Multiple Multiplicative Neurons Model for Time Series Prediction

In recent years, the single multiplicative neuron (SMN) model, rooted in polynomial design, has garnered substantial scholarly attention and practical application. Building on SMN research, this study introduces an innovative multiple multiplicative neurons (MMN) model designed to enhance model robustness and adaptability. The MMN model incorporates customized backpropagation (BP), particle swarm optimization (PSO), and a cooperative random learning particle swarm optimization (CRPSO) algorithm, offering significant advancements in optimization efficiency and performance. These augmentations are strategically devised to enhance the versatility and efficacy of the multiplicative neuron model within diverse applications. To empirically substantiate the proposed MMN model's effectiveness, two benchmark time series prediction tasks were undertaken. The ensuing results unequivocally underscore the superior predictive performance of the MMN model relative to both the SMN model and the conventional feed-forward neural network. While the BP algorithm was computationally less efficient and prone to local optima in non-differentiable scenarios, and the PSO algorithm exhibited sensitivity to initial values, the CRPSO algorithm overcame these challenges by maintaining population diversity and enhancing optimization through a cooperative stochastic learning mechanism. The evaluated algorithm (MMN-CRPSO) demonstrates a remarkable efficacy in error reduction within data measurements, achieving a precision level of one in ten thousand. This empirical demonstration not only substantiates the proficiency of the MMN model in time series prediction but also positions it as a promising advancement within the broader landscape of neural network modelling and time series analysis.