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Partition of Interval-Valued Observations Using Regression

Author

Listed:
  • Fei Liu

    (Bank of America)

  • L. Billard

    (University of Georgia,)

Abstract

Both regression modeling and clustering methodologies have been extensively studied as separate techniques. There has been some activity in using regression-based algorithms to partition a data set into clusters for classical data; we propose one such algorithm to cluster interval-valued data. The new algorithm is based on the k-means algorithm of MacQueen (1967) and the dynamical partitioning method of Diday and Simon (1976), with the partitioning criteria being based on establishing regression models for each sub-cluster. This also depends on distance measures between the underlying regression models for each sub-cluster. Several types of simulated data sets are generated for several different data structures. The proposed k-regressions algorithm consistently out-performs the k-means algorithm. Elbow plots are used to identify the total number of clusters K in the partition. The new method is also applied to real data.

Suggested Citation

  • Fei Liu & L. Billard, 2022. "Partition of Interval-Valued Observations Using Regression," Journal of Classification, Springer;The Classification Society, vol. 39(1), pages 55-77, March.
    • Handle: RePEc:spr:jclass:v:39:y:2022:i:1:d:10.1007_s00357-021-09394-5
    DOI: 10.1007/s00357-021-09394-5
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    References listed on IDEAS

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    1. Billard L. & Diday E., 2003. "From the Statistics of Data to the Statistics of Knowledge: Symbolic Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 470-487, January.
    2. Stéphanie Bougeard & Hervé Abdi & Gilbert Saporta & Ndèye Niang, 2018. "Clusterwise analysis for multiblock component methods," 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. 12(2), pages 285-313, June.
    3. Lima Neto, Eufrasio de A. & de Carvalho, Francisco de A.T., 2008. "Centre and Range method for fitting a linear regression model to symbolic interval data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1500-1515, January.
    4. Francisco Carvalho & Paula Brito & Hans-Hermann Bock, 2006. "Dynamic clustering for interval data based on L 2 distance," Computational Statistics, Springer, vol. 21(2), pages 231-250, June.
    5. Robert Tibshirani & Guenther Walther & Trevor Hastie, 2001. "Estimating the number of clusters in a data set via the gap statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 411-423.
    6. Wayne DeSarbo & William Cron, 1988. "A maximum likelihood methodology for clusterwise linear regression," Journal of Classification, Springer;The Classification Society, vol. 5(2), pages 249-282, September.
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