Probabilistic Supervised Classifier and Unsupervised Clustering

Abstract

Let p(c _k) be the prior probability of the class k. Also p(c _k∕x) be the posterior probability of the class c _k given x. The class conditional density function is given as p(x∕c _k). We assign the test vector x belonging to the class r as $arg_{r=1}^{r=K} max p(c_{r}/\mathbf {x})$. Probabilistic approach for the classification technique is broadly classified into (a) probabilistic generative model approach and (b) probabilistic discriminative model approach. In the case of probabilistic generative model, the parametric model of p(x∕c _k) is considered. In the case of probabilistic discriminative model, the parametric model of p(c _k∕x) is considered.