Comments on: Topological Data Analysis
https://normaldeviate.wordpress.com/2012/07/01/topological-data-analysis/
Thoughts on Statistics and Machine Learning
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By: Topological Inference « Normal Deviate
https://normaldeviate.wordpress.com/2012/07/01/topological-data-analysis/comment-page-1/#comment-8055
Sun, 31 Mar 2013 01:39:46 +0000http://normaldeviate.wordpress.com/?p=118#comment-8055[…] Inference For Persistent Homology on arXiv. (I posted about topological data analysis earlier here.) The paper is written with Siva Balakrishnan, Brittany Fasy, Fabrizio Lecci, Alessandro Rinaldo […]
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By: Always the Last to Know: Ayasdi | Spark Consulting
https://normaldeviate.wordpress.com/2012/07/01/topological-data-analysis/comment-page-1/#comment-6779
Mon, 28 Jan 2013 11:47:10 +0000http://normaldeviate.wordpress.com/?p=118#comment-6779[…] firm built on “topological data analysis,” which physically maps complex data, allowing various types of patterns to […]
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By: Artificial Intelligence Blog · Some links from Nuit Blanche
https://normaldeviate.wordpress.com/2012/07/01/topological-data-analysis/comment-page-1/#comment-2304
Sun, 04 Nov 2012 13:48:51 +0000http://normaldeviate.wordpress.com/?p=118#comment-2304[…] Topological Data Analysis […]
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By: Ross Gayler
https://normaldeviate.wordpress.com/2012/07/01/topological-data-analysis/comment-page-1/#comment-1382
Sun, 02 Sep 2012 21:41:23 +0000http://normaldeviate.wordpress.com/?p=118#comment-1382We were psychologists and looking at things like environmental psychology (reactions of people to their environments) and experimental asthetics. From memory the empirical work that Atkin reported in IJMMS consisted of analyses of the physical and organisational structure of his unviversity (I particularly enjoyed the description of the Vice Chancellor as an object filling a q-hole in the committe structure of the university) and the English town of Saffron Walden. I think the issues we had arose from our data not having a naturally combinatoric structure and our relations beings graded rather than naturally binary. (Also, from memory) Atkin’s analysis was about representing the structure in a particular way which was then subbjectively interpreted rather than subsjected to statistical analysis – so the reults were very much dependent on the skill (and biases) of the interpreter.
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By: normaldeviate
https://normaldeviate.wordpress.com/2012/07/01/topological-data-analysis/comment-page-1/#comment-1136
Wed, 22 Aug 2012 12:02:13 +0000http://normaldeviate.wordpress.com/?p=118#comment-1136Ouch! Good point.
It is indeed two applications of the boundary operator that
(always) vanishes. Thanks for the correction.

Larry

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By: Ramsay
https://normaldeviate.wordpress.com/2012/07/01/topological-data-analysis/comment-page-1/#comment-1134
Wed, 22 Aug 2012 11:42:33 +0000http://normaldeviate.wordpress.com/?p=118#comment-1134Thanks for the concise summary. I am not an expert in this, but nobody else has pointed out what I see as a problem in an example given. The boundary of a triangle is not empty. Geometrically it is obvious that the boundary consists of three edges, and the combinatorics should reflect that. In most expositions an orientation of the simplex is taken into account, so that the boundary of $[Y_1,Y_2,Y_3]$ would be written as $[Y_2,Y_3] – [Y_1,Y_3] + [Y_1,Y_2]$. The negative sign is a detail, but the main point is that we cannot reduce or simplify this expression as it stands. It is a formal sum representing the three (oriented) edges of the triangle, and that is the boundary of the triangle. If we apply the boundary operator again to this chain of three edges we get $Y_3 – Y_2 – Y_3 + Y_1 + Y_2 – Y_1 = 0$, and this reflects the fact that the boundary operator applied twice vanishes identically.
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By: A Workshop on Topology and Machine Learning « Normal Deviate
https://normaldeviate.wordpress.com/2012/07/01/topological-data-analysis/comment-page-1/#comment-1114
Tue, 21 Aug 2012 18:23:39 +0000http://normaldeviate.wordpress.com/?p=118#comment-1114[…] may recall my previous post on Topological Data Analysis. I am happy to report that, in the interest of helping to advance this area of research, we (= […]
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By: John Wilder
https://normaldeviate.wordpress.com/2012/07/01/topological-data-analysis/comment-page-1/#comment-1099
Mon, 20 Aug 2012 17:57:17 +0000http://normaldeviate.wordpress.com/?p=118#comment-1099What were the problems that you cared about?

Atkin (still alive!) recently published MATHEMATICAL PHYSICS, An In-Depth Study, which I found interesting.

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By: normaldeviate
https://normaldeviate.wordpress.com/2012/07/01/topological-data-analysis/comment-page-1/#comment-1075
Fri, 17 Aug 2012 21:25:00 +0000http://normaldeviate.wordpress.com/?p=118#comment-1075Yes. The Matlab program called Plex.
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By: Keila
https://normaldeviate.wordpress.com/2012/07/01/topological-data-analysis/comment-page-1/#comment-1074
Fri, 17 Aug 2012 21:13:28 +0000http://normaldeviate.wordpress.com/?p=118#comment-1074Is there available some routine of an program, some code, or a software for to apply this methodology”Topological Data Analysis” in clustering of a data set?
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