Noise clustering algorithm revisited

Dave's noise clustering (NC) algorithm is revisited. In the original NC algorithm, the distance of a noise prototype from all the points was defined to be a constant value δ. While this idea works well in detecting a variety of cluster shapes in noisy data, use of the same constant value of δ makes NC somewhat limited in its scope. In this paper, we allow δ to take different values for different feature vectors, and find interesting results due to this modification. It is shown that the membership generated by NC algorithm is a product of two terms, one is the original fuzzy c-means (FCM) membership responsible for data partitioning, and the other is a robust M-estimator type weight (or like a generalized possibilistic membership) that achieves a mode seeking effect, and imparts robustness. In this light, it is shown that the NC technique is a generalization of the possibilistic clustering technique. An interesting fact about the robust component of the NC membership is regarding the appearance of term related to the harmonic mean distance of a point from all the classes. The role of this term is discussed along with other possible generalizations, including one that makes the generalized NC a fuzzy c-class extension of robust M-estimators.