Advances in Data Analysis and Classification

, Volume 10, Issue 4, pp 441–464 | Cite as

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

  • Cristina Tortora
  • Mireille Gettler Summa
  • Marina Marino
  • Francesco PalumboEmail author
Regular Article


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.


Factor clustering Probabilistic distance clustering Tucker3 k-means 

Mathematics Subject Classification

6207 62H30 



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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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Cristina Tortora
    • 1
  • Mireille Gettler Summa
    • 2
  • Marina Marino
    • 3
  • Francesco Palumbo
    • 4
    Email author
  1. 1.Department of Mathematics and StatisticsMcMaster UniversityHamiltonCanada
  2. 2.CEREMADE, Université Paris DauphineParisFrance
  3. 3.Dipartimento di Scienze SocialiUniversity of Naples Federico IINaplesItaly
  4. 4.Dipartimento di Scienze PoliticheUniversity of Naples Federico IINaplesItaly

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