Robust Fuzzy Clustering via Trimming and Constraints

Producción CientíficaA methodology for robust fuzzy clustering is proposed. This methodology can be widely applied in very different statistical problems given that it is based on probability likelihoods. Robustness is achieved by trimming a fixed proportion of “most outlying” observations which are indeed self-determined by the data set at hand. Constraints on the clusters’ scatters are also needed to get mathematically well-defined problems and to avoid the detection of non-interesting spurious clusters. The main lines for computationally feasible algorithms are provided and some simple guidelines about how to choose tuning parameters are briefly outlined. The proposed methodology is illustrated through two applications. The first one is aimed at heterogeneously clustering under multivariate normal assumptions and the second one migh be useful in fuzzy clusterwise linear regression problems.Ministerio de Economía, Industria y Competitividad (MTM2014-56235-C2-1-P)Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA212U13

Fuzzy clustering with high contrast

AbstractIn a fuzzy clustering an object typically receives strictly positive memberships to all clusters, even when the object clearly belongs to one particular cluster. Consequently, each cluster's estimated center and scatter matrix are influenced by many objects that have small positive memberships to it. This effect may keep the fuzzy method from finding the true clusters. We analyze the cause and propose a remedy, which is a modification of the objective function and the corresponding algorithm. The resulting clustering has a high contrast in the sense that outlying and bridging objects remain fuzzy, whereas the other objects become crisp. The enhanced version of fuzzy k-means is illustrated with an example, as well as the enhanced version of the fuzzy minimum volume method