Evaluation of Classifiers with Continuous Response

The Bhattacharyya coefficient B is a measure of the overlap of two density functions. 

Another approach to the characterization of a classifier with a continuous response is the transinformation (Chapter 11.6.2). The entropy of a continuous distribution of signals depends on the unit in which the signal is measured and is therefore less useful. In contrast to the entropy the transinformation is independent of the unit of measure C417, 4273. A binary classifier with a continuous response s corresponds to a communication channel with two discrete inputs (patterns of class 1 or class 2) and one continuous output s. 

FIGURE 57- Probability density functions for a binary classifier with a continuous response s and 92 are the probability densities for class 1 and 2. The shaded areas correspond to the predictive abilities of a discrete classifier with a zero threshold- 

The a priori probabilities p(1) and p(2) of both classes at the input are connected by the classification procedure with the probabiIi-ty densities g (s) and g2ls) at the output. The transinformation of this channel is given by equation (145). 

The predictive abilities of each class are fundamental and easy to calculate criteria of a classifier. Therefore, it is important to estimate the confidence of these values. 

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