Abstract
Breast cancer remains a leading cause of mortality worldwide, necessitating accurate and timely
classification and survival prediction to improve patient outcomes. While conventional machine
learning (ML) algorithms are effective, they are limited by an inability to capture the complex,
nonlinear shapes and structures inherent in high-dimensional datasets. Topological data analysis
(TDA), particularly the Mapper algorithm, offers a powerful technique to extract topological
features that encode this underlying topology of the data. However, the utility of the Mapper
algorithm for ML is highly dependent on its parameter configurations, often chosen heuristically.
In this study, we propose an optimized Topological Machine Learning (TML) framework that
integrates parameter-optimized Mapper with parameter-tuned ML algorithms to improve breast
cancer classification and survival prediction. Akey contribution is the comprehensive exploration
of Singlescale and combined Multiscale Mapper parameters to determine configurations that
maximize ML performance. TDA Mapper extracted features were combined with conventional
features to form hybrid feature sets and evaluated using selected supervised ML algorithms,
namely Random Forest (RF), Gradient Boosting (GB), SupportVector Machines (SVM), Logistic
Regression (LR), K-Nearest Neighbors (KNN), Neural Networks (NN), and Gaussian Naive
Bayes (GNB). The framework was benchmarked against conventional ML algorithms.
Evaluated on four breast cancer datasets, namelyWisconsin Breast Cancer Diagnostic (WBCD),
The Cancer Genome Atlas Breast Cancer (TCGA-BRCA), Surveillance, Epidemiology, and
End Results (SEER), and Synthetic Breast Cancer Survival Prediction Dataset (SBCSP), the
TML framework demonstrated significant and consistent improvements over conventional ML
algorithms across all datasets. Experimental results revealed that Mapper parameter optimization
is critical to these improvements. In TCGA-BRCA, RF and GB achieved 100% accuracy,
although results should be interpreted cautiously. In SBCSP dataset, TDA lifted GB from a best
accuracy of 56.5% to 96.5%. Multiscale Mapper improved minority class sensitivity in datasets,
raising malignant recall to 97.6% for RF and GB in the WBCD dataset. The TML framework
introduces additional computational cost compared to conventional ML, but improves predictive
performance and interpretability through Mapper graphs. The proposedTMLapproach improved
accuracy, interpretability, and generalizability across breast cancer datasets and delivered an
optimized, reproducible framework. The findings contribute to growing research supporting the
integration of TDA and ML in medical data analysis, bridging the gap between data complexity
and actionable insights. The findings confirmthat parameter-optimized TDAprovides a powerful
feature representation that enables ML algorithms to capture intricate topological patterns.