ANALYSIS OF TOPOLOGICAL DATA ANALYSIS FOR HIGH-DIMENSIONAL DATA ANALYSIS

Due to the dimensionality curse and the complex interactions between variables, high-dimensional data analysis is a difficult undertaking. The intricate structures and patterns found in such data are frequently difficult to accurately capture and analyse using traditional statistical techniques. Topological Data Analysis (TDA) has become a promising methodology for analysing high-dimensional data in recent years. In this paper, topological data analysis (TDA) and its use in high-dimensional data analysis are examined. To analyse the shape and organisation of data, TDA employs algebraic topology with a focus on comprehending the underlying topological properties and their interactions. It provides insights into the global and local structure of the data, providing a distinct viewpoint that supports conventional statistical techniques. The main benefit of TDA is its capacity to capture the inherent characteristics of high-dimensional data without primarily relying on data distribution or linearity assumptions. TDA creates topological representations of the data by using methods like persistent homology and mapper, exposing hidden clusters, gaps, and connectivity patterns. These representations can be seen and understood, which makes it easier to comprehend large, complex data sets. TDA has also shown to be efficient at handling huge data sets and resistant against noise. It has been successfully used in a variety of fields, including biology, computer vision, neuroscience, and social sciences, and has produced insightful findings that were difficult to make using conventional techniques