This looks like a gem, thanks!

Under my elbow as I type is a small introductory book called Topology for Computing, which I’d recommend to anyone trying to investigate such links, for its concise clarity and elegant figures.

https://www.amazon.com/Computing-Cambridge-Monographs-Comput...

Gunnar wrote a review article a few years ago called Topology and Data (http://www.ams.org/journals/bull/2009-46-02/S0273-0979-09-01...). It is an amazingly well written and accessible paper for a technical audience.

Pair it with Afra's book (http://www.amazon.com/Computing-Cambridge-Monographs-Computa...)

Hey,

Some reading material: A very general blog about philosophy : http://radar.oreilly.com/2015/07/data-has-a-shape.html

		A slightly more in-depth blog : https://shapeofdata.wordpress.com/2013/08/27/mapper-and-the-choice-of-scale/  		A very accessible book about topology (especially from an algorithms perspective) : http://www.amazon.com/Computing-Cambridge-Monographs-Computational-Mathematics/dp/0521136091/ref=sr_1_1?ie=UTF8&qid=1444971634&sr=8-1&keywords=topology+for+computing  		Blog exposing persistent homology : https://normaldeviate.wordpress.com/2012/07/01/topological-data-analysis/  		Videos exposing persistent homology :  			https://www.youtube.com/watch?v=CKfUzmznd9g 			https://www.youtube.com/watch?v=CKfUzmznd9g  	Some free software: 		Python Mapper by Daniel Müllner : http://danifold.net/mapper/index.html  		JPlex library by Harlan Sexton : http://www.math.colostate.edu/~adams/jplex/index.html  		Dionysus by Dimitriy Morozov : http://www.mrzv.org/software/dionysus/  		Topological Data Analysis in R : https://cran.r-project.org/web/packages/TDA/vignettes/article.pdf  	Infrastructure 		Our tech stack is: 			Backend 				HDFS for storage 				Our ML and Math code is hand-rolled C++ and Assembly(7% LOC) 				All coordination/distributed systems code is in Java 				ZMQ for communication 				Protocol Buffers for protocol 			Frontend 				D3 				Backbone 				Hand-rolled webGL graph visualization (we open sourced it at https://github.com/ayasdi/grapher)  		We currently don't use GPUs or any other fancy hardware primarily because today, our customers use commodity hardware and getting F1000 companies to buy cutting-edge hardware is just plain horrible.  		We have an awesome GPU rig at our offices that we test algorithms on and it can really make our algorithms scream, but again, none of our customers have/are willing to invest in GPUs.  		Apache Spark - it is interesting that in our experience, making it work for ML algorithms is really too much work unless you invest the time to understand the framework and its fundamentals. It performs very well for ETL type tasks, which is what we use it for.  	On a public offering: no comment :)  	If you have more questions - I am easy to find :) 

Gurjeet

I recommend Afra's book:

http://www.amazon.com/Computing-Cambridge-Monographs-Computa...

Happy to help if you need it!