Factorial and reduced K-means reconsidered
AbstractFactorial K-means analysis (FKM) and Reduced K-means analysis (RKM) are clustering methods that aim at simultaneously achieving a clustering of the objects and a dimension reduction of the variables. Because a comprehensive comparison between FKM and RKM is lacking in the literature so far, a theoretical and simulation-based comparison between FKM and RKM is provided. It is shown theoretically how FKM's versus RKM's performances are affected by the presence of residuals within the clustering subspace and/or within its orthocomplement in the observed data. The simulation study confirmed that for both FKM and RKM, the cluster membership recovery generally deteriorates with increasing amount of overlap between clusters. Furthermore, the conjectures were confirmed that for FKM the subspace recovery deteriorates with increasing relative sizes of subspace residuals compared to the complement residuals, and that the reverse holds for RKM. As such, FKM and RKM complement each other. When the majority of the variables reflect the clustering structure, and/or standardized variables are being analyzed, RKM can be expected to perform reasonably well. However, because both RKM and FKM may suffer from subspace and membership recovery problems, it is essential to critically evaluate their solutions on the basis of the content of the clustering problem at hand.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Computational Statistics & Data Analysis.
Volume (Year): 54 (2010)
Issue (Month): 7 (July)
Contact details of provider:
Web page: http://www.elsevier.com/locate/csda
Cluster analysis Factorial model K-means Dimensional reduction;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Glenn Milligan & Martha Cooper, 1988. "A study of standardization of variables in cluster analysis," Journal of Classification, Springer, vol. 5(2), pages 181-204, September.
- Norman Cliff, 1966. "Orthogonal rotation to congruence," Psychometrika, Springer, vol. 31(1), pages 33-42, March.
- Douglas Steinley & Michael Brusco, 2008. "Selection of Variables in Cluster Analysis: An Empirical Comparison of Eight Procedures," Psychometrika, Springer, vol. 73(1), pages 125-144, March.
- 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.
- Henry Kaiser, 1958. "The varimax criterion for analytic rotation in factor analysis," Psychometrika, Springer, vol. 23(3), pages 187-200, September.
- Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer, vol. 2(1), pages 193-218, December.
- 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, vol. 25(1), pages 67-85, June.
- Douglas Steinley & Robert Henson, 2005. "OCLUS: An Analytic Method for Generating Clusters with Known Overlap," Journal of Classification, Springer, vol. 22(2), pages 221-250, September.
- Roberto Rocci & Stefano Gattone & Maurizio Vichi, 2011. "A New Dimension Reduction Method: Factor Discriminant K-means," Journal of Classification, Springer, vol. 28(2), pages 210-226, July.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wendy Shamier).
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.