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A polythetic clustering process and cluster validity indexes for histogram-valued objects

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  • Kim, Jaejik
  • Billard, L.

Abstract

Clustering is an explanatory procedure which helps to understand data with complex structure and multivariate relationships, and is a very useful method to extract knowledge and information especially from large datasets. When such datasets are aggregated into categories (as driven by scientific questions underlying the analysis), the resulting observations will perforce be expressed as so-called symbolic data (though symbolic data can occur "naturally" in any sized datasets). The focus of this work is to provide a divisive polythetic algorithm to establish clusters for p-dimensional histogram-valued data. In addition, two cluster validity indexes for use in establishing the optimal number of clusters are also developed. Finally, the proposed procedure is applied to a large forestry cover type dataset.

Suggested Citation

  • Kim, Jaejik & Billard, L., 2011. "A polythetic clustering process and cluster validity indexes for histogram-valued objects," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2250-2262, July.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:7:p:2250-2262
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    References listed on IDEAS

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    1. Glenn Milligan & Martha Cooper, 1985. "An examination of procedures for determining the number of clusters in a data set," Psychometrika, Springer;The Psychometric Society, vol. 50(2), pages 159-179, June.
    2. Chavent, Marie & Lechevallier, Yves & Briant, Olivier, 2007. "DIVCLUS-T: A monothetic divisive hierarchical clustering method," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 687-701, October.
    3. Struyf, Anja & Hubert, Mia & Rousseeuw, Peter, 1997. "Clustering in an Object-Oriented Environment," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 1(i04).
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    Cited by:

    1. Kim, Jaejik & Billard, L., 2012. "Dissimilarity measures and divisive clustering for symbolic multimodal-valued data," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2795-2808.
    2. Francisco de A. T. Carvalho & Antonio Irpino & Rosanna Verde & Antonio Balzanella, 2022. "Batch Self-Organizing Maps for Distributional Data with an Automatic Weighting of Variables and Components," Journal of Classification, Springer;The Classification Society, vol. 39(2), pages 343-375, July.
    3. Soroosh Shalileh, 2023. "An Effective Partitional Crisp Clustering Method Using Gradient Descent Approach," Mathematics, MDPI, vol. 11(12), pages 1-23, June.
    4. Nataša Kejžar & Simona Korenjak-Černe & Vladimir Batagelj, 2021. "Clustering of modal-valued symbolic data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(2), pages 513-541, June.

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