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Barcodes: The Persistent Topology of Data

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POSTED IN: Data Analytics & Visualization Blog

Overview of 

  • How one infers high dimensional structure from low dimensional representations 
  • Converting data sets into topological objects
  • Shows data through the 'lens of algebraic topology'
  • Presents the Barcode - a parameterized version of a Betti number

http://www.ams.org/journals/bull/2008-45-01/S0273-0979-07-01191-3/S0273-0979-07-01191-3.pdf

 (R. Ghrist)

Great article for the new arrival to TDA, Betti Numbers and Topology.  Probably a bit too much to try to read in one sitting, but the concepts are conveyed quite clearly 

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responded March 2014

Post Author
edited March 2014
This PPT is very good for learning the basics (it's not easy to get my head around this all at once, so I find nice to circle back a few times)
Topology in Manifold Learning - PowerPoint PPT Presentation:
http://www.powershow.com/view/11e33d-Y2I2O/Topology_in_Manifold_Learning_powerpoint_ppt_presentation

and this really helped me get my head around things:
http://www.youtube.com/watch?v=CKfUzmznd9g
"Persistent Homology on a noisy torus"

About the Author

Ryan Anderson

Ryan Anderson

Hi! I like to play with data, analytics and hack around with robots and gadgets in my garage. Lately I've been learning about machine learning.

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Data Analytics & Visualization Blog - Generating insights from Data since 2013

Created: July 25, 2014

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