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   null (Ed.)

   Abstract We develop a cluster process which is invariant with respect to unknown affine transformations of the feature space without knowing the number of clusters in advance. Specifically, our proposed method can identify clusters invariant under (I) orthogonal transformations, (II) scaling-coordinate orthogonal transformations, and (III) arbitrary nonsingular linear transformations corresponding to models I, II, and III, respectively and represent clusters with the proposed heatmap of the similarity matrix. The proposed Metropolis-Hasting algorithm leads to an irreducible and aperiodic Markov chain, which is also efficient at identifying clusters reasonably well for various applications. Both the synthetic and real data examples show that the proposed method could be widely applied in many fields, especially for finding the number of clusters and identifying clusters of samples of interest in aerial photography and genomic data. 

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