From data to probabilistic mixtures

The issue for the BADDYR is to support the decision making process with multiple participants asserting generally different criteria. Nevertheless COMPUREG devoted the initial phase of the project to verification of a very basic element of the decision-support system - mixture identification.

Approximation of data distribution and/or representation of their dynamic relations by a probabilistic mixture are the key problem of the given approach. For a two-dimensional case (two data channels) the mixture can be depicted as follows:

The probability density is differentiated by color. The particular mixture consists of four components having Gaussian pdfs. Resulting pdf is given by their weighted superposition.

A key issue for a successful Bayesian identification is definition of a priori information, i.e. specification of a prior mixture. The developed algorithm adjusts its starting conditions automatically. Nevertheless it is contributive to repeat the identification run twice for most cases. The mixture identified by the first run is used as a prior mixture for the second one.

Picture gallery depicts mixture identification for various cases – varying number of data channels and samples, simulated and real data, static and dynamic estimations.