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If the training dataset is not very large, image recognition is usuallyimplemented with the transfer learning methods. In these methods the featuresare extracted using a deep convolutional neural network, which waspreliminarily trained with an external very-large dataset. In this paper weconsider the nonparametric classification of extracted feature vectors with theprobabilistic neural network (PNN). The number of neurons at the pattern layerof the PNN is equal to the database size, which causes the low recognitionperformance and high memory space complexity of this network. We propose toovercome these drawbacks by replacing the exponential activation function inthe Gaussian Parzen kernel to the complex exponential functions in the Fej\'erkernel. We demonstrate that in this case it is possible to implement thenetwork with the number of neurons in the pattern layer proportional to thecubic root of the database size. Thus, the proposed modification of the PNNmakes it possible to significantly decrease runtime and memory complexitieswithout loosing its main advantages, namely, extremely fast training procedureand the convergence to the optimal Bayesian decision. An experimental study invisual object category classification and unconstrained face recognition withcontemporary deep neural networks have shown, that our approach obtains veryefficient and rather accurate decisions for the small training sample incomparison with the well-known classifiers.

Probabilistic Neural Network with Complex Exponential Activation Functions in Image Recognition using Deep Learning Framework