Investigation of Computational Topology for Data Analysis and Visualization Applications

Abstract

In a variety of disciplines, from biology and physics to computer science and the social sciences, computational topology has become a potent tool for data analysis and visualisation. This study explores computational topology's uses in data analysis and visualisation, showing its potential for revealing hidden structures and patterns in large, complicated datasets.The paper starts out by giving a general introduction of computational topology and outlining its core ideas and methods. The use of it for extracting important information from big, high-dimensional datasets is then explored in relation to data analysis. Computational topology allows for the discovery of topological properties such as holes, voids, and connection patterns by modelling data as topological structures, such as simplicial complexes or persistent homology diagrams.The study also explores the function of computational topology in data visualisation, highlighting its capacity to offer clear and insightful visual representations of challenging datasets. Computational topology enables the construction of simpler and aesthetically pleasing representations while preserving the fundamental topological properties of the data through methods like topological simplification and dimensionality reduction.The usefulness of computational topology in several application domains, such as genomics, image analysis, and network analysis, is demonstrated through a number of case studies. These instances show how computational topology can improve activities like data exploration, clustering, classification, and anomaly detection, resulting in fresh perceptions and learnings.This study emphasises the enormous potential of computational topology for applications in data processing and visualisation. Computational topology provides a new perspective that complements current approaches by utilising the inherent geometric and topological properties of data. This allows researchers and practitioners to better understand complex datasets and make decisions based on the knowledge gleaned from them.