Comparison of the probabilistic model of a fuzzy Bayesian classifier and the Gaussian mixture problem

The article shows that the problem of fuzzy classification and the problem of separation of Gaussian mixtures have different theoretical solution models based on the results of the classical probability theory. A probabilistic model of the clustering and classification process based on the Bayesian approach is the joint distribution of multidimensional data points across clusters and cluster prototypes. The model is built for datasets with a normal distribution. Unknown membership values for each data point are assumed to be a random variable with some empirical distribution. The cluster prototype is also assumed to be a normally distributed random variable. The model is compared with the Gaussian mixture separation model and the main difference between them is highlighted: in the Bayesian fuzzy classification model, the product of all component probabilities is used, which means taking into account the possibility of the xn value falling into different clusters. The computational algorithm of this model may have a wider application compared to the traditional fuzzy c-means approach, due to the lack of restrictions on clustering parameters. Some numerical results are presented that confirm the model’s operability for an artificial data set both with parameters within the traditional limitations of the c-means method and for an extended range of parameter values.