A Novel Patch-Based TDA Approach for Computed Tomography

The development of machine learning models based on computed tomography (CT) imaging has been a major focus due to the promise that imaging holds for diagnosis, staging, and prognostication. These models often rely on the extraction of hand-crafted features where incorporating robust feature engineering improves the performance of these models. Topological data analysis (TDA), based on the mathematical field of algebraic topology, focuses on data from a topological perspective, extracting deeper insight and higher dimensional structures. Persistent homology (PH), a fundamental tool in TDA, extracts topological features such as connected components, cycles, and voids. A popular approach to construct PH from 3D CT images is to utilize 3D cubical complex filtration, a method adapted for grid-structured data. However, this approach is subject to poor performance and high computational cost with higher resolution images. This study introduces a novel patch-based PH construction approach designed for volumetric CT imaging data that improves performance and reduces computational time. This study conducts a series of experiments to comprehensively analyze the performance of the proposed method and benchmarks against the cubical complex algorithm and radiomic features. Our results highlight the dominance of the patch-based TDA approach in terms of both classification performance and computational time. The proposed approach outperformed the cubical complex method and radiomic features, achieving average improvement of 7.2%, 3.6%, 2.7%, 8.0%, and 7.2% in accuracy, AUC, sensitivity, specificity, and F1 score, respectively, across all datasets. Finally, we provide a convenient Python package, Patch-TDA, to facilitate the utilization of the proposed approach.