Skip to main content
Springer Nature Link
Log in

Grouping Around Different Dimensional Affine Subspaces

  • Conference paper
  • First Online:
Statistical Models for Data Analysis

  • 5144 Accesses

Abstract

Grouping around affine subspaces and other types of manifolds is receiving a lot of attention in the literature due to its interest in several fields of application. Allowing for different dimensions is needed in many applications. This work extends the TCLUST methodology to deal with the problem of grouping data around different dimensional linear subspaces in the presence of noise. Two ways of considering error terms in the orthogonal of the linear subspaces are considered.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  • Banfield, J. D., & Raftery, A. E. (1993). “Model-based Gaussian and non-Gaussian clustering”. Biometrics, 49, 803–821.

    Article  MathSciNet  MATH  Google Scholar 

  • Celeux, G., & Govaert, A. (1992). “Classification EM algorithm for clustering and two stochastic versions”. Computational Statistics & Data Analysis, 13, 315–332.

    Article  MathSciNet  Google Scholar 

  • Dasgupta, A., & Raftery, A. E. (1998). “Detecting features in spatial point processes with clutter via model-based clustering.” Journal of the American Statistical Association, 93, 294–302.

    Article  MATH  Google Scholar 

  • Gallegos, M. T., & Ritter, G. (2005). “A robust method for cluster analysis.” Annals of Statistics, 33, 347–380.

    Article  MathSciNet  MATH  Google Scholar 

  • García-Escudero, L. A., Gordaliza, A., Matrán, C., & Mayo-Iscar, A. (2008a). “A general trimming approach to robust clustering”. Annals of Statistics, 36, 1324–1345.

    Article  MathSciNet  MATH  Google Scholar 

  • García-Escudero, L. A., Gordaliza, A., San Martín, R., Van Aelst, S., & Zamar, R. (2008b). “Robust linear grouping”. Journal of the Royal Statistical Society: Series B, 71, 301–319.

    Google Scholar 

  • Hathaway, R. J. (1985). “A constrained formulation of maximum likelihood estimation for normal mixture distributions.” Annals of Statistics, 13, 795–800.

    Article  MathSciNet  MATH  Google Scholar 

  • Kotz, S. (1975). “Multivariate distributions at a cross-road”. In G. P. Patil, S. Kotz, J. K. Ord (Eds.) Statistical distributions in scientific work (vol. 1, pp. 247270).

    Google Scholar 

  • Standford, D. C., & Raftery, A. E. (2000). “Finding curvilinear features in spatial point patterns: principal curve clustering with noise”. IEEE Transactions on Pattern Recognition, 22, 601–609.

    Article  Google Scholar 

  • Van Aelst, S., Wang, X., Zamar, R. H., & Zhu, R. (2006). “Linear grouping using orthogonal regression”. Computational Statistics & Data Analysis, 50, 1287–1312.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Facultad de Ciencias, Universidad de Valladolid, Paseo Belén 7, 47011, Valladolid, Spain

    L. A. García-Escudero, A. Gordaliza, C. Matrán & A. Mayo-Iscar

  2. Dpto. Estadística e I.O, Universidad de Valladolid and IMUVA, Valladolid, Spain

    L. A. García-Escudero, A. Gordaliza, C. Matrán & A. Mayo-Iscar

Authors
  1. L. A. García-Escudero
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Gordaliza
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. Matrán
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Mayo-Iscar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. A. García-Escudero .

Editor information

Editors and Affiliations

  1. Department of Economics, and Management, University of Pavia, Via San Felice 7, Pavia, 27100, Italy

    Paolo Giudici

  2. Department of Economics, and Business, University of Catania, Corso Italia 55, Catania, 95129, Italy

    Salvatore Ingrassia

  3. , Department of Statistics, University of Rome "La Sapienza", Piazzale Aldo Moro 5, Rome, 00185, Italy

    Maurizio Vichi

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer International Publishing Switzerland

About this paper

Cite this paper

García-Escudero, L.A., Gordaliza, A., Matrán, C., Mayo-Iscar, A. (2013). Grouping Around Different Dimensional Affine Subspaces. In: Giudici, P., Ingrassia, S., Vichi, M. (eds) Statistical Models for Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00032-9_16

Download citation

Publish with us

Policies and ethics