A Modified Weight Optimization for Artificial Higher Order Neural Networks in Physical Time Series

Abstract

Many methods and approaches have been proposed for analyzing and forecasting time series data. There are different Neural Network (NN) variations for specific tasks (e.g., Deep Learning, Recurrent Neural Networks, etc.). Time series forecasting are a crucial component of many important applications, from stock markets to energy load forecasts. Recently, Swarm Intelligence (SI) techniques including Cuckoo Search (CS) have been established as one of the most practical approaches in optimizing parameters for time series forecasting. Several modifications to the CS have been made, including Modified Cuckoo Search (MCS) that adjusts the parameters of the current CS, to improve algorithmic convergence rates. Therefore, motivated by the advantages of these MCSs, we use the enhanced MCS known as the Modified Cuckoo Search-Markov Chain Monté Carlo (MCS-MCMC) learning algorithm for weight optimization in Higher Order Neural Networks (HONN) models. The Lévy flight function in the MCS is replaced with Markov Chain Monté Carlo (MCMC) since it can reduce the complexity in generating the objective function. In order to prove that the MCS-MCMC is suitable for forecasting, its performance was compared with the standard Multilayer Perceptron (MLP), standard Pi-Sigma Neural Network (PSNN), Pi-Sigma Neural Network-Modified Cuckoo Search (PSNN-MCS), Pi-Sigma Neural Network-Markov Chain Monté Carlo (PSNN-MCMC), standard Functional Link Neural Network (FLNN), Functional Link Neural Network-Modified Cuckoo Search (FLNN-MCS) and Functional Link Neural Network-Markov Chain Monté Carlo (FLNN-MCMC) on various physical time series and benchmark dataset in terms of accuracy. The simulation results prove that the HONN-based model combined with the MCS-MCMC learning algorithm outperforms the accuracy in the range of 0.007% to 0.079% for three (3) physical time series datasets.