Questions tagged [topological-data-analysis]
Methods in data analysis that use features and/or techniques from topology.
Use of normalized persistent Betti number
This recent paper proposes a quantum algorithm to approximate normalized persistent Betti number. However, the authors have noted that they are not aware of any usage of normalized persistent Betti ...
Does adding features from "persistent homology" of the data increase multicollinearity, condition numbers of hessian, and endogenous variable?
Does adding features the "persistent homology" of the data increase multicollinearity, condition numbers of hessian, and endogenous variable? The persistent homology is a summary statistic ...
Does persistent homology based on variance-balancing ellipsoids give the same simplicial complexes as with spheres?
In persistent homology estimation the standard approach involves using $\epsilon$-balls. When two balls intersect, an edge is drawn between the points. Faces are formed in a similar way (although the ...
Does persistent homology really make sense for mixed variable types?
Purpose Persistent homology is a fascinating approach to exploring data (see Chazal & Michel 2021 for an introduction). I have seen many impressive examples of it through AATRN. I'm considering ...
How to determine if a given sample size is appropriate for Betti number estimation?
A popular approach in topological data analysis is persistent homology (Chazal and Michel 2021 for an intro), but it is not clear to me what sample sizes are appropriate. Some talks seem to use ...
Measure of distance between two survey responses
I've found some survey data where respondents answer 63 question by giving a response for each question between 0-10 (0 for strong disagreement, 10 for strong agreement). So I can view every ...
What are the best known techniques to verify that a GAN samples correctly from a given distribution?
I would like to know what are the best known techniques to check that a generative adversarial network (GAN) samples from the correct distribution. Naively, I would say it all boils down to a ...
What are the 3-dimensional subspaces (or quotient spaces) to which the projections are made in the given figures? (Topological Data Analysis)
EDIT: I was told by my supervisor to implement the algorithm first and then look back over the question because "biologists' papers do not always contain the information that is necessary to reproduce ...
Persistent Homology of High dimensional data
I'm new to Python (and to coding in general), so this question may be trivial. I need to compute persistent homology for a high dimensional dataset ( d ~ 1000) embedded in a vector space, but I'm ...
Which methods can help us to understand clustering model is good or bad?
In some clustering algorithm, ex: K-Means cluster, it is very sensitive with outliers, so we need to remove outliers before aplly ...
Topological data analysis and evaluating dimensionality reduction
I did an exploration some time ago on using TDA tools to see how topological features change after application of some nonlinear dimensionality reduction methods. For example I found out that, for ...
Cases where TDA outperforms public benchmarks?
Precise Question What are some specific examples where topological data analysis (TDA) outperforms other models on publicly available data? Context When new ML algorithms are developed, it seems ...
Topology of Confidence Intervals
I hope this is the right site to post this. The example I have in my mind is a GLMM model, where we infer random effects, and a random effect caterpillar plot (with confidence intervals): Now, ...
Measuring robustness of network constructed with python mapper
I am trying to visualize a large multidimensional data set with the help of the Python Mapper (open source software package using the Mapper-Algorithm, a method of Topological Data Analysis). http:/...
Intrinsic topology and metrics... (looking for name of a method) [duplicate]
Suppose I have an n-dimensional dataset and its points are roughly in the shape of an n-dimensional horseshoe or something along those lines. Using euclidian distance might be a bad idea, since points ...