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@tonireyes844 Ай бұрын
Great teacher, where can we find more about this application?
@tonireyes844 Ай бұрын
What are the prerequisites for the math behind these concepts? Any good intro book to persistence homology we study here?
@TudorStoica2001 Ай бұрын
Great video! Excellent intuitive explanation for anyone with a basic understanding of math and probability theory. Keep it up!!
@aatrn1 25 күн бұрын
Thank you!
@gabrielazunigarojas7084 Ай бұрын
Thank you incredibly helpful and clear😀
@aatrn1 25 күн бұрын
Glad it was helpful!
@guitarras73 Ай бұрын
❤️❤️❤️❤️❤️❤️
@DavidConnerCodeaholic Ай бұрын
Hmmm I’ve never been able to download like half the papers I’m interested in
@DavidConnerCodeaholic Ай бұрын
Thanks for clearing this up. This was so much simpler & clearer than reading the Greek … which will now make more sense. As for the Cech complex, assuming a Euclidean space, can’t you use the Vietoris-Rips as a starting point to search for at least one point that satisfies the condition for a simplex in the cech complex? IE: place normal vectors on each edge or triangular plane oriented towards the “center” of the potential simplex, then start searching the space between by adding a point to the simple and calculating the distance to other vertices in the same simplex. This itself is like a geometric realization of the nerve… whether it works or not it does give me some intuition into the nerve.
@aatrn1 25 күн бұрын
That's a great point - the connection between the Vietoris-Rips and Cech complexes is definitely worth exploring!
@DeepFindr 2 ай бұрын
Very interesting talk! Thanks for sharing 🎉
@aatrn1 25 күн бұрын
Glad you enjoyed it!
@Mede_N 2 ай бұрын
Thanks for this great talk! Regarding determining the relative importance of the different plant species, i wondered: Have you checked, if the Wasserstein distance correlates (strongly) with something like the change in average shortest path length, if the same plant is removed? Or something like the Eigenvector centrality?
@DavidConnerCodeaholic 2 ай бұрын
Interesting. I would like to know more about the implementation of the Boolean methods.
@avnishpanwar9502 2 ай бұрын
Nice I could use it in pedestrian dynamics on road.
@aatrn1 25 күн бұрын
Yes, indeed!
@Abacuscalcus 3 ай бұрын
Helpful intro, nice to see where this is being discussed in academia.
@aatrn1 25 күн бұрын
Glad it was helpful!
@Qhsjahajw 4 ай бұрын
where's the audio
@aatrn1 4 ай бұрын
Apologies, this was an old video (from 2015), and so it seems the recording cut out at times.
@anaa2615 5 ай бұрын
very good explanation, great video
@aatrn1 5 ай бұрын
We agree!
@christopherboon1677 5 ай бұрын
A true gem on TDA. Clear application and great results. Awesome video
@aatrn1 5 ай бұрын
Couldn't agree more!
@davidhand9721 5 ай бұрын
Can someone please explain _how_ homology groups are abelian groups? In homotopy, the group operation was very well defined; if you had homotopy < A, B > then AB was a path that went around B then went around A. It was a function that mapped a t parameter to a point in the space. It all made perfect sense at every step. In homology, we just sort of assert that the "group" allows us to put things together in any order, but I struggle to imagine an object or function that is both the same regardless of order _and_ allows any number of path crossings _and_ has an inverse. What _is_ A + B (being 1-simplices, for example) if they don't form a full cycle? What is the difference between that and 2A - C? Maybe I'm just having a math-foreigner freakout. Maybe I'm looking at it as a scientist and I want objects to _mean_ something, and I'm offended that we're just sort of inventing rules. Maybe I'm looking at it like a coder, thinking that if two things are different, they must contain or refer to something different from one another. Either way, it would be _very_ helpful if someone could give me some sense of what we are doing by adding and (scalar) multiplying these little path fragments together. Even just an analogy would make a world of difference to me.
