Optimization Strategies for Two-Mode Partitioning |
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Authors: | Joost van Rosmalen Patrick J F Groenen Javier Trejos William Castillo |
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Institution: | (1) Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands;(2) CIMPA, Escuela de Matematicá, Universidad de Costa Rica, San José, Costa Rica |
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Abstract: | Two-mode partitioning is a relatively new form of clustering that clusters both rows and columns of a data matrix. In this
paper, we consider deterministic two-mode partitioning methods in which a criterion similar to k-means is optimized. A variety of optimization methods have been proposed for this type of problem. However, it is still unclear
which method should be used, as various methods may lead to non-global optima. This paper reviews and compares several optimization
methods for two-mode partitioning. Several known methods are discussed, and a new fuzzy steps method is introduced. The fuzzy
steps method is based on the fuzzy c-means algorithm of Bezdek (1981) and the fuzzy steps approach of Heiser and Groenen (1997) and Groenen and Jajuga (2001). The performances of all methods are compared in a large simulation study. In our simulations, a two-mode k-means optimization method most often gives the best results. Finally, an empirical data set is used to give a practical example
of two-mode partitioning.
We would like to thank two anonymous referees whose comments have improved the quality of this paper. We are also grateful
to Peter Verhoef for providing the data set used in this paper. |
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Keywords: | Two-mode partitioning Optimization methods Meta-heuristics |
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