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The problem of clustering, that is, the partitioning of data into groups of similar objects, is a key step for many data-mining problems. The algorithm we propose for clustering is based on the symmetric nonnegative matrix factorization (SymNMF) of a similarity matrix. The algorithm is first presented for the case of a prescribed number k of clusters, then it is extended to the case of a not a priori given k. A heuristic approach improving the standard multistart strategy is proposed and validated by the experimentation.

Adaptive Clustering via Symmetric Nonnegative Matrix Factorization of the Similarity Matrix