Simple SummaryThe appearance of microcalcifications in mammogram images is an essential predictor for radiologists to detect early-stage breast cancer. This study aims to demonstrate the strength of persistent homology (PH) in noise filtering and feature extraction integrated with machine learning models in classifying microcalcifications into benign and malignant cases. The methods are implemented on two public mammography datasets: the Mammographic Image Analysis Society (MIAS) and Digital Database for Screening Mammography (DDSM). This study discovered that PH-based machine learning techniques can improve classification accuracy, which could benefit radiologists and clinicians in early diagnosis.AbstractMicrocalcifications in mammogram images are primary indicators for detecting the early stages of breast cancer. However, dense tissues and noise in the images make it challenging to classify the microcalcifications. Currently, preprocessing procedures such as noise removal techniques are applied directly on the images, which may produce a blurry effect and loss of image details. Further, most of the features used in classification models focus on local information of the images and are often burdened with details, resulting in data complexity. This research proposed a filtering and feature extraction technique using persistent homology (PH), a powerful mathematical tool used to study the structure of complex datasets and patterns. The filtering process is not performed directly on the image matrix but through the diagrams arising from PH. These diagrams will enable us to distinguish prominent characteristics of the image from noise. The filtered diagrams are then vectorised using PH features. Supervised machine learning models are trained on the MIAS and DDSM datasets to evaluate the extracted features’ efficacy in discriminating between benign and malignant classes and to obtain the optimal filtering level. This study reveals that appropriate PH filtering levels and features can improve classification accuracy in early cancer detection.