Classifying Scaled-Turned-Shifted Objects with Optimal Pixel-to-Scale-Turn-Shift Standard Deviations Ratio in Training 2-Layer Perceptron on Scaled-Turned-Shifted 4800-Featured Objects under Normally Distributed Feature Distortion
The problem of classifying diversely distorted objects is considered. The classifier is a 2-layer perceptron capable of classifying greater amounts of objects in a unit of time. This is an advantage of the 2-layer perceptron over more complex neural networks like the neocognitron, the convolutional neural network, and the deep learning neural networks. Distortion types are scaling, turning, and shifting. The object model is a monochrome 60 × 80 image of the enlarged English alphabet capital letter. Consequently, there are 26 classes of 4800-featured objects. Training sets have a parameter, which is the ratio of the pixel-to-scale-turn-shift standard deviations, which allows controlling normally distributed feature distortion. An optimal ratio is found, at which the performance of the 2-layer perceptron is still unsatisfactory. Then, the best classifier is further trained with additional 438 passes of training sets by increasing the training smoothness tenfold. This aids in decreasing the ultimate classification error percentage from 35.23 % down to 12.92 %. However, the expected practicable distortions are smaller, so the percentage corresponding to them becomes just 1.64 %, which means that only one object out of 61 is misclassified. Such a solution scheme is directly applied to other classification problems, where the number of features is a thousand or a few thousands by a few tens of classes.
 V. V. Romanuke, “Two-layer perceptron for classifying scaled-turned-shifted objects by 26 classes general totality of monochrome 60-by-80-images via training with pixel-distorted scaled-turned-shifted images,” Information processing systems, iss. 7 (132), pp. 98–107, 2015.
 V. V. Romanuke, “Optimal Pixel-to-Shift Standard Deviation Ratio for Training 2-Layer Perceptron on Shifted 60 × 80 Images with Pixel Distortion in Classifying Shifting-Distorted Objects,” Applied Computer Systems, vol. 19, no. 1, Jan. 2016. https://doi.org/10.1515/acss-2016-0008
 V. V. Romanuke, “Boosting ensembles of heavy two-layer perceptrons for increasing classification accuracy in recognizing shifted-turned-scaled flat images with binary features,” Journal of Information and Organizational Sciences, vol. 39, no. 1, pp. 75–84, 2015.
 V. V. Romanuke, “Accuracy improvement in wear state discontinuous tracking model regarding statistical data inaccuracies and shifts with boosting mini-ensemble of two-layer perceptrons,” Problems of tribology, no. 4, pp. 55–58, 2014.
 V. V. Romanuke, “Two-layer perceptron for classifying flat scaled-turned-shifted objects by additional feature distortions in training,” Journal of Uncertain Systems, vol. 9, no. 4, pp. 286–305, 2015.
 K. Hagiwara, T. Hayasaka, N. Toda, S. Usui, and K. Kuno, “Upper bound of the expected training error of neural network regression for a Gaussian noise sequence,” Neural Networks, vol. 14, no. 10, pp. 1419–1429, Dec. 2001. https://doi.org/10.1016/s0893-6080(01)00122-8
 V. Romanuke, “Setting the Hidden Layer Neuron Number in Feedforward Neural Network for an Image Recognition Problem under Gaussian Noise of Distortion,” Computer and Information Science, vol. 6, no. 2, Mar. 2013. https://doi.org/10.5539/cis.v6n2p38
 C.-H. Yoo, S.-W. Kim, J.-Y. Jung, and S.-J. Ko, “High-dimensional feature extraction using bit-plane decomposition of local binary patterns for robust face recognition,” Journal of Visual Communication and Image Representation, vol. 45, pp. 11–19, May 2017. https://doi.org/10.1016/j.jvcir.2017.02.009
 V. V. Romanuke, “An attempt for 2-layer perceptron high performance in classifying shifted monochrome 60-by-80-images via training with pixel-distorted shifted images on the pattern of 26 alphabet letters,” Radio Electronics, Computer Science, Control, no. 2, pp. 112–118, 2013.
 V. V. Romanuke, “A 2-layer perceptron performance improvement in classifying 26 turned monochrome 60-by-80-images via training with pixel-distorted turned images,” Research Bulletin of the National Technical University of Ukraine “Kyiv Polytechnic Institute”, no. 5, pp. 55–62, 2014.
