Topological Machine Learning: Integrating Topological Data Analysis with Machine Learning to Enhance Breast Cancer Classification

Accurate classification tools are essential for improving patient outcomes in breast cancer diagnosis and treatment. Oncologists face the challenge of interpreting diverse patientspecific datasets such as mammograms, ultrasounds, and biopsy reports. Manual assessment of datasets is time-consuming and error-prone, complicating breast cancer classification. To address these issues, we explore the integration of Topological Data Analysis (TDA) with Machine Learning (ML), known as Topological Machine Learning (TML). TDA provides a systematic framework to uncover topological structures in highdimensional datasets, while ML offers powerful classification tools to analyze complex data. We present a comprehensive overview of TDA and ML, highlighting their individual strengths and the synergistic benefits of their integration. Topological features extracted through TDA are fed into ML models, including K-Nearest Neighbors (KNN), Random Forest (RF), Decision Tree (DT), Gaussian Naive Bayes (GNB), Logistic Regression (LR), and Support Vector Machine (SVM), to improve classification accuracy. Results show significant classification accuracy compared to traditional ML methods.