@aatrn1 5 ай бұрын
Let me start with an analogy, and then discuss homology with "Z/2Z coefficients" (whatever that means), and then briefly mention homology with Z coefficients at the end (which is what you are asking about most directly). Okay, here's the analogy. If A and B are sets, then (A union B) is the same as (B union A). So the operation of set union is commutative. There's a related operation called "exclusive union", where (A exclusive union B) contains all of the elements of (A union B) that are not in both A and B --- see www.oreilly.com/library/view/sql-and-relational/9781449319724/ch07s01.html. It turns out that we still have (A exclusive union B) = (B exclusive union A). In a very real sense, homology with Z/2Z coefficients forms an abelian group simply because exclusive union is commutative. Now let me discuss homology with Z/2Z coefficients. Intuitively, Z/2Z coefficients means we can ignore signs and orientations, since 1+1=0 in Z/2Z, which means 1 is its own inverse in Z/2Z. Okay, in this context, a cycle is simply a set of simplices with empty boundary. So, a 1-cycle is a set of edges with empty boundary. These 1-cycles generate the 1-dimensional homology group. And, the group operation is exclusive union. So the sum or the concatenation of two 1-cycles is simply the exclusive union of both sets of edges. It doesn't matter in which order you take the exclusive union --- you still get the same exclusive union set --- which again has no boundary. This is why homology is abelian. In your post, you talk about orientations, and you include negative signs. So I can tell you are reading about homology with Z coefficients, instead of homology with Z/2Z coefficients. But, it turns out that even when you include orientations and multiplicities, homology is still abelian for the same reason. When you have Z coefficients, a cycle is a collection of oriented simplices, perhaps counted with multiplicity, that has no boundary. But again, when you take two such cycles A and B and add them, you still get the same multiplicities regardless of whether you do this addition as A+B or as B+A.
@ruelapas6240 5 ай бұрын
How a vector window becomes a point?
@aatrn1 5 ай бұрын
Perhaps the following forum contains some helpful thoughts: math.stackexchange.com/questions/645672/what-is-the-difference-between-a-point-and-a-vector
@hanchen2355 6 ай бұрын
Very helpful!!! Thanks!!!
@aatrn1 6 ай бұрын
You're welcome!
@conradmorris8881 6 ай бұрын
thank you so much! super helpful
@aatrn1 6 ай бұрын
You're welcome!
@AlaapHasan 6 ай бұрын
I have a real tough time installing this on mac ventura Is this to be used mainly on linux systems?
@zackaryleady 7 ай бұрын
Hello, I see in your talk that you utilize k-mean clustering with a frequency matrix over 1000 solves of k-means where k=5. Was the input for the k-means clustering a MxN (samples, features) matrix where the number of features is 100x100 or 10,000 pixel values from the persistence image (gaussian over the persistence diagrams)? If so, may I ask why you didn't use *HDBSCAN (can also be setup for single-linkage clustering)? I believe that *HDBSCAN will give you the linkage tree and the minimum spanning tree which it looks like you use later in your analysis from the frequency matrix. Also what distance calculation did you use? Usually Euclidean at 10,000 dimensions would kind of break-down due to the curse of dimensionality. Did you perhaps use the wasserstein 1D on the histogram of the persistence image or a fisher metric? Would you be able to explain briefly how the connect community algorithm worked (name?) and how it is different than say UMAP? I'm very familiar with UMAP, but less familiar with community graph algorithms (i.e what is the edge). Later in your presentation you do an analysis on representative samples and boundary samples --- if you had used *HDBSCAN then you have access to the boundary points and exemplar points (the points that are most persistent in the cluster, and thus most representative) and these are actual samples and not artificially generated centroids. Did you consider this and reject it for some other set of reasons? Did you also consider that different property areas have different rules when properties are reassessed for taxes (i.e. property taxes may not be reassessed until a property is sold, so a property with higher taxes or lower taxes than its neighbors could just be a result of recent purchase activities)?
@jeonghwankim8973 7 ай бұрын
Great explanation!
@aatrn1 6 ай бұрын
Glad it was helpful!
@nebularwinter 7 ай бұрын
asuka is the best!
@renormalization 8 ай бұрын
Beautiful visualization, thanks!
@aatrn1 6 ай бұрын
Glad you liked it!
@jacksonstenger 8 ай бұрын
Nice lecture, thanks
@aatrn1 6 ай бұрын
Glad you liked it!
@akathevip 8 ай бұрын
awesome video
@aatrn1 6 ай бұрын
We agree!
@christopherlegarda5164 9 ай бұрын
Where can I obtain these slides if this is possible. Thank you.
