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I'm one of the authors of the simplicial neural networks paper cited in the article. Happy to take questions :-)

by gspr 5y ago

dpaleka 5y ago
I feel the current marketing of topological data analysis and similar is directed towards people who have at least taken several graduate math courses. I'm really not an expert in TDA, I only know Ghrist's book and have read Hatcher. Are there really important topology ideas in topological learning, or it can all be phrased combinatorially? If it's an important research area, the current language really raises the bar to entry.
- gspr 5y ago
  > I feel the current marketing of topological data analysis and similar is directed towards people who have at least taken several graduate math courses. Oh I don't know about that. Lots of TDA is accessible at an undergrad level, as for example the book by Ghrist that you mention shows. I may be biased as I did my PhD in the field, but I also supervised several master's students, and some came from engineering or science backgrounds with little more math than undergrad level under their belts. They mostly did well and learned the basics of the field enough to make contributions during their thesis work. I would say that the field spans a vast range of applied-ness (from straight up data analysis with persistent homology as merely a tool, to fully theoretical work on e.g. multi-persistence). The more applied areas of the field tends to be far more accessible to people without a deep math background. > Are there really important topology ideas in topological learning, or it can all be phrased combinatorially? I think topological machine learning is still in its (very exciting!) infancy, and there's nothing I'd like more than to be able to answer that question! I think there's lots of potential for an extremely interesting fusion of two disciplines. And I never forget something the above-mentioned Ghrist once told me (during a discussion unrelated to ML): Never underestimate the treasure-hunting way of doing research – there's lots of be had from bringing together ideas from seemingly unrelated fields, especially when combining old and young ones. (That's me paraphrasing from memory, obviously, Ghrist is a lot more eloquent than that!) TDA is in some sense just that: the very old of algebraic topology meets the very new of computation, data analysis, etc. And I think the meeting of topology and machine learning has potential to be very exciting too! PS: When you say "or can it all be phrased combinatorially?", I wanna point out that topology and combinatorics are not mutually exclusive. This is a nice book that straddles the realms of TDA, topology and combinatorics: https://www.springer.com/gp/book/9783540719618 https://www.springer.com/gp/book/9783540719618 . See also Matt Kahle's fabulous works on showing the probabilistic properties of certain randomly generated combinatorial topological spaces (in some sense generalizing the classical work of Erdős and Rényi pertaining to properties of graphs that you may know, https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_...).
lmeyerov 5y ago
awesome! any recommendations on papers / tutorials here, + any libs, esp. scalable? For context, we have been looking at rgcn and transfer gns for handling identity graphs and event hypergraphs (= big & dynamic heterogeneous property graphs), esp for node classification and edge prediction, and with libs that handle multi-gpu w bigger-than-memory processing. Something like pattern mining / motif mining would also be interesting, which I'm guessing your approach may open up as well :)
- gspr 5y ago
  > any recommendations on papers / tutorials There's essentially two sides to the story: the convolutional deep network side and the topological side. The former is is excellently covered by my coauthor in another paper of his (https://arxiv.org/abs/1606.09375 https://arxiv.org/abs/1606.09375), and the latter is covered by many a textbook or intro text (like http://graphics.stanford.edu/courses/cs164-09-spring/Handouts/paper_barcodes.pdf http://graphics.stanford.edu/courses/cs164-09-spring/Handout...). > + any libs, esp. scalable? https://paperswithcode.com/paper/simplicial-neural-networks https://paperswithcode.com/paper/simplicial-neural-networks The code isn't very performant, but there's lots of room for improvement. It's more a proof of concept, with lots of low-hanging improvements that can be made. > For context, we have been looking at rgcn and transfer gns for handling identity graphs and event hypergraphs (= big & dynamic heterogeneous property graphs), esp for node classification and edge prediction, and with libs that handle multi-gpu w bigger-than-memory processing. Something like pattern mining / motif mining would also be interesting, which I'm guessing your approach may open up as well :) Very interesting!

