Convexity-based clustering criteria: theory, algorithms, and applications in statistics

Hans-Hermann Bock ()
Additional contact information
Hans-Hermann Bock: Aachen University of Technology

Statistical Methods & Applications, 2004, vol. 12, issue 3, No 3, 293-317

Abstract: Abstract. This paper deals with the construction of optimum partitions ${\cal B} = (B_1,...,B_m)$ of $I\hspace{-4.0pt}R^p$ for a clustering criterion which is based on a convex function of the class centroids $E[X\vert X\in B_i]$ as a generalization of the classical SSQ clustering criterion for n data points. We formulate a dual optimality problem involving two sets of variables and derive a maximum-support-plane (MSP) algorithm for constructing a (sub-)optimum partition as a generalized k-means algorithm. We present various modifications of the basic criterion and describe the corresponding MSP algorithm. It is shown that the method can also be used for solving optimality problems in classical statistics (maximizing Csiszár’s $\phi$ -divergence) and for simultaneous classification of the rows and columns of a contingency table.

Keywords: Clustering with convex functions; maximum-support-plane partition; generalized k-means; optimum stratification; $\phi$ -divergence; two-way classification (search for similar items in EconPapers)
Date: 2004
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10260-003-0069-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stmapp:v:12:y:2004:i:3:d:10.1007_s10260-003-0069-8

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10260/PS2

DOI: 10.1007/s10260-003-0069-8

Access Statistics for this article

Statistical Methods & Applications is currently edited by Tommaso Proietti

More articles in Statistical Methods & Applications from Springer, Società Italiana di Statistica
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().