A fast computation of inter-class overlap measures using prototype reduction schemes

In most Pattern Recognition (PR) applications, it is advantageous if the accuracy (or error rate) of the classifier can be evaluated or bounded prior to testing it in a real-life setting. It is also well known that if the two class-conditional distributions have a large overlapping volume, the classification accuracy is poor. This is because, if we intend to use the classification accuracy as a criterion for evaluating a PR system, the points within the overlapping volume tend to have less significance in determining the prototypes. Unfortunately, the computation of the indices which quantify the overlapping volume is expensive. In this vein, we propose a strategy of using a Prototype Reduction Scheme (PRS) to approximately compute the latter. In this paper, we show that by completely discarding the points not included by the PRS, we can obtain a reduced set of sample points, using which, in turn, the measures for the overlapping volume can be computed. The value of the corresponding figures is comparable to those obtained with the original training set (i.e., the one which considers all the data points) even though the computations required to obtain the prototypes and the corresponding measures are significantly less. The proposed method has been rigorously tested on artificial and real-life data sets, and the results obtained are, in our opinion, quite impressive - sometimes faster by two orders of magnitude