Geometric and topological inference: Topological data analysis

Topological data analysis (TDA) is an approach to the analysis of datasets using topology techniques. It is often difficult to extract information from high-dimensional, incomplete, and noisy datasets. By enabling the visualization of high-dimensional data, TDA provides a general framework for analyzing such data in a way that is insensitive to the particular metric chosen. The purpose of topological data analysis (TDA) is to understand the topological and geometric structure of data. It provides mathematical and algorithmic tools for this purpose. It is a developing field today. Considering the topological information extracted from the data, the focus is on mathematical foundations. It is now widely accepted that such topological analyzes can yield qualitative information about datasets that are not easily obtained by other means. This thesis provides a brief introduction to this new field. In this thesis, the main lines of Topological Data Analysis were mentioned and an application was made using the data set obtained from Boğaziçi University Kandilli Observatory and Earthquake Research Institute (KRDAE) through the R STUDIO program.