Applied topology 8: An introduction to persistent homology

[@katalinabiondi]

I am new to this field and have read and watched a bunch on this...and this has been by far the BEST introduction to this topic. Bravo.

[@aatrn1]

Thanks so much - glad it was helpful!

[@tonireyes844]

What are the prerequisites for the math behind these concepts? Any good intro book to persistence homology we study here?

[@amiltonwong]

Thanks Prof. Henry Adams for the great materials on TDA. I have a question. It's clear that the n-dim bar represents the lifetime of the corresponding n-dim hole. Could we say that the n-dim bar represents the topological feature of the corresponding n-dim hole?

[@HenryAdamsMath]

You're welcome! Yes, I think that's totally correct to say --- each n-dimensional persistent homology bar represents a topological feature which is an n-dimensional hole.

[@amiltonwong]

@@HenryAdamsMath Thanks! Got it :)

[@mohmadthakur4891]

Thank you for the nice video. Can you please give an advice on how to learn more about topology/persistent homology if you have no background on topology. I am looking to apply persistent homology on an engineering problem. Most of the textbooks and papers on persistent homology do not provide enough background information.

[@aatrn1]

Hi Mohmad, you may be interested in some of the following surveys www.ams.org/journals/bull/2008-45-01/S0273-0979-07-01191-3/S0273-0979-07-01191-3.pdf www.ams.org/journals/bull/2009-46-02/S0273-0979-09-01249-X/S0273-0979-09-01249-X.pdf dsweb.siam.org/The-Magazine/Article/topological-data-analysis-1 drive.google.com/file/d/0B3Www1z6Tm8xV3ozTmN5RE94bDg/view?resourcekey=0-tE7y-zXFtV3OWSGmjUebYA or books www.math.colostate.edu/~adams/advising/appliedTopologyBooks/ or software tutorials associated to any of the following software packages www.math.colostate.edu/~adams/advising/appliedTopologySoftware/

[@mohmadthakur4891]

@@aatrn1 Thank you so much for your response. Looking forward to reading this material.

[@HenryAdamsMath]

@@mohmadthakur4891 You bet!

[@milandoshi7640]

where are the triangles in the barcodes ? why are they not shown ?. Thanks.

[@HenryAdamsMath]

Good question! In this example, the triangles definitely contribute to killing or filling-in 1-dimensional holes. Otherwise, if we only had the edges and vertices (but no triangles), we would have a whole lot more 1-dimensional holes! In this particular example, no 2-dimensional holes (say hollow spheres or hollow tori) form, and for this reason we have not plotted the 2-dimensional persistent homology, as it would be an empty barcode. But you're exactly right that triangles could have given birth to 2-dimensional homology!

[@muskduh]

thanks

[@aatrn1]

You are welcome!