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Detecting Clusters in the Data from Variance Decompositions of Its Projections

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  • Yannis Yatracos

Abstract

A new projection-pursuit index is used to identify clusters and other structures in multivariate data. It is obtained from the variance decompositions of the data’s one-dimensional projections, without assuming a model for the data or that the number of clusters is known. The index is affine invariant and successful with real and simulated data. A general result is obtained indicating that clusters’ separation increases with the data’s dimension. In simulations it is thus confirmed, as expected, that the performance of the index either improves or does not deteriorate when the data’s dimension increases, making it especially useful for “large dimension-small sample size” data. The efficiency of this index will increase with the continuously improved computer technology. Several applications are presented. Copyright Springer Science+Business Media New York 2013

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  • Yannis Yatracos, 2013. "Detecting Clusters in the Data from Variance Decompositions of Its Projections," Journal of Classification, Springer;The Classification Society, vol. 30(1), pages 30-55, April.
    • Handle: RePEc:spr:jclass:v:30:y:2013:i:1:p:30-55
    DOI: 10.1007/s00357-013-9124-9
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    References listed on IDEAS

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    1. Vichi, Maurizio & Saporta, Gilbert, 2009. "Clustering and disjoint principal component analysis," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3194-3208, June.
    2. Jon R. Kettenring, 2006. "The Practice of Cluster Analysis," Journal of Classification, Springer;The Classification Society, vol. 23(1), pages 3-30, June.
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    Cited by:

    1. Yatracos, Yannis G., 2018. "Residual'S Influence Index (Rinfin), Bad Leverage And Unmasking In High Dimensional L2-Regression," IRTG 1792 Discussion Papers 2018-060, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    2. Álvaro Herrero & Alfredo Jiménez & Secil Bayraktar, 2019. "Hybrid Unsupervised Exploratory Plots: A Case Study of Analysing Foreign Direct Investment," Complexity, Hindawi, vol. 2019, pages 1-14, June.
    3. Pele, Daniel Traian & Wesselhöfft, Niels & Härdle, Wolfgang Karl & Kolossiatis, Michalis & Yatracos, Yannis, 2019. "Phenotypic convergence of cryptocurrencies," IRTG 1792 Discussion Papers 2019-018, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    4. 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.

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