IDEAS home Printed from https://ideas.repec.org/a/spr/jclass/v29y2012i3p297-320.html
   My bibliography  Save this article

Lowdimensional Additive Overlapping Clustering

Author

Listed:
  • Dirk Depril
  • Iven Mechelen
  • Tom Wilderjans

Abstract

To reveal the structure underlying two-way two-mode object by variable data, Mirkin (1987) has proposed an additive overlapping clustering model. This model implies an overlapping clustering of the objects and a reconstruction of the data, with the reconstructed variable profile of an object being a summation of the variable profiles of the clusters it belongs to. Grasping the additive (overlapping) clustering structure of object by variable data may, however, be seriously hampered in case the data include a very large number of variables. To deal with this problem, we propose a new model that simultaneously clusters the objects in overlapping clusters and reduces the variable space; as such, the model implies that the cluster profiles and, hence, the reconstructed data profiles are constrained to lie in a lowdimensional space. An alternating least squares (ALS) algorithm to fit the new model to a given data set will be presented, along with a simulation study and an illustrative example that makes use of empirical data. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Dirk Depril & Iven Mechelen & Tom Wilderjans, 2012. "Lowdimensional Additive Overlapping Clustering," Journal of Classification, Springer;The Classification Society, vol. 29(3), pages 297-320, October.
    • Handle: RePEc:spr:jclass:v:29:y:2012:i:3:p:297-320
    DOI: 10.1007/s00357-012-9112-5
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00357-012-9112-5
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00357-012-9112-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Daniel D. Lee & H. Sebastian Seung, 1999. "Learning the parts of objects by non-negative matrix factorization," Nature, Nature, vol. 401(6755), pages 788-791, October.
    2. Depril, Dirk & Van Mechelen, Iven & Mirkin, Boris, 2008. "Algorithms for additive clustering of rectangular data tables," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4923-4938, July.
    3. Wei‐Chien Chang, 1983. "On Using Principal Components before Separating a Mixture of Two Multivariate Normal Distributions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 32(3), pages 267-275, November.
    4. Vichi, Maurizio & Kiers, Henk A. L., 2001. "Factorial k-means analysis for two-way data," Computational Statistics & Data Analysis, Elsevier, vol. 37(1), pages 49-64, July.
    5. Douglas Steinley & Michael J. Brusco, 2007. "Initializing K-means Batch Clustering: A Critical Evaluation of Several Techniques," Journal of Classification, Springer;The Classification Society, vol. 24(1), pages 99-121, June.
    6. Tom Wilderjans & E. Ceulemans & I. Mechelen, 2012. "The SIMCLAS Model: Simultaneous Analysis of Coupled Binary Data Matrices with Noise Heterogeneity Between and Within Data Blocks," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 724-740, October.
    7. Roberto Rocci & Maurizio Vichi, 2005. "Three-Mode Component Analysis with Crisp or Fuzzy Partition of Units," Psychometrika, Springer;The Psychometric Society, vol. 70(4), pages 715-736, December.
    8. Lawrence Hubert & Phipps Arabie & Matthew Hesson-Mcinnis, 1992. "Multidimensional scaling in the city-block metric: A combinatorial approach," Journal of Classification, Springer;The Classification Society, vol. 9(2), pages 211-236, December.
    9. Eva Ceulemans & Iven Mechelen, 2005. "Hierarchical classes models for three-way three-mode binary data: interrelations and model selection," Psychometrika, Springer;The Psychometric Society, vol. 70(3), pages 461-480, September.
    10. Jan Schepers & Eva Ceulemans & Iven Mechelen, 2008. "Selecting Among Multi-Mode Partitioning Models of Different Complexities: A Comparison of Four Model Selection Criteria," Journal of Classification, Springer;The Classification Society, vol. 25(1), pages 67-85, June.
    11. Eva Ceulemans & Iven Mechelen & Iwin Leenen, 2007. "The Local Minima Problem in Hierarchical Classes Analysis: An Evaluation of a Simulated Annealing Algorithm and Various Multistart Procedures," Psychometrika, Springer;The Psychometric Society, vol. 72(3), pages 377-391, September.
    12. Anil Chaturvedi & J. Carroll, 1994. "An alternating combinatorial optimization approach to fitting the INDCLUS and generalized INDCLUS models," Journal of Classification, Springer;The Classification Society, vol. 11(2), pages 155-170, September.
