TOPOLOGY-BASED APPROACHES IN DATA SCIENCE AND MACHINE LEARNING
TL;DR
This work starts by introducing fundamental ideas from algebraic topology, including homology, persistent homology, and simplicial complexes, and how these ideas can be used to describe and analyze data.
Abstract
In order to gain an understanding of the underlying structure and relationships of complex and high-dimensional information, topological approaches provide effective tools. the use of topological techniques in data analysis, with an emphasis on how they relate to challenges involving machine learning. We start by introducing fundamental ideas from algebraic topology, including homology, persistent homology, and simplicial complexes. We next go into how these ideas can be used to describe and analyze data. Several machine learning applications of topological techniques, such as anomaly detection, clustering, classification, and dimensionality reduction. Researchers can identify significant aspects of the data that are difficult to identify using conventional techniques by utilizing topological descriptors like persistent homology. We use realworld examples to explain these ideas and show how well they work to reveal hidden patterns and structures in a variety of datasets. Keywords: Algebraic topology, topological techniques, data analysis, machine learning, and simplicial complexes.