Inner Matrix Norms in evolving Cauchy Possibilistic Clustering for Classification and Regression from Data Streams

This paper presents the unification and generalization of different evolving clustering methods based on Cauchy density. This can be done by introducing different inner matrix norms to obtain different functionalities of the algorithm. This unified approach with a general inner matrix norm is called eCauchy recursive clustering. The well-known possibilistic c-means clustering (PCM) can be seen as a special example of the proposed eCauchy algorithm. The main motivation of the proposed method is to solve and overcome the problems of modelling the nonlinear data streams in highly noisy environments with frequently appearing outliers. By introducing the different inner matrix into the density metric, the algorithm can be modified in different ways to deal with different clustering problems, from classical classification to the preprocessing for solving regression problems. The evolving nature of the algorithm and simple computation also make it appropriate for dealing with big-data problems. The described eCauchy algorithm needs just a few initial parameters such as minimal and maximal density. The algorithm incrementally changes the structure of the model based on the flow of samples from the data stream, more specifically it evolves the structure of the model during the operation by adding, merging, splitting and removing the clusters. This approach allows the identification of very different clusters in size and shape and is also quite insensitive to the outliers and significant noise. In the paper, the universality of the proposed algorithm is shown on various examples.