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Affine-transformation invariant clustering models

Author

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  • Hsin-Hsiung Huang

    (University of Central Florida)

  • Jie Yang

    (University of Illinois at Chicago)

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.

Suggested Citation

  • Hsin-Hsiung Huang & Jie Yang, 2020. "Affine-transformation invariant clustering models," Journal of Statistical Distributions and Applications, Springer, vol. 7(1), pages 1-24, December.
    • Handle: RePEc:spr:jstada:v:7:y:2020:i:1:d:10.1186_s40488-020-00111-y
    DOI: 10.1186/s40488-020-00111-y
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    References listed on IDEAS

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    1. Fraley C. & Raftery A.E., 2002. "Model-Based Clustering, Discriminant Analysis, and Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 611-631, June.
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    3. Dudoit S. & Fridlyand J. & Speed T. P, 2002. "Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 77-87, March.
    4. Chris Fraley & Adrian E. Raftery, 2007. "Bayesian Regularization for Normal Mixture Estimation and Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 24(2), pages 155-181, September.
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    Cited by:

    1. Yuqing Kong, 2021. "Information Elicitation Meets Clustering," Papers 2110.00952, arXiv.org.

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