B0609
Title: Fuzzy Pseudo-F: One- and two-mode clustering cases
Authors: Maria Brigida Ferraro - Sapienza University of Rome (Italy) [presenting]
Paolo Giordani - Sapienza University of Rome (Italy)
Maurizio Vichi - University La Sapienza, Rome (Italy)
Abstract: One of the main problems in the clustering framework is how to determine the optimal number of clusters. Cluster validity measures may assist in this task. Most of them are based on the concepts of compactness and separation. One of the most used measures is the pseudo-F (pF) one which is based on the sum of squares decomposition. In order to extend pF to the fuzzy case, such a decomposition is generalized by considering the soft membership information. This can be done by incorporating the elements of the membership degree matrix in the definitions of the total, between and within the sum of squares. The fuzzy within the sum of squares is related to the compactness of the fuzzy partition whilst the fuzzy between the sum of squares to separation. Furthermore, this idea is also extended to the case of two-mode clustering, which consists of simultaneously clustering not only the objects (standard one-mode clustering) but also the variables of an observed data matrix. In the latter case, there are two partitions and two membership degree matrices that are included in the definitions of the sum of squares and consequently of the fuzzy two-mode pseudo-F measure. The adequacy of the proposed measures is evaluated by means of simulation and real case studies.
