Topological insights and hybrid feature extraction for breast cancer detection: a persistent homology classification approach

Early detection of breast cancer by mammography scans is crucial for improving treatment outcomes. However, low image resolutions, size, and location of lesions in dense breast tissue prove to be challenges in mammography, underscoring the importance of accurate and efficient computer-aided diagnostic systems. This article introduces a novel classification framework that utilizes histogram of oriented gradients (HOG) as a feature extractor and principal component analysis (PCA) for dimensionality reduction. Classification is implemented using the persistent homology classification algorithm (PHCA), which leverages persistent homology (PH) to capture topological properties of mammography images. The framework was evaluated on 7,632 images from the INbreast dataset with an extensive use of grid-search cross-validation to optimize preprocessing parameters. Two optimal combinations of HOG parameters and scaler were identified, with the best configuration (16 × 16 pixels per cell, 3 × 3 cells per block, and Minmax scaler) achieving strong performance. Validating on the test set, PHCA achieved an overall accuracy, precision, recall, F1-score, and specificity of 97.31%, 96.86%, 97.09%, 96.97%, and 96.86%, respectively. Clinically, the high precision (98.23%) and high recall (97.75%) for malignant cases highlight PHCA’s sensitivity in identifying malignancies, ensuring that very few malignant cases go undetected with highly trustworthy predictions. These results are shown to be competitive with existing state-of-the-art models, even exceeding in some cases, while requiring lower computational cost than deep learning-based approaches. Although the proposed method trails advanced deep models by 3–4% in some metrics, it offers a computationally efficient alternative and a potential for deployment in large-scale screening systems, demonstrating the promise of topological data analysis for breast cancer classification.