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Cluster analysis is the task of partitioning data into subsets of objects according to their mutual "similarity," without using preexisting knowledge such as class labels. [Clustered-standard-errors and/or cluster-samples should be tagged as such; do NOT use the "clustering" tag for them.]

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k-means clustering on a probability distribution instead of a dataset

I am wondering if we can just define the clustering algorithm on the distribution itself, and segment the input space into Voronoi cells without reference to a dataset. … For example, to work out quantities like the expected sum of within cluster distances, and expected error rates if the clustering is made into a classification task. …
Harry Partridge's user avatar