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?
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.
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.
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/
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!
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.
Thanks so much - glad it was helpful!
What are the prerequisites for the math behind these concepts? Any good intro book to persistence homology we study here?
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?
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.
@@HenryAdamsMath Thanks! Got it :)
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.
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/
@@aatrn1 Thank you so much for your response. Looking forward to reading this material.
@@mohmadthakur4891 You bet!
where are the triangles in the barcodes ? why are they not shown ?. Thanks.
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!
thanks
You are welcome!