Breast Cancer Detection with Topological Deep Learning

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Abstract

In this paper, we investigate the integration of topological data analysis (TDA) techniques with deep learning (DL) models to improve breast cancer diagnosis from ultrasound images. By leveraging persistent homology, a TDA method that captures global structural patterns, we enrich the local spatial features typically learned by DL models. We in-corporate topological features into various pre-trained architectures, including CNNs and vision transformers (VTs), aiming to enhance screening accuracy for breast cancer, which remains the most common cancer among women. Experiments on publicly available ultrasound datasets demonstrate that combining CNNs and VTs with topological features consistently yields statistically significant performance improvements. Notably, this approach also helps to address challenges faced by DL models, such as interpretability and reliance on large labeled datasets. Further-more, we generalize the Alexander duality theorem to cubical persistence, showing that persistent homology remains invariant under sublevel and superlevel filtrations for image data. This advancement reduces computational costs, making TDA methods more practical for image analysis.

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