Precise Question
What are some specific examples where topological data analysis (TDA) outperforms other models on publicly available data?
Context
When new ML algorithms are developed, it seems common practice to apply them to publicly-available data and provide accuracy comparisons in order to illustrate the novelty of the algorithm in a scientific way.
As a concrete example, consider the KDD cup references in this XGBoost paper http://dmlc.cs.washington.edu/data/pdf/XGBoostArxiv.pdf