We have given a solution to the problem of unsupervised classifica,tioll of multidinlensional 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 hasn't been considered. 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 prohability density. It can also ut,ilize 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. We also focus on robust regression which is a special case of unsupervised classification with two classes; inliers and outliers. The problem of intensity image segmentation is posed as an unsupervised classification problem and solved using the Bayesian formulation a multiscale set up. The proposed method is also applied to data sets that occur in statistical literature and target tracking. The results ohbtained demonstrate the power of Bayesian approach for unsupervised classification.


Unsupervised classification, Bayesian est, imat, ion, cluster validation, robust regression

Date of this Version

July 1998