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## Probabilistic Neural Network With Complex Exponential Activation Functions in Image Recognition

If the training data set in image recognition task is not very large, the feature extraction with a convolutional neural network is usually applied. Here, we focus on the nonparametric classification of extracted feature vectors using the probabilistic neural network (PNN). The latter is characterized by the high runtime and memory space complexity. We propose to overcome these drawbacks by replacing the exponential activation function in the Gaussian kernel to the complex exponential functions. Such complex nonlinearities make it possible to accurately approximate the unknown density function using the network with the number of neurons proportional to only cubic root of the database size. As a result, the proposed approach decreases the runtime and memory complexities of the PNN without losing its main advantages, namely, fast training and convergence to the Bayesian decision. In the experimental study, we describe a protocol for comparing recognition methods using the well-known visual object category data sets in the context of the small sample size problem. It has been experimentally shown that our approach rapidly obtains accurate decisions when compared to the known classifiers including the baseline PNN.