Introduction:

A vast amount of methods have been developed for classification. Despite its age the Linear Discriminant Analysis (LDA) developed by R. A. Fisher in 1936 does perform well even in situations, where the underlying premises like normally distributed data with constant covariance matrices over all classes are not met. So it is not astonishing that for the problem at hand, classification of business phases, Weihs and Garczarek (2006) show the good performance of LDA. As LDA, however, includes matrix inversion it may run into problems in high dimensional situations or when the variables are highly correlated like macroeconomic variables. Hastie et al. (1995), to overcome this problem, utilize the fact that LDA is equivalent to canonical correlation analysis and optimal scoring and therefore can be transformed into a regression problem. They use a penalty term for the within-covariance matrix as well as smoothing of the estimates. As such a penalty term is not directly linked to the classification problem, Luebke and Weihs (2003) propose a projection on latent factors optimized for classification. By using latent factors, Luebke and Weihs (2004a) also obtain better predictions than e. g. Partial Least Squares in a linear r

egression model. In the present paper, both ideas are combined to obtain a Prediction Optimal Classification (POC) criterion to evaluate projection matrices for predictive classification. The optimal solution, i. e. the corresponding projection matrix, is found by Simulated Annealing, the flexibility of which allows including cost terms for deviations of estimators from zero so that variable selection or measurement of importance can be included in the method.

The paper is organized as follows: In the next section we introduce the underlying scoring function of the classification problem which is minimized by Simulated Annealing. In section 3 the implementation of the Simulated Annealing Algorithm is described. A performance criterion for time related data is proposed in section 4. The data and the results of the new method are shown in section 5. Some remarks will conclude the paper.