Affine-transformation invariant clustering models

Journal of Statistical Distributions and Applications

Jie Yang¹  Hsin-Hsiung Huang² 

[1] Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, USA;Department of Statistics and Data Science, University of Central Florida, Orlando, USA;

关键词: Dirichlet process;    Ewens process;    Metropolis-Hastings algorithm;    Markov chain Monte Carlo sampling;    Unsupervised learning;   

DOI  :  10.1186/s40488-020-00111-y

来源: Springer

【 摘 要 】

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.

【 授权许可】

CC BY