Comparative numerical analysis of Bayesian decision rule and probabilistic neural network for pattern recognition

Abstract

At present, neural networks are increasingly used to solve many problems instead of traditional methods for solving them. This involves comparing the neural network and the traditional method for specific tasks. In this paper, computer modeling of the Bayesian decision rule and the probabilistic neural network is carried out in order to compare their operational characteristics for recognizing Gaussian patterns. Recognition of four and six images (classes) with the number of features from 1 to 6 was simulated in cases where the images are well and poorly separated. The sizes of the training and test samples are chosen quiet big: 500 implementations for each image. Such characteristics as training time of the decision rule, recognition time on the test sample, recognition reliability on the test sample, recognition reliability on the training sample were analyzed. In framework of these conditions it was found that the recognition reliability on the test sample in the case of well separated patterns and with any number of the instances is close to 100 percent for both decision rules. The neural network loses 0,1–16 percent to Bayesian decision rule in the recognition reliability on the test sample for poorly separated patterns. The training time of the neural network exceeds the training time of the Bayesian decision rule in 4–5 times and the recognition time – in 4–6 times. As a result, there are no obvious advantages of the probabilistic neural network over the Bayesian decision rule in the problem of Gaussian pattern recognition. The existing generalization of the Bayesian decision rule described in the article is an alternative to the neural network for the case of non-Gaussian patterns.