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Factor probabilistic distance clustering (FPDC): a new clustering method

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Abstract

Factor clustering methods have been developed in recent years thanks to improvements in computational power. These methods perform a linear transformation of data and a clustering of the transformed data, optimizing a common criterion. Probabilistic distance (PD)-clustering is an iterative, distribution free, probabilistic clustering method. Factor PD-clustering (FPDC) is based on PD-clustering and involves a linear transformation of the original variables into a reduced number of orthogonal ones using a common criterion with PD-clustering. This paper demonstrates that Tucker3 decomposition can be used to accomplish this transformation. Factor PD-clustering alternatingly exploits Tucker3 decomposition and PD-clustering on transformed data until convergence is achieved. This method can significantly improve the PD-clustering algorithm performance; large data sets can thus be partitioned into clusters with increasing stability and robustness of the results. Real and simulated data sets are used to compare FPDC with its main competitors, where it performs equally well when clusters are elliptically shaped but outperforms its competitors with non-Gaussian shaped clusters or noisy data.

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Acknowledgments

The authors are grateful to an associate editor and anonymous reviewers for their very helpful comments and suggestions, the cumulative effect of which has been a stronger manuscript.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, Hamilton, Canada

    Cristina Tortora

  2. CEREMADE, Université Paris Dauphine, Paris, France

    Mireille Gettler Summa

  3. Dipartimento di Scienze Sociali, University of Naples Federico II, Naples, Italy

    Marina Marino

  4. Dipartimento di Scienze Politiche, University of Naples Federico II, Naples, Italy

    Francesco Palumbo

Authors
  1. Cristina Tortora
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  2. Mireille Gettler Summa
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  3. Marina Marino
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  4. Francesco Palumbo
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Corresponding author

Correspondence to Francesco Palumbo.

Appendix 1

Appendix 1

Correlation matrix of wine data set (Table 2), values equal to or higher than 0.5 in bold.

Table 2 Correlation matrix of wine data set
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Tortora, C., Summa, M.G., Marino, M. et al. Factor probabilistic distance clustering (FPDC): a new clustering method. Adv Data Anal Classif 10, 441–464 (2016). https://doi.org/10.1007/s11634-015-0219-5

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