An exponential-time exact algorithm is provided for the task of clustering nitems of data into k clusters. Instead of seeking one partition, posteriorprobabilities are computed for summary statistics: the number of clusters, andpairwise co-occurrence. The method is based on subset convolution, and yieldsthe posterior distribution for the number of clusters in O(n * 3^n) operations,or O(n^3 * 2^n) using fast subset convolution. Pairwise co-occurrenceprobabilities are then obtained in O(n^3 * 2^n) operations. This isconsiderably faster than exhaustive enumeration of all partitions.
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