@PavelKonovalov-q4r 9 ай бұрын
Great video, very informative. I have a question: How would you apply the techniques you shared on a signal with a trend?
@gen2497 9 ай бұрын
Great job. Thanks for sharing!
@aatrn1 8 ай бұрын
Thanks for watching!
@al-imran0013 10 ай бұрын
Could you please attach the related articles and books as references to the lecture video? This will help us understand the topic comprehensively from its foundational level.
@al-imran0013 10 ай бұрын
Is there a library or article or lecture note to convert a grayscale image to a cubical complex?
@aatrn1 10 ай бұрын
Yes! Many software packages (see for example the list at www.math.colostate.edu/~adams/advising/appliedTopologySoftware/ ) can do this. For example, GUDHI can do this, as can other software packages.
@quercus3290 10 ай бұрын
Hi there, I am a total layman with regards to the scientific subject which is being covered here, however I am an extremely experienced user with AI image generation and recently have began exploring advanced topology. Is it possible to have a quick chat with someone?
@vicentegonzalez1867 10 ай бұрын
Amazing work and speaker!
@aatrn1 10 ай бұрын
We agree!
@iamsiddhantsahu 10 ай бұрын
Great talk -- do you know where can I find the slides?
@aaaab384 10 ай бұрын
It took me ages to understand that what you write as a big ALPHA is actually THE NUMBER 2.
@aatrn1 10 ай бұрын
Whoops!
@saurabhyadav-nx9pf 10 ай бұрын
Herbert is my motivational prof. and my dream is to work with under the guidance herbert on topology.
@nikolaossampanis 10 ай бұрын
Contrats 🎉
@JosefGruber-br5bw 11 ай бұрын
Wow ... thanks a lot Sarah ... this is one of the best presentation I have seen on TDA. Very cool ...
@aatrn1 10 ай бұрын
We agree!
@이형석-g9m 11 ай бұрын
Great video😮
@aatrn1 11 ай бұрын
Glad you enjoyed it!
@micahscopes Жыл бұрын
Wonderful! Thank you!
@aatrn1 11 ай бұрын
Glad you enjoyed the video!
@josueantonio2123 Жыл бұрын
Thanks for this nice intro! If I'm working with 2D images (png's) and I resize, transform them to greyscale for preprocessing, then use the imgs as numpy arrays to get persistence diagrams (using sublevel set filtration on pixel intesity), do I still need to standardize my images before getting PD's or maybe after? I'm asking because I want to then compute the persistence images for hom. dim. 1 from the PD's to train a classification model. Thanks!
@aatrn1 11 ай бұрын
It may first be worthwhile to try both ways --- both standardizing the images and not --- and see if there are significant differences!
@marccastillo606 Жыл бұрын
very cool work!
@aatrn1 11 ай бұрын
We agree!
@koftu Жыл бұрын
Well done, Alex!
@gp85759 Жыл бұрын
Thank you! My science group and I are writing a paper, and since I’m the youngest member, I was kinda struggling with the algorithm I have to write, this really helped!
@aatrn1 Жыл бұрын
Glad it was helpful!
@yoshcn Жыл бұрын
very clear thanks
@aatrn1 Жыл бұрын
Great!
@persistenthomology Жыл бұрын
how does this notion of dimension relate to doubling dimension or KR dimension?
@aatrn1 Жыл бұрын
This is a great question - it may be the case that a rigorous answer to your question is currently unknown!
@omererylmaz3619 Жыл бұрын
Thank you so much for the insightful video! I'm currently exploring Vietoris-Rips complexes in the context of 3D data. Do you have any recommendations for visualizing these complexes in 3D point cloud data? I want to use my own data to visualize the complexes. Any guidance would be greatly appreciated!
@theoreticalorigamiresearch186 Жыл бұрын
Who is she? Her work is very similar to what I've been looking for after having read neural sheaf diffusion on Michael Bronstein's Medium blog.
@aatrn1 Жыл бұрын
You can find out more about her fantastic research at her webpage: shreyaarya.github.io/minimal/
@rabiasagheer1426 Жыл бұрын
it's sad that the video does not have the clear audio 😥
@aatrn1 Жыл бұрын
2015 was by now a long time ago, unfortunately.
@HannahKAmundson Жыл бұрын
Amazing explanation! Thank you
@aatrn1 Жыл бұрын
You're very welcome!