Gunnar Carlsson on the Shape of Data (2012) [video] | Hacker News Reader

Gunnar Carlsson on the Shape of Data (2012) [video]

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I find the topic intriguing, but can someone who is well versed with both topology and machine learning comment on what is the key innovation here?

On first glance, the methods here seem a lot like the toolbox of dimensionality reduction techniques (PCA, spectral embedding, or more general manifold learning, etc.) from machine learning literature.

What specific insights from the field of topology have helped further our understanding of data that we missed earlier?

Prof Carlsson's (http://math.stanford.edu/~gunnar/) "Topology and Data" paper provides a good overview: http://www.ams.org/journals/bull/2009-46-02/S0273-0979-09-01...

My recent dive into the literature has enlightened my thinking in terms of database and systems design. It has led me to think more in terms of properties, invariants, intervals, constraints, and dynamic fluidity -- "there are no things" (only actions and properties): https://edge.org/response-detail/11514

Maybe the antiquated abstractions we have been using for database systems is what limits us. Maybe we need to stop thinking in terms of things -- objects, partitions, and static state -- and start thinking in terms of millions of fluid dynamic processes. Maybe Jim Starkey is on the right track: http://www.nuodb.com/about-us/jim-starkey.

Sussman seems to be converging there too -- see his talk "We Really Don't Know How to Compute" (http://www.infoq.com/presentations/We-Really-Dont-Know-How-T...) and his work on the Propagator (https://github.com/ProjectMAC/propagators).

The rapid flow of data id stressing our system designs is making this more apparent, and we're starting to see stream processing systems emerge like Google Dataflow and Apache Flink. Ideas from functional programming and immutable state are looking more prescient. Now our database management systems need to evolve.

  "At no period in human culture have men understood the     
  psychic mechanisms involved in invention and technology. 
  Today it is the instant speed of electric information that, 
  for the first time, permits easy recognition of the 
  patterns and the formal contours of change and development. 
  The entire world, past and present, now reveals itself to 
  us like a growing plant in an enormously accelerated movie. 
  Electric speed is synonymous with light and with the 
  understanding of causes."

  — Marshal McLuhan, Understanding Media: The Extensions of Man (1964)

'okram's recent paper provides a new graph-based model for stateless functional flows that could be applied in other systems: See "Quantum Walks with Gremlin" (http://arxiv.org/pdf/1511.06278v1.pdf)

And Vladimir Kornyak touches on some of these ideas in these papers:

1. On Compatibility of Discrete Relations (2005) http://arxiv.org/pdf/math-ph/0504048.pdf

2. Structural and Symmetry Analysis of Discrete Dynamical Systems (2010) http://arxiv.org/pdf/1006.1754.pdf

3. Discrete Dynamical Models: Combinatorics, Statistics and Continuum Approximations (2015) http://mmg.tversu.ru/images/publications/2015-vol3-n1/Kornya...

It's quite clear from the Ayasdi website that they're targeting enterprise customers. I wish they had an API similar to clarif.ai or wit.ai.

Javaplex: Persistent Homology and Topological Data Analysis Library (http://appliedtopology.github.io/javaplex/) -- primarily developed by the Computational Topology workgroup at Stanford.

Thank you!

Thanks for references.

I've read the topology and data paper; it lays down motivations for TDA, but it doesn't quite connect it to existing literature on dimensionality reduction and manifold learning and explain -- "Here's something you can learn by using tools from TDA, but not existing methods." The best I could see was that it produces results similar to existing methods.

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