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.

中文翻译：

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仿射变换不变聚类模型

我们开发了一个聚类过程，该过程对于特征空间的未知仿射变换而言是不变的，而无需事先知道聚类的数量。具体而言，我们提出的方法可以识别在（I）正交变换，（II）比例坐标正交变换和（III）分别对应于模型I，II和III的任意非奇异线性变换下不变的聚类，并用提出的聚类表示聚类相似度矩阵的热图。提出的Metropolis-Hasting算法导致了不可约和非周期性的马尔可夫链，这对于识别各种应用的聚类也很有效。综合和实际数据实例均表明，该方法可广泛应用于许多领域，