Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [topological-data-analysis]

Methods in data analysis that use features and/or techniques from topology.

'One of the key messages around topological data analysis is that data has shape and the shape matters.' - Gunnar Carlson

Topological data analysis deals with applying tools from topology to study point cloud data. These methods exploit 'shape' which is captured by definitions mostly from algebraic and differential topology.

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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 common practice to apply them to publicly-available…
Quetzalcoatl
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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, suppose we start applying topological data analysis…
Alex R.
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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 K-Means, or it will be bad clustering. So : How can we know some points are outliers if we can not plot it ( high…
voxter
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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 Natural Image Patches dataset, reducing dimension…
Jakub Bartczuk
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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 estimating a distance (or divergence such as…
mic
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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 their calculations". That is to say that I will…
rlamesch
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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 having some troubles: First, I don't even know if…
Alfred
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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://danifold.net/mapper/ With the Python Mapper one…
ahbon
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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 respondent as a integer point in $[0,10]^{63}$. Question:…
user10039910
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Topological approach to create a space between clouds

I have a dataset associated with labels. According to https://arxiv.org/pdf/1802.03426.pdf --> UMAP (Uniform Manifold Approximation and Projection) which is a novel manifold learning technique for dimension reduction and the data, I succeeded to…
davegaut
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Consider a directed network as an undirected one for topology parameter comparisons

I have a set of biologically relevant transcriptional regulatory networks which are bipartite with a set of transcription factors and the genes that they regulate. However, when I put my network on Cytoscape to get the centrality measures, average…
Charles
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Intrinsic topology and metrics... (looking for name of a method)

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 on the tip of the horseshoe would the appear…
BootstrapBill
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