A Non-Mathy Introduction to Persistent Homology

#1

I warned Kyle I probably won’t be active in this group, but he hath banged his spoon that I at least post here.

I’m working as a Data Scientist now for a company called Geometric Data Analytics, a small government contractor run by Topologists. I’ve been asked to use / understand / implement aspects of persistent homology on several occasions already, but I had to ask a ton of dumb questions seeing as this lives in the realm of algebraic topology (I never took topology and those of you in abstract algebra with me need no more information on that front).

Anyway, through an extensive series of very dumb questions with my superiors, I’ve condensed some of the concepts into non-mathematical explanations and fun (animated and / or interactive) use cases:

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#2

Very cool! I love the interactive widgets. You really are a data scientist :smiley:

I think the persistence visualizations would make more sense to me if, rather than waiting for something to die before plotting it on the birth/death graph, you place a dot as soon as it is born and have the dot move vertically until it dies.

#3

I see your point in the sense that new values on the persistence diagram pop up at you in the gifs / widgets, but that would get pretty weird when persistence values are (birth, death) pairs though. The intermediate representation you’re proposing would not actually be a persistence diagram. You also lose some other rich information in a diagram. For example, one of the utilities of the 0d persistence diagram is being able to see the gap in persistence values, which says something about the robustness of a cluster (in the same way you can see a gap on a dendrogram when running hierarchical clustering).

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