Probabilistic Neural Network with Complex Exponential Activation Functions in Image Recognition using Deep Learning Framework
This incremental improvement addresses efficiency issues in PNNs for image recognition tasks with limited data, benefiting researchers and practitioners using deep learning frameworks.
The paper tackled the high computational and memory costs of probabilistic neural networks (PNN) in image recognition by replacing the exponential activation function with complex exponential functions, reducing neurons in the pattern layer to the cubic root of the database size and achieving efficient, accurate results for small training samples.
If the training dataset is not very large, image recognition is usually implemented with the transfer learning methods. In these methods the features are extracted using a deep convolutional neural network, which was preliminarily trained with an external very-large dataset. In this paper we consider the nonparametric classification of extracted feature vectors with the probabilistic neural network (PNN). The number of neurons at the pattern layer of the PNN is equal to the database size, which causes the low recognition performance and high memory space complexity of this network. We propose to overcome these drawbacks by replacing the exponential activation function in the Gaussian Parzen kernel to the complex exponential functions in the Fejér kernel. We demonstrate that in this case it is possible to implement the network with the number of neurons in the pattern layer proportional to the cubic root of the database size. Thus, the proposed modification of the PNN makes it possible to significantly decrease runtime and memory complexities without loosing its main advantages, namely, extremely fast training procedure and the convergence to the optimal Bayesian decision. An experimental study in visual object category classification and unconstrained face recognition with contemporary deep neural networks have shown, that our approach obtains very efficient and rather accurate decisions for the small training sample in comparison with the well-known classifiers.