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A new approach to cluster analysis: the clustering‐function‐based method

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  • Baibing Li

Abstract

Summary. The purpose of the paper is to present a new statistical approach to hierarchical cluster analysis with n objects measured on p variables. Motivated by the model of multivariate analysis of variance and the method of maximum likelihood, a clustering problem is formulated as a least squares optimization problem, simultaneously solving for both an n‐vector of unknown group membership of objects and a linear clustering function. This formulation is shown to be linked to linear regression analysis and Fisher linear discriminant analysis and includes principal component regression for tackling multicollinearity or rank deficiency, polynomial or B‐splines regression for handling non‐linearity and various variable selection methods to eliminate irrelevant variables from data analysis. Algorithmic issues are investigated by using sign eigenanalysis.

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  • Baibing Li, 2006. "A new approach to cluster analysis: the clustering‐function‐based method," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 457-476, June.
    • Handle: RePEc:bla:jorssb:v:68:y:2006:i:3:p:457-476
    DOI: 10.1111/j.1467-9868.2006.00549.x
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    Cited by:

    1. Alan Jessop, 2010. "An optimising approach to alternative clustering schemes," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(3), pages 293-309, September.
    2. Timothy I. Cannings & Richard J. Samworth, 2017. "Random-projection ensemble classification," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 959-1035, September.
    3. De la Cruz-Mesia, Rolando & Quintana, Fernando A. & Marshall, Guillermo, 2008. "Model-based clustering for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1441-1457, January.
    4. Gallegos, María Teresa & Ritter, Gunter, 2010. "Using combinatorial optimization in model-based trimmed clustering with cardinality constraints," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 637-654, March.

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