Statistical Pattern Recognition

Abstract

Probability theory is the basis for understanding and modeling random error. Conditional probability leads to Bayes’ rule and allows us to incorporate measured class-conditional probability density functions into a statistical classifier. The naïve Bayes classifier is a simple probabilistic classifier that assumes independent features. The multivariate Gaussian describes normal distributions in multi-dimensional feature space and is characterized by elliptical isocontours. The covariance matrix summarizes the relationships between the various features. Diagonalization of the covariance matrix by Principal Component Analysis results in independent feature combinations. The Mahalanobis distance is a generalization of the Euclidean distance and can be used to classify objects on the basis of the distance to the class center.