 A. Y. Alanis, J. D. Rios, J. Rivera, N. Arana-Daniel, and C. Lopez-Franco, “Real-time discrete neural control applied to a Linear Induction Motor,” Neurocomputing, vol. 164, pp. 240–251, Sep. 2015. https://doi.org/10.1016/j.neucom.2015.02.065
 Z. Chen, F. Cao, and J. Hu, “Approximation by network operators with logistic activation functions,” Applied Mathematics and Computation, vol. 256, pp. 565–571, Apr. 2015. https://doi.org/10.1016/j.amc.2015.01.049
 T. Kathirvalavakumar and S. Jeyaseeli Subavathi, “Neighborhood based modified backpropagation algorithm using adaptive learning parameters for training feedforward neural networks,” Neurocomputing, vol. 72, no. 16–18, pp. 3915–3921, Oct. 2009. https://doi.org/10.1016/j.neucom.2009.04.010
 A. Nied, S. I. Seleme, G. G. Parma, and B. R. Menezes, “On-line neural training algorithm with sliding mode control and adaptive learning rate,” Neurocomputing, vol. 70, no. 16–18, pp. 2687–2691, Oct. 2007. https://doi.org/10.1016/j.neucom.2006.07.019
 S. J. Yoo, J. B. Park, and Y. H. Choi, “Indirect adaptive control of nonlinear dynamic systems using self recurrent wavelet neural networks via adaptive learning rates,” Information Sciences, vol. 177, no. 15, pp. 3074–3098, Aug. 2007. https://doi.org/10.1016/j.ins.2007.02.009
 C. Yu, M. T. Manry, J. Li, and P. Lakshmi Narasimha, “An efficient hidden layer training method for the multilayer perceptron,” Neurocomputing, vol. 70, no. 1–3, pp. 525–535, Dec. 2006. https://doi.org/10.1016/j.neucom.2005.11.008
 V. V. Romanuke, “Pixel-to-scale standard deviations ratio optimization for two-layer perceptron training on pixel-distorted scaled 60-by-80-images in scaled objects classification problem,” Visnyk of Kremenchuk National University of Mykhaylo Ostrogradskyy, iss. 2 (85), pp. 96–105, 2014.
 V. V. Romanuke, “Classification error percentage decrement of two-layer perceptron for classifying scaled objects on the pattern of monochrome 60-by-80-images of 26 alphabet letters by training with pixel-distorted scaled images,” Scientific bulletin of Chernivtsi National University of Yuriy Fedkovych. Series: Computer systems and components, vol. 4, iss. 3, pp. 53–64, 2013.
 V. V. Romanuke, “Optimal hidden layer neurons number in two-layer perceptron and pixel-to-turn standard deviations ratio for its training on pixel-distorted turned 60 × 80 images in turned objects classification problem,” Visnyk of Kremenchuk National University of Mykhaylo Ostrogradskyy, iss. 5 (94), pp. 86–93, 2015.
 R. E. Walpole, R. H. Myers, S. L. Myers, and K. Ye, Probability & Statistics for Engineers & Scientists (9th ed.). Boston, Massachusetts: Prentice Hall, 2012.
 V. V. Romanuke, “Optimal Training Parameters and Hidden Layer Neuron Number of Two-Layer Perceptron for Generalised Scaled Object Classification Problem,” Information Technology and Management Science, vol. 18, no. 1, Jan. 2015. https://doi.org/10.1515/itms-2015-0007
 V. V. Romanuke, “Dependence of performance of feed-forward neuronet with single hidden layer of neurons against its training smoothness on noised replicas of pattern alphabet,” Herald of Khmelnytskyi national university. Technical sciences, no. 1, pp. 201–206, 2013.
 M. J. Kochenderfer, C. Amato, G. Chowdhary, J. P. How, H. J. Davison Reynolds, J. R. Thornton, P. A. Torres-Carrasquillo, N. K. Üre, and J. Vian, Decision Making Under Uncertainty: Theory and Application. Cambridge, Massachusetts, London, England: The MIT Press, 2015.
 H. R. Tavakoli, A. Borji, J. Laaksonen, and E. Rahtu, “Exploiting inter-image similarity and ensemble of extreme learners for fixation prediction using deep features,” Neurocomputing, vol. 244, pp. 10–18, Jun. 2017. https://doi.org/10.1016/j.neucom.2017.03.018