Annealed Discriminant Analysis

Motivated by the analogies to statistical physics, the deterministic annealing (DA) method has successfully been demonstrated in a variety of applications. In this paper, we explore a new methodology to devise the classifier under the DA method. The differential cost function is derived subject to a constraint on the randomness of the solution, which is governed by the temperature T. While gradually lowering the temperature, we can always find a good solution which can both solve the overfitting problem and avoid poor local optima. Our approach is called annealed discriminant analysis (ADA). It is a general approach, where we elaborate two classifiers, i.e., distance-based and inner product-based, in this paper. The distance-based classifier is an annealed version of linear discriminant analysis (LDA) while the inner product-based classifier is a generalization of penalized logistic regression (PLR). As such, ADA provides new insights into the workings of these two classification algorithms. The experimental results show substantial performance gains over standard learning methods.