REVIEW OF THE APPLICATION OF MODERN METHODS OF TOPOLOGICAL DATA ANALYSIS

Abstract

This article provides a brief overview of the application of the basic tools of modern topological data analysis, particularly those related to persistent homologies. These are persistent diagrams, Betti numbers and Betti curves. Analysis and comparison of point cloud data using these tools have been widely used in the last decade. In such fields as: computer vision, analysis of biomedical data, analysis of time series, materials science, study of the large-scale structure of the universe, analysis of stochastic and percolation processes and in a number of other fundamental and applied areas of science. Based on the simplified definitions of the mathematical concepts of simplexes, persistent homologies and tools based on them, we will review and highlight the most vivid examples of their application in topological data analysis.