Application of Reinforcement Learning Algorithms for the Adaptive Computation of the Smoothing Parameter for Probabilistic Neural Network

Abstract

In this paper, we propose new methods for the choice and adaptation of the smoothing parameter of the probabilistic neural network (PNN). These methods are based on three reinforcement learning algorithms: Q(0)-learning, Q(λ)-learning, and stateless Q-learning. We regard three types of PNN classifiers: the model that uses single smoothing parameter for the whole network, the model that utilizes single smoothing parameter for each data attribute, and the model that possesses the matrix of smoothing parameters different for each data variable and data class. Reinforcement learning is applied as the method of finding such a value of the smoothing parameter, which ensures the maximization of the prediction ability. PNN models with smoothing parameters computed according to the proposed algorithms are tested on eight databases by calculating the test error with the use of the cross validation procedure. The results are compared with state-of-the-art methods for PNN training published in the literature up to date and, additionally, with PNN whose sigma is determined by means of the conjugate gradient approach. The results demonstrate that the proposed approaches can be used as alternative PNN training procedures.

Determining the significance of features with the use of Sobol' method in probabilistic neural network classification tasks

“…PNN is frequently utilized in many applications, e.g. : medical diagnosis and prediction [18], [19], [20], [21], image classification and recognition [22], [23], [24], multiple partial discharge sources classification [25], interval information processing [26], [27], phoneme recognition [28], email security enhancement [29], intrusion detection systems [30] or classification in a time-varying environment [31].…”

“…Such a form of kernel function allows us to define summation neuron output as follows (20) where: P g stands for the number of cases in the gth class (g = 1, . .…”

“…The formula (20) is also referred to as the kernel density estimator (KDE) for the gth class in the context of PNN operation.…”

“…The calculation ofσ is solved iteratively using second-order level approximation [34], [33]. As presented in both (20) and (21), KDE for the gth class depends on the value of the modification coefficient s p . For PNN, it is computed separately for each class and is related to the pth training vector.…”

Assessment of prediction ability for reduced probabilistic neural network in data classification problems

“…Four approaches are usually regarded: single parameter for whole PNN, single parameter for each class, separate parameter for each variable and separate parameter for each variable and class. In the research, diverse procedures have been developed to solve these tasks (Chtioui et al 1998;Specht 1992;Mao et al 2000;Georgiou et al 2008;Gorunescu et al 2005;Specht and Romsdahl 1994;Zhong et al 2007;Kusy and Zajdel 2015).…”