On the universal clustering under a broad class of loss functions

Determination of the number of significant clusters in the sample represents a very important problem. It is expected that the outcome of clustering under a broad class of loss functions will be more stable if the correct number of clusters is used. In order to illustrate the model of universal clustering we consider 1) family of power loss functions in probabilistic space; 2) family of exponential loss functions in Euclidean space. The proposed model is general, and proved to be effective in application to the synthetic datasets