On parameter setting in applying Dave's noise fuzzy clustering to Gaussian mixture models

Gaussian mixture models (GMM) for density estimation uses maximum likelihood approach, whereas fuzzy c-means (FCM) clustering is based on an objective function method. The close relationship between them has been pointed out. When applying the robust fuzzy clustering approach by Dave to the GMM, careful parameter setting is required. From the consideration of the Gustafson and Kessel's constraint we propose a way of defining a parameter in a fuzzy counterpart of the GMM. Numerical examples show that the Dave's noise clustering approach is quite robust for detecting linear clusters from heavily noisy data sets. This approach is further applied to a relational version in which clusters are formed using the matrix R of relational data corresponding to pairwise distances between objects.