Pattern classifiers based on conditional class probabilities

Abstract

The output of a classifier is usually determined by the value of a discriminant function and a decision is made based on this output which does not necessarily represent the posterior probability for the soft decision of classification. In this context, it is desirable that the output of a classifier be calibrated in such a way to give the meaning of the posterior probability of class membership. This paper presents a new method of postprocessing for the probabilistic scaling of classifier`s output. For this purpose, the output of a classifier is analyzed and the distribution of the output is described by the beta distribution parameters. For more accurate approximation of class output distribution, the beta distribution parameters as well as the kernel parameters describing the discriminant function are adjusted in such a way to improve the uniformity of beta cumulative distribution function (CDF) values for the given class output samples. As a result, the classifier with the proposed scaling method referred to as the class probability output network (CPON) can provide accurate posterior probabilities for the soft decision of classification. To show the effectiveness of the proposed method, the simulation for pattern classification using the support vector machine (SVM) classifiers is performed for the University of California at Irvine (UCI) data sets. The simulation results using the SVM classifiers with the proposed CPON demonstrated a statistically meaningful performance improvement over the SVM and SVM-related classifiers, and also other probabilistic scaling methods. However, sometimes the output of CPON is small: that is, small confidence for the class and it makes hard to decide the class. We call this sample which has a small CPON output as an uncertain sample and we try to find the uncertain samples and reconsider about decision of uncertain sample`s class. From the simulation result of selecting uncertain sample we can see that the proposed method i...