The homology of a space can be thought of as a way to measure its shape: How many connected components it has, and if there are any holes or voids. Persistent homology, in a similar manner, provides a method for measuring the shape of complex data sets; this has applications in machine learning, the natural sciences and engineering. In this lecture, we will learn what persistent homology is, how to compute it and how it can be applied to problems in the real world.
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