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MIA Talks

Topological data analysis: What is persistent homology?

October 12, 2016
Cancer Program, Broad Institute

A fundamental question in big data analysis is if or how these points may be sampled, noisily, from an intrinsically low-dimensional geometric shape, called a manifold, embedded in a high dimensional “sensor” space. Topological data analysis (TDA) aims to measure the “intrinsic shape” of data and identify this manifold despite noise and the likely nonlinear embedding. I will discuss the basics of the fundamental tool in TDA called persistent homology, which assigns to a point cloud a count of topological features –roughly “holes” of various dimensions – with a measure of importance of each feature recorded in a “barcode” of the data to help distinguish the significant features from the noise.