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Generalized Co-clustering Analysis via Regularized Alternating Least Squares

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  • Li, Gen

Abstract

Biclustering is an important exploratory analysis tool that simultaneously clusters rows (e.g., samples) and columns (e.g., variables) of a data matrix. Checkerboard-like biclusters reveal intrinsic associations between rows and columns. However, most existing methods rely on Gaussian assumptions and only apply to matrix data. In practice, non-Gaussian and/or multi-way tensor data are frequently encountered. A new CO-clustering method via Regularized Alternating Least Squares (CORALS) is proposed, which generalizes biclustering to non-Gaussian data and multi-way tensor arrays. Non-Gaussian data are modeled with single-parameter exponential family distributions and co-clusters are identified in the natural parameter space via sparse CANDECOMP/PARAFAC tensor decomposition. A regularized alternating (iteratively reweighted) least squares algorithm is devised for model fitting and a deflation procedure is exploited to automatically determine the number of co-clusters. Comprehensive simulation studies and three real data examples demonstrate the efficacy of the proposed method. The data and code are publicly available at https://github.com/reagan0323/CORALS.

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  • Li, Gen, 2020. "Generalized Co-clustering Analysis via Regularized Alternating Least Squares," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:csdana:v:150:y:2020:i:c:s0167947320300803
    DOI: 10.1016/j.csda.2020.106989
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    References listed on IDEAS

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    1. Shen, Haipeng & Huang, Jianhua Z., 2008. "Sparse principal component analysis via regularized low rank matrix approximation," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1015-1034, July.
    2. Hongya Zhao & Debby D Wang & Long Chen & Xinyu Liu & Hong Yan, 2016. "Identifying Multi-Dimensional Co-Clusters in Tensors Based on Hyperplane Detection in Singular Vector Spaces," PLOS ONE, Public Library of Science, vol. 11(9), pages 1-27, September.
    3. Neng Fan & Nikita Boyko & Panos M. Pardalos, 2010. "Recent Advances of Data Biclustering with Application in Computational Neuroscience," Springer Optimization and Its Applications, in: Wanpracha Chaovalitwongse & Panos M. Pardalos & Petros Xanthopoulos (ed.), Computational Neuroscience, chapter 0, pages 85-112, Springer.
    4. Xiaoshan Li & Da Xu & Hua Zhou & Lexin Li, 2018. "Tucker Tensor Regression and Neuroimaging Analysis," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(3), pages 520-545, December.
    5. Gen Li & Jianhua Z. Huang & Haipeng Shen, 2018. "Exponential Family Functional data analysis via a low‐rank model," Biometrics, The International Biometric Society, vol. 74(4), pages 1301-1310, December.
    6. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    7. Govaert, Gérard & Nadif, Mohamed, 2008. "Block clustering with Bernoulli mixture models: Comparison of different approaches," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3233-3245, February.
    8. Eric C. Chi & Genevera I. Allen & Richard G. Baraniuk, 2017. "Convex biclustering," Biometrics, The International Biometric Society, vol. 73(1), pages 10-19, March.
    9. Mihee Lee & Haipeng Shen & Jianhua Z. Huang & J. S. Marron, 2010. "Biclustering via Sparse Singular Value Decomposition," Biometrics, The International Biometric Society, vol. 66(4), pages 1087-1095, December.
    10. Will Wei Sun & Junwei Lu & Han Liu & Guang Cheng, 2017. "Provable sparse tensor decomposition," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 899-916, June.
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    Cited by:

    1. C. Biernacki & J. Jacques & C. Keribin, 2023. "A Survey on Model-Based Co-Clustering: High Dimension and Estimation Challenges," Journal of Classification, Springer;The Classification Society, vol. 40(2), pages 332-381, July.
    2. Binhuan Wang & Lanqiu Yao & Jiyuan Hu & Huilin Li, 2023. "A New Algorithm for Convex Biclustering and Its Extension to the Compositional Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 193-216, April.

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