clustering, and PAM Clustering. The goal of the analysis was to find out which cluster's method is proper for a given numerical data set. By testing the data, we tried to find the agglomerative hierarchical clustering method that will be the optimal clustering algorithm among these three; K-Means, PAM, and Random Forest methods. By comparing each model's accuracy value with cultivar coefficients, we came with a conclusion that K-Means methods are the most helpful when working with numerical variables. On the other hand, PAM clustering and Gower with random forest are the most beneficial approaches when working with categorical variables. All these tests can determine the optimal number of clustering groups, given the data set, and by doing the proper analysis. Using those the project, we can apply our method to several industrial areas such that clinical, business, and others. For example, people can make different groups based on each patient who has a common disease, required therapy, and other things in the clinical society. Additionally, for the business area, people can expect to get several clustered groups based on the marginal profit, marginal cost, or other economic indicators.