How TDA and Machine Learning Enhance Each Other

People new to topological data analysis (TDA) often ask me some form of the question, “What’s the difference between Machine Learning and TDA?” It’s a hard question to answer, in part because it depends on what you mean by Machine Learning (ML). Wikipedia has this to say about ML: “Machine learning explores the study and construction of algorithms that can learn from and make predictions on data. Such algorithms operate by building a model from example inputs in order to make data-driven predictions or decisions, rather than following strictly static program instructions.” At this level of generality one could argue that TDA is a form of ML, but I think most people who work in both of these areas would disagree. Concrete examples of ML are rather more similar to one…


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