Heywood MI, Noakes PD (1993) Simple addition to backpropagation learning for dynamic weight pruning, sparse network extraction and faster learning. PhD Thesis, Department of Electrical Engineering, Brunel University, Middlesex, UK, available as: Technical Memo CN/R/144 Gurney K (1989) Learning in nets of structured hypercubes. Gupta KK, Kumar S (2019) A novel high-order fuzzy time series forecasting method based on probabilistic fuzzy sets. Goyal G, Bisht DC (2022) Adaptive hybrid fuzzy time series forecasting technique based on particle swarm optimization. In: Applications of artificial neural networks. Granul Comput 6(1):207–216įei G, Yu YL (1994) Modified sigma-pi BP network with self-feedback and its application in time series. įan MH, Chen MY, Liao EC (2021) A deep learning approach for financial market prediction: utilization of Google trends and keywords. Comput Econ 59:1355–1383Įgrioglu E, Bas E, Karahasan O (2022) Winsorized dendritic neuron model artificial neural network and a robust training algorithm with Tukey’s biweight loss function based on particle swarm optimization. Appl Comput and Inform 19(1–2):22–40Įğrioğlu E, Fildes R (2022) A new bootstrapped hybrid artificial neural network approach for time series forecasting. Neural Comput Appl 5(2):66–75ĭash R, Rautray R, Dash R (2023) Utility of a shuffled differential evolution algorithm in designing of a Pi-Sigma Neural network-based predictor model. Granul Comput 5(4):449–459Ĭhow TWS, Cho SY (1997) Development of a recurrent Sigma-Pi neural network rainfall forecasting system in Hong Kong. IEEE Transa Syst Man Cybern Part B Cybern 40(5):1343–1358Ĭhen J, Yuan W, Cao J, Lv H (2020) Traffic-flow prediction via granular computing and stacked autoencoder. Knowl-Based Syst 118:204–216Ĭhen SM, Wang NY (2010) Fuzzy forecasting based on fuzzy-trend logical relationship groups. Inf Sci 391–392:65–79Ĭhen SM, Phuong BDH (2017) Fuzzy time series forecasting based on optimal partitions of intervals and optimal weighting vectors. Granul Comput 7(2):411–420Ĭhen SM, Jian WS (2017) Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups, similarity measures and PSO techniques. ![]() Granul Comput 7:813–820īas E, Egrioglu E, Kolemen E (2022b) Training simple recurrent deep artificial neural network for forecasting using particle swarm optimization. Neural Comput Appl 34:12895–12917īas E, Egrioglu E, Karahasan O (2022a) A Pi-Sigma artificial neural network based on sine cosine optimization algorithm. The proposed method took first place in this ranking and is determined as the best method among all methods.Īrslan SN, Cagcag Yolcu O (2022) A hybrid sigma-pi neural network for combined intuitionistic fuzzy time series prediction model. For the comparison of all methods, the mean rank calculation is made for each method. According to the analysis results, the proposed method has a 60% success rate for both FTSE and S&P 500 time series. In the evaluation of the performance of the proposed method, the closing prices of the FTSE and S&P 500 are analyzed for different years. Thus, a training process that does not require complex derivative calculations in derivative-based algorithms is performed. In this study, the grey wolf optimization algorithm is used for the first time in the literature in the training of Sigma-Pi artificial neural networks. Like many artificial neural networks, the training of the Sigma-Pi neural network is one of the important factors affecting the performance of the network. Sigma-Pi artificial neural networks, one of the high-order artificial neural networks, have been used frequently in many problems in recent years. ![]() Although there are many high-order artificial neural networks with different properties in the literature, one of the most important problems of these high-order artificial neural networks is to determine the optimization method to be used in the training of the network structure. Although multi-layer perceptron neural networks are one of the most frequently used artificial neural networks in the literature, high-order neural networks using high-order combinations of inputs have superior performance compared to multi-layer perceptron artificial neural networks in recent years. Artificial neural network models have been frequently used in time series forecasting problems as an alternative to many classical forecasting models.
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