I'm one of the authors of the simplicial neural networks paper cited in the article. Happy to take questions :-)

by gspr 5y ago

I'm one of the authors of the simplicial neural networks paper cited in the article. Happy to take questions :-)

I feel the current marketing of topological data analysis and similar is directed towards people who have at least taken several graduate math courses. I'm really not an expert in TDA, I only know Ghrist's book and have read Hatcher. Are there really important topology ideas in topological learning, or it can all be phrased combinatorially? If it's an important research area, the current language really raises the bar to entry.

gspr 5y ago
> I feel the current marketing of topological data analysis and similar is directed towards people who have at least taken several graduate math courses. Oh I don't know about that. Lots of TDA is accessible at an undergrad level, as for example the book by Ghrist that you mention shows. I may be biased as I did my PhD in the field, but I also supervised several master's students, and some came from engineering or science backgrounds with little more math than undergrad level under their belts. They mostly did well and learned the basics of the field enough to make contributions during their thesis work. I would say that the field spans a vast range of applied-ness (from straight up data analysis with persistent homology as merely a tool, to fully theoretical work on e.g. multi-persistence). The more applied areas of the field tends to be far more accessible to people without a deep math background. > Are there really important topology ideas in topological learning, or it can all be phrased combinatorially? I think topological machine learning is still in its (very exciting!) infancy, and there's nothing I'd like more than to be able to answer that question! I think there's lots of potential for an extremely interesting fusion of two disciplines. And I never forget something the above-mentioned Ghrist once told me (during a discussion unrelated to ML): Never underestimate the treasure-hunting way of doing research – there's lots of be had from bringing together ideas from seemingly unrelated fields, especially when combining old and young ones. (That's me paraphrasing from memory, obviously, Ghrist is a lot more eloquent than that!) TDA is in some sense just that: the very old of algebraic topology meets the very new of computation, data analysis, etc. And I think the meeting of topology and machine learning has potential to be very exciting too! PS: When you say "or can it all be phrased combinatorially?", I wanna point out that topology and combinatorics are not mutually exclusive. This is a nice book that straddles the realms of TDA, topology and combinatorics: https://www.springer.com/gp/book/9783540719618 https://www.springer.com/gp/book/9783540719618 . See also Matt Kahle's fabulous works on showing the probabilistic properties of certain randomly generated combinatorial topological spaces (in some sense generalizing the classical work of Erdős and Rényi pertaining to properties of graphs that you may know, https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_...).

lmeyerov 5y ago

awesome! any recommendations on papers / tutorials here, + any libs, esp. scalable? For context, we have been looking at rgcn and transfer gns for handling identity graphs and event hypergraphs (= big & dynamic heterogeneous property graphs), esp for node classification and edge prediction, and with libs that handle multi-gpu w bigger-than-memory processing. Something like pattern mining / motif mining would also be interesting, which I'm guessing your approach may open up as well :)

gspr 5y ago
> any recommendations on papers / tutorials There's essentially two sides to the story: the convolutional deep network side and the topological side. The former is is excellently covered by my coauthor in another paper of his (https://arxiv.org/abs/1606.09375 https://arxiv.org/abs/1606.09375), and the latter is covered by many a textbook or intro text (like http://graphics.stanford.edu/courses/cs164-09-spring/Handouts/paper_barcodes.pdf http://graphics.stanford.edu/courses/cs164-09-spring/Handout...). > + any libs, esp. scalable? https://paperswithcode.com/paper/simplicial-neural-networks https://paperswithcode.com/paper/simplicial-neural-networks The code isn't very performant, but there's lots of room for improvement. It's more a proof of concept, with lots of low-hanging improvements that can be made. > For context, we have been looking at rgcn and transfer gns for handling identity graphs and event hypergraphs (= big & dynamic heterogeneous property graphs), esp for node classification and edge prediction, and with libs that handle multi-gpu w bigger-than-memory processing. Something like pattern mining / motif mining would also be interesting, which I'm guessing your approach may open up as well :) Very interesting!