[Statistics & Probability Seminar]
Topological Data Analysis: theory, applications and the future
Topological Data Analysis (TDA) is a new research area on the interface between algebraic topology and computational geometry. TDA quantifies topological features hidden in unstructured data such as a cloud of points in a metric space. The key idea is to analyse a point cloud across all scales and output a persistence diagram summarising life spans of features such as components, holes, voids etc. The main foundation is the stability theorem saying that the persistence diagram is stable under bounded noise. More formally, the map from a point cloud to a diagram is continuous with respect to well-defined distances. As a result TDA leads to new skeletonisation algorithms with theoretical guarantees.
The next natural step is to combine TDA with Bayesian Statistics to make topological summaries stable under outliers, so new collaborations are welcome. The papers and C++ software are available on author's webpage http://kurlin.org.
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