Robust learning algorithm for multiplicative neuron model artificial neural networks |
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| Affiliation: | 1. Giresun University, Faculty of Arts and Science, Department of Statistics, Gure Campus, Gure Area Giresun 28100, Turkey\n;2. University of Ondokuz Mayis, Faculty of Arts and Science, Department of Statistics, Kurupelit Campus, Kurupelit Samsun 55139, Turkey;1. Department of Mechanical Engineering, École Polytechnique de Montréal, Québec H3C 3A7, Canada;2. Department of Mathematics and Industrial Engineering, École Polytechnique de Montréal, Montréal, Québec H3C 3A7, Canada;3. Department of Management, Urmia Branch, Islamic Azad University, Urmia, Iran;1. University of Guanajuato, Engineering Division, Campus Irapuato–Salamanca, Carr. Salamanca–Valle de Santiago km 3.5 + 1.8 km, Comunidad de Palo Blanco, C.P. 36885 Salamanca, Guanajuato, Mexico;2. Universidad Industrial de Santander, Carrera 27 - Calle 9, C.P. 680002 Bucaramanga, Colombia;3. Department of Neurosurgery, University of Leipzig, University Hospital, Germany;4. Innovation Center Computer Assisted Surgery (ICCAS), University of Leipzig, Germany;1. Dept. of Biomedical Engineering, Amirkabir University of Technology, Tehran 15914, Iran;2. Dept. of Electrical Engineering, Amirkabir University of Technology, Tehran 15914, Iran;1. Department of Applied Electronics and Instrumentation Engineering, Haldia Institute of Technology, Haldia, India;2. Department of Applied Physics, University of Calcutta, Calcutta, India;1. Department of Industrial and Systems Engineering, Faculty of Engineering, University of Florida, Gainesville, United States;2. Department of Industrial Engineering, Faculty of Management, Istanbul Technical University, Istanbul, Turkey |
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| Abstract: | The two most commonly used types of artificial neural networks (ANNs) are the multilayer feed-forward and multiplicative neuron model ANNs. In the literature, although there is a robust learning algorithm for the former, there is no such algorithm for the latter. Because of its multiplicative structure, the performance of multiplicative neuron model ANNs is affected negatively when the dataset has outliers. On this issue, a robust learning algorithm for the multiplicative neuron model ANNs is proposed that uses Huber's loss function as fitness function. The training of the multiplicative neuron model is performed using particle swarm optimization. One principle advantage of this algorithm is that the parameter of the scale estimator, which is an important factor affecting the value of Huber's loss function, is also estimated with the proposed algorithm. To evaluate the performance of the proposed method, it is applied to two well-known real world time series datasets, and also a simulation study is performed. The algorithm has superior performance both when it is applied to real world time series datasets and the simulation study when compared with other ANNs reported in the literature. Another of its advantages is that, for datasets with outliers, the results are very close to the results obtained from the original datasets. In other words, we demonstrate that the algorithm is unaffected by outliers and has a robust structure. |
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