Questions tagged [topological-data-analysis]

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

Filter by
Sorted by
Tagged with
0
votes
1answer
47 views

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 ...
2
votes
0answers
57 views

How does the coloring of dendrograms in SciPy work?

So I am clustering my data using linkage extensions. When I plot the diagrams of the dendrograms scipy chooses to color branches in different colors according to a "color threshold". As I ...
1
vote
0answers
27 views

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 ...
1
vote
0answers
35 views

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 ...
0
votes
0answers
96 views

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 ...
1
vote
0answers
82 views

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 ...
0
votes
0answers
54 views

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 ...
3
votes
1answer
804 views

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 ...
3
votes
0answers
273 views

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 ...
6
votes
1answer
300 views

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 ...
4
votes
0answers
98 views

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, ...
1
vote
0answers
123 views

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:/...
0
votes
0answers
36 views

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 ...
6
votes
3answers
3k views

How to get a valid distance metric?

I have got a problem to devise a distance metric to get the similarity measurement of vectors. Someone suggested me to use dot product, which seems to me the same as the Cosine similarity metric; ...