Bayesian framework for unsupervised classification with application to target tracking

We have given a solution to the problem of unsupervised classification of multidimensional data. Our approach is based on Bayesian estimation which regards the number of classes, the data partition and the parameter vectors that describe the density of classes as unknowns. We compute their MAP estimates simultaneously by maximizing their joint posterior probability density given the data. The concept of partition as a variable to be estimated is a unique feature of our method. This formulation also solves the problem of validating clusters obtained from various methods. Our method can also incorporate any additional information about a class while assigning its probability density. It can also utilize any available training samples that arise from different classes. We provide a descent algorithm that starts with an arbitrary partition of the data and iteratively computes the MAP estimates. The proposed method is applied to target tracking data. The results obtained demonstrate the power of Bayesian approach for unsupervised classification.