    13. Maurizio Vichi & Roberto Rocci & Henk A.L. Kiers, 2007. "Simultaneous Component and Clustering Models for Three-way Data: Within and Between Approaches," Journal of Classification, Springer;The Classification Society, vol. 24(1), pages 71-98, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Julian Rossbroich & Jeffrey Durieux & Tom F. Wilderjans, 2022. "Model Selection Strategies for Determining the Optimal Number of Overlapping Clusters in Additive Overlapping Partitional Clustering," Journal of Classification, Springer;The Classification Society, vol. 39(2), pages 264-301, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tom Wilderjans & Dirk Depril & Iven Van Mechelen, 2013. "Additive Biclustering: A Comparison of One New and Two Existing ALS Algorithms," Journal of Classification, Springer;The Classification Society, vol. 30(1), pages 56-74, April.
    2. Naoto Yamashita & Shin-ichi Mayekawa, 2015. "A new biplot procedure with joint classification of objects and variables by fuzzy c-means clustering," 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. 9(3), pages 243-266, September.
    3. Tom Wilderjans & Dirk Depril & Iven Mechelen, 2012. "Block-Relaxation Approaches for Fitting the INDCLUS Model," Journal of Classification, Springer;The Classification Society, vol. 29(3), pages 277-296, October.
    4. Donatella Vicari & Paolo Giordani, 2023. "CPclus: Candecomp/Parafac Clustering Model for Three-Way Data," Journal of Classification, Springer;The Classification Society, vol. 40(2), pages 432-465, July.
    5. Michael C. Thrun & Alfred Ultsch, 2021. "Using Projection-Based Clustering to Find Distance- and Density-Based Clusters in High-Dimensional Data," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 280-312, July.
    6. Julian Rossbroich & Jeffrey Durieux & Tom F. Wilderjans, 2022. "Model Selection Strategies for Determining the Optimal Number of Overlapping Clusters in Additive Overlapping Partitional Clustering," Journal of Classification, Springer;The Classification Society, vol. 39(2), pages 264-301, July.
    7. Jan Schepers & Iven Mechelen & Eva Ceulemans, 2011. "The Real-Valued Model of Hierarchical Classes," Journal of Classification, Springer;The Classification Society, vol. 28(3), pages 363-389, October.
    8. Tom Wilderjans & Eva Ceulemans & Iven Mechelen, 2008. "The CHIC Model: A Global Model for Coupled Binary Data," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 729-751, December.
    9. DeSarbo, Wayne S. & Selin Atalay, A. & Blanchard, Simon J., 2009. "A three-way clusterwise multidimensional unfolding procedure for the spatial representation of context dependent preferences," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3217-3230, June.
    10. Roberto Rocci & Stefano Gattone & Maurizio Vichi, 2011. "A New Dimension Reduction Method: Factor Discriminant K-means," Journal of Classification, Springer;The Classification Society, vol. 28(2), pages 210-226, July.
    11. Vichi, Maurizio & Saporta, Gilbert, 2009. "Clustering and disjoint principal component analysis," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3194-3208, June.
    12. Tom Wilderjans & E. Ceulemans & I. Mechelen, 2012. "The SIMCLAS Model: Simultaneous Analysis of Coupled Binary Data Matrices with Noise Heterogeneity Between and Within Data Blocks," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 724-740, October.
    13. Yoshikazu Terada, 2015. "Strong consistency of factorial $$K$$ K -means clustering," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 335-357, April.
    14. Ginette Lafit & Kristof Meers & Eva Ceulemans, 2022. "A Systematic Study into the Factors that Affect the Predictive Accuracy of Multilevel VAR(1) Models," Psychometrika, Springer;The Psychometric Society, vol. 87(2), pages 432-476, June.
    15. Lazhar Labiod & Mohamed Nadif, 2021. "Efficient regularized spectral data embedding," 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. 15(1), pages 99-119, March.
    16. Nadja Bodner & Laura Bringmann & Francis Tuerlinckx & Peter Jonge & Eva Ceulemans, 2022. "ConNEcT: A Novel Network Approach for Investigating the Co-occurrence of Binary Psychopathological Symptoms Over Time," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 107-132, March.
    17. Laura Bocci & Donatella Vicari, 2019. "ROOTCLUS: Searching for “ROOT CLUSters” in Three-Way Proximity Data," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 941-985, December.
    18. Van Mechelen, Iven & Schepers, Jan, 2007. "A unifying model involving a categorical and/or dimensional reduction for multimode data," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 537-549, September.
    19. Stephen L. France & Wen Chen & Yumin Deng, 2017. "ADCLUS and INDCLUS: analysis, experimentation, and meta-heuristic algorithm extensions," 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. 11(2), pages 371-393, June.
    20. Timmerman, Marieke E. & Ceulemans, Eva & Kiers, Henk A.L. & Vichi, Maurizio, 2010. "Factorial and reduced K-means reconsidered," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1858-1871, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jclass:v:29:y:2012:i:3:p:297-320. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.