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I am performing extensive customer segmentation analysis and so far implemented Gaussian Mixture Models, K-Means, and Hierarchical Clustering. For the most part, the algorithms agree on the structure of the clusters and well as the number (7-8). I would like to know if there is a common method to either...

  • compare similarity between clusters. Can you apply Adjusted Rand Index to two different clusterings of the same data (k-means clusters vs gmm)? I was under the impression ARI is used in instances where you know the truth of the data.
  • Find the common clusters within the clusterings. If all of the algorithms say one cluster is defined by high spending, then is there a way to determine the best centroid(s) to use for a "Master" cluster? Is it common to cluster the cluster results?
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If you just want to see how similar the clustering is between 2 algorithms, using the sklearn.metrics.adjusted_rand_score() function is a good starting point. This will work for unsupervised learning, no need for a label.

https://scikit-learn.org/stable/modules/generated/sklearn.metrics.adjusted_rand_score.html

Or are you looking at choosing the best combined grouping overall? I think "clustering the cluster" results is not a common approach, however there are a few articles online on how this could be done. But I don't know of any packages that will do this for you. One idea is to create a new column for each algorithm with the grouping chosen and then do some comparisions or calculations on these columns to get a final composite clustering.

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