Questions tagged [topological-data-analysis]

Questions about persistent homology, computational topology, discrete morse theory, and applied algebraic topology in general.

Questions about persistent homology, computational topology, discrete morse theory, and applied algebraic topology in general. All things persistence theory belong here including those not directly related to data analysis applications.

Tag proposal can be viewed here. Proposals to separate any of the aforementioned topics into their own tags should be discussed in meta under the tag current tag management thread, provided that there are enough questions to justify the interest in a new tag.

139 questions
41
votes
7 answers

Why does topology rarely come up outside of topology?

I am currently taking topology and it seems like a completely different branch of math than anything else I have encountered previously. I find it a little strange that things are not defined more concretely. For example, a topological space is…
40
votes
5 answers

Where to start learning about topological data analysis?

I was wondering if anyone could help me out with finding a nice introductory text for topological data analysis (I'm speaking as somebody who has two semesters of experience with topology, and much less experience with data analysis.) Are there any…
27
votes
2 answers

What are good references to self study persistent homology?

I am a graduate student in mathematics interested in persistent homology. Can anyone recommend good books or resources to self study persistent homology? I am taking a course in Algebraic Topology, studying the book by Hatcher.
25
votes
2 answers

Roadmap for learning Topological Data Analysis?

I'm a math major who has recently graduated and I will be starting full time work in 'data analysis'. Having finished with decent marks and still being incredibly interested in mathematics, I was thinking of pursuing graduate study/research at some…
11
votes
3 answers

References for Topology with applications in Engineering, Computer Science, Robotics

I am reading a book on motion planning for mobile robots, I have a really hard time with the mathematics. Some parts it is talking about the topology of the space and manifolds and compactness of the space.... I am too lost. I also have some…
11
votes
1 answer

Good Stopping Criteria for Persistent Homology

I've recently coded up a suite of algorithms for computing the persistent homology for various data sets (small data sets roughly around 30 data points). A question has come to my mind about how to find an optimal stopping criterion for generating…
10
votes
0 answers

Topological Features and Graph Spectra

I was just thinking recently about if there are any possible meaningful connections between tools such as persistent homology used for things like topological data analysis and tools used in spectral graph theory (I don’t have really any experience…
8
votes
1 answer

Introduction to Computational Topology

Question: Besides generally learning Algebraic Topology, what are some prerequisites for studying Computational Topology? Are there any accessible papers which introduce the field and the methods being used? Motivation: A number of my peers do…
8
votes
1 answer

Complexity of computing Persistent Homology vs Homology

I am curious whether it is significantly harder (computational-wise) to compute persistent homology as compared to computing homology. Or is it the same time complexity. I am aware that there is a reduction algorithm for homology. I vaguely recall…
7
votes
0 answers

TDA and knot theory

I'm new to topological data analysis, and I learned some basics of it including persistent homology and mapper. In this paper, authors suggest a method to detect circle $S^{1}$, which is 1-dimensional object but can't be embedded into $\mathbb{R}$.…
6
votes
1 answer

TDA - Persistence diagrams and Barcodes

I am relatively new in the field of persistent homology and topological data analysis. I would like to use RIPSER, DIPHA or GUDHI to calculate barcodes which will give a persistence diagram. Here are my questions: 1.) How many data points are…
6
votes
1 answer

Beginner's Guide to Persistent Homology (focusing on Theoretical Mathematical Aspects)

I am interested in seeking out a reference for learning Persistence Homology (more of the theoretical mathematical aspects rather than the applications/ computer science aspects). Currently, the two books I have attempted to read: Elementary…
6
votes
3 answers

Applications of Persistent Homology

Can anyone describe to me in Layman's terms what kind of use topology has through applying techniques of persistent homology in data analysis? Can you give me some real life examples in which which this has been used with success?
5
votes
2 answers

Difference between Topological Data Analysis and Graph Technology

I'm trying to understand the difference between Oracle's graph technology, which apparently has an inherent understanding of topology, and Ayasdi's Topological Data Analysis technology. Are these two completely different and where does one draw the…
5
votes
0 answers

Can I get a spherical coordinate from a real cocycle?

The Setting I am currently working on a project in Topological Data Analysis (TDA), where I aim to construct a density-robust spherical coordinate associated with a dataset $X$, sampled from a Riemannian manifold $\mathcal{M}$ with some probability…
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