Reading 3 – Topological Data Analysis

tda

Up until now, we’ve focused mainly on low-level concepts and definitions—for our next reading, we’ll take a high-level look at some very cool, contemporary algorithmic tools that leverage simplicial topology to make sense of large data sets in high dimensions. These tools fall under the broad heading of topological data analysis (TDA). One particular tool that’s received a lot of buzz in recent years (both within computer science as well as in applications in material science, imaging, biology, etc.) is persistent homology. The following video provides an excellent introduction, and should be mostly understandable based on what you’ve already learned in class:

Introduction to Persistent Homology (video)

Your reading assignment between now and February 2nd is to find one paper or survey on persistent homology that piques your interest (could be theory, could be applications) and summarize it to whatever degree you feel capable. Don’t worry if a lot of the terminology still seems alien—an important skill in reading academic papers is being able to extract the key idea without decoding every little detail and definition. If you find this subject interesting, you might consider doing your course project on TDA. More broadly, the emerging field of computational topology spans a broad range of beautiful and fascinating topics that could make good course projects.

Here are some pointers to get you started with persistent homology:

You might also try to give a rough summary of the different types of complexes that show up in topological data analysis (e.g., Vietoris-Rips, Čech, Witness, …).

Submission: As usual, please send an email to kmcrane@cs.cmu.edu and nsharp@cs.cmu.edu no later than 10:00 AM on Tuesday, February 2nd including the string DDGSpring2016 in your subject line.  Your email for readings should always include:

  1. a short (2-3 sentence) summary of what you read, and
  2. at least one question about something you found confusing / interesting / incomplete / not addressed.

1 thought on “Reading 3 – Topological Data Analysis”

  1. Hi folks,

    Just to be clear: you really only need to write 2–3 brief sentences for your summary. And of course if you want to write more, terrific! But you shouldn’t be killing yourselves over writing these summaries. Basically we just want to (i) be sure that you really did read something and (ii) get a sense of how well people are following the key ideas. Likewise, you need only submit a single question, which should be enough to spark an interesting discussion (either online or in class).

    Hope that helps,

    Keenan

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