Software! Math! Data! The blog of R. Sean Bowman
The blog of R. Sean Bowman

Posts with tag “topological data analysis”

February 11 2016

In a previous article, we saw how to compute the (zeroth) persistent homology of a filtered simplicial complex. But how do we obtain such a complex, anyway? Scientists and others who work with data often start with a bunch of points in a high dimensional space. What are some good ways to turn that information into a filtered simplicial complex we can compute the persistent homology from?

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February 09 2016

I’d like to introduce an algorithm for finding clusters in graphs. This is an important problem in machine learning, in part because so many problems can be phrased as finding “nice” clusters in a given graph, where the meaning of "nice" tends to depend on the particular application. It’s easy to imagine simple applications of a good clustering algorithm, like finding groups of friends in a social network. But things only get more interesting from there.

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September 18 2015

I’d love to write more about persistent homology, and eventually I’ll get around to it, but right now I wanted to talk about some math that undergraduate math majors who know a little algebra can understand. Although this is prerequisite stuff for really understanding persistent homology, you’ll certainly be able to understand the basics of persistent homology without understaing this. You might not ever decide to, but you could also come back later, after you’ve learned a bit about persistent homology, to get an idea of how the details work. (I should mention that this stuff is worth studying because it’s cool in its own right, and one reason I’m writing it is as an opportunity for me to try to remember some of it!)

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