Algebraic Topology for Data Analysis

TL;DR

This paper explores Topological Data Analysis (TDA), a mathematical approach rooted in algebraic topology, that uses computational and statistical methods to extract meaningful insights from complex data sets.

Contribution

It introduces TDA as a novel tool for data analysis, combining algebraic topology with computation and statistics to derive data characteristics.

Findings

TDA effectively captures data shape and structure.

TDA provides robust features for data classification.

TDA enhances understanding of high-dimensional data.

Abstract

This research addresses a new tool for data analysis known as Topological Data Analysis TDA It underlies an area of Mathematics known as Combinatorial Algebra or more recently Algebraic Topology which through making strong use of Computation Statistics Probability and Topology among other concepts extracts mathematical characteristics from a set of data that allow us associate create and infer general and quality information about them