IEEE Second International Conference on Data Stream Mining & Processing August 21-25, 2018, Lviv, Ukraine 978-1-5386-2874-4/18/$31.00 ©2018 IEEE 305 Hybrid Multidimensional Wavelet-Neuro-System and its Learning Using Cross Entropy Cost Function in Pattern Recognition Olena Vynokurova IT Step University Lviv, Ukraine vynokurova@gmail.com Semen Oskerko IT Step University Lviv, Ukraine semenosker@gmail.com Dmytro Peleshko IT Step University Lviv, Ukraine dpeleshko@gmail.com Viktor Voloshyn IT Step University Lviv, Ukraine voloshyn_v@itstep.org Yuriy Borzov Department of Project Management, Information Technologies and Telecommunications Lviv State University of Life Safety Lviv, Ukraine uob1968@gmail.com Abstract— In this paper, the hybrid multidimensional wavelet-neuro-system for pattern recognition tasks is proposed. Also learning algorithm for all its parameters (synaptic weights, the centers, and widths of wavelet activation functions) based on cross entropy cost function was proposed. The proposed system is characterized by high learning speed and high approximation properties in comparison with well- known approaches. The efficiency of the proposed approach has been justified based on different benchmarks and real data sets. Keywords— patterns recognition, hybrid wavelet-neuro- system, learning algorithm, wavelet transform, cross entropy cost function. I. INTRODUCTION Machine grouping, classification, and recognition of patterns are important problems in a variety of engineering and scientific areas, such as artificial intelligence [1-2], computer vision [3], internet of things (IoT) [4], biology, medicine [5], marketing, etc. The patterns could be the handwritten cursive words and symbols, the biometrical images, or a speech signal. Nowadays the machine learning methods (especially artificial neural networks) [6-15] are widely spread for solving the pattern recognition and images classification tasks due to their universal approximating properties and their learning abilities. Since there’s a number of practical tasks when a learning sample volume is restricted, a learning rate factor goes in the forefront. However, not all approaches (first of all, based on multilayer architectures, which are learned using the error backpropagation procedure) satisfy to the conditions of the real tasks because of a low speed of a learning process and a possible overfitting effect. Therefore, hybrid systems are the most effective systems in machine learning, especially neuro-fuzzy and wavelet- neuro-fuzzy systems that combine neural networks’ universal approximation ability, fuzzy inference systems’ interpretability and detection of the local features of patterns using wavelet transform. Today, a lot of machine learning approaches are proposed for pattern recognition and classification, among them in [16] authors have proposed the spiking neural network for pattern recognition and a learning algorithm based on the relative ordering of output spikes, in [17] approach for a face recognition based on recurrent regression neural network is proposed, in [18] authors have proposed a novel convolutional neural network for prediction of the emotion, in this case, the proposed model has two parts: classification network for a positive-or-negative emotion recognition and a deep neural network for specific emotion recognition, in [19] an efficient face feature extraction method based on local Gabor binary pattern histogram sequence and wavelet neural network for classification have been proposed, in [20] authors present a single image super resolution technique in which we estimate wavelet detail coefficients of a desired high resolution image using a convolutional neural network on the given low resolution image, in [21] a novel hybrid approach called switching particle swarm optimization–wavelet neural network has been proposed. For most proposed approaches the choice of the type and parameters of the activation functions is the problem, which is solved by the empirical fit. To solve this problem, the hybrid system has to adjust all his parameters in process of training. Therefore, in this paper, the architecture of hybrid multidimensional wavelet-neuro-system and its learning algorithm of all its parameters based on cross entropy cost function are proposed. The proposed hybrid system has only one layer of information processing and is characterized by high learning speed and increased approximation properties. II. THE ARCHITECTURE OF HYBRID MULTIDIMENSIONAL WAVELET-NEURO-SYSTEM The structure element of proposed hybrid multidimensional wavelet-neuro-system is one-dimensional wavelet neuron, which had been proposed in [22, 23]. Thereafter, in [24] the wavelet neuron with adaptive learning algorithm for the activation functions parameters using quadratic criterion had been proposed. But such learning algorithm is not effective for pattern recognition tasks, especially for the image classification tasks. Lviv Polytechnic National University Institutional Repository http://ena.lp.edu.ua