Topological Data Analysis - A Novel and Effective Approach for Feature Extraction

Abstract

The paper demonstrates how Topological Data Analysis (TDA) can be effectively used for qualitative feature extraction and studying shape of the data. This paper aims twofold: the first is using persistent homology for extracting important image features, and the other is mapper to generate topological networks. Medical imaging plays an essential role in the diagnosis of various diseases. Feature extraction is required to apply a predictive model for any disease diagnosis; one can think about TDA to extract features using persistent homology. Every real-time data can be visualized and explored using various data visualization techniques; in short, every data has a shape. Why shape? Because data points in proximity have qualitative behavior. Why TDA? Because it deals with the shape of the data, we can extract meaning from that shape & importantly, it is a branch of mathematics. TDA summarizes irrelevant stories to get something interesting; one can do this using mapper. An experimental study using persistent homology and mapper is explained & how it can be effectively used for feature extraction and to find hidden patterns in data, respectively.