Persistent Homology for Breast Tumor Classification using Mammogram Scans

TL;DR

This paper applies persistent homology with various vectorizations to mammogram images, achieving over 90% sensitivity in breast abnormality detection and providing insights into combining topological data analysis with machine learning.

Contribution

It introduces a landmark-based persistent homology approach with multiple vectorizations for breast tumor classification in mammograms, enhancing detection accuracy.

Findings

Sensitivity over 90% in abnormality detection

Multiple PD vectorizations improve classification

Insights into combining PH with machine learning

Abstract

An Important tool in the field topological data analysis is known as persistent Homology (PH) which is used to encode abstract representation of the homology of data at different resolutions in the form of persistence diagram (PD). In this work we build more than one PD representation of a single image based on a landmark selection method, known as local binary patterns, that encode different types of local textures from images. We employed different PD vectorizations using persistence landscapes, persistence images, persistence binning (Betti Curve) and statistics. We tested the effectiveness of proposed landmark based PH on two publicly available breast abnormality detection datasets using mammogram scans. Sensitivity of landmark based PH obtained is over 90% in both datasets for the detection of abnormal breast scans. Finally, experimental results give new insights on using different types of PD vectorizations which help in utilising PH in conjunction with machine learning classifiers.