Solve tough clustering problem

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Lorenco Santos Vasconcelos 2023-9-1

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https://ww2.mathworks.cn/matlabcentral/answers/2015831-solve-tough-clustering-problem

编辑： Lorenco Santos Vasconcelos 2023-9-1

data.mat

Hi, I'm having some trouble to solve a hard clustering problem.

I have a 2D dataset characterized by non spherical and partially overlaping clusters with different densities.

I've read a lot about clustering methods and for this type of data DBSCAN, Optics and other stuff wouldn't work very well. I think fuzzy clustering with mahalanobis inducing norm is a good choice. I've coded fuzzy c-means, k-means++ initialization, gustafson-kessel and gath-geva clustering methods but none of then can really separate the data. They are working really well for non overlapping clusters.

I also know that the problem is not the initialization, because even if I manually initialize the prototypes where I want, the algorithms converge to points that are not well separating the data. Typically I'm running kmeans++ and fcm to initialize the fuzzy partition and than I run gustafson-kessel or gath-geva

Also, tried different data normalization, like normalization by variance, by range, zscore, pca. None of this helps.

Here is the data:

Here is the typical result of gustafson-kessel and gath-geva

The desired result would be some thing like this: ( i know that because these groups represent different physical processes and we can realize that by eye)