Cluster based modular nonlinear autoregressive neural network to predict daily reservoir inflow

Abstract

Despite the ability of Artificial Neural Network (ANN) to handle nonlinear relationships in data, there are instances where ANNs have not been able to predict accurately in the presence of extremes values or other inherent groupings in the data. Although the ANN modeling expects the data to be evenly distributed over an entire data space, in practical situations data often consist of clusters or extreme values. Thus, instead of modeling the data as it is, appropriate mechanisms should be followed to handle those inconsistancies. This paper presents one such mechanism based on two clustering algorithms, k-means and fuzzy c-means. The base model is Nonlinear Autoregressive Artificial Neural Network (NAR-ANN). Altogether 14 model formulations of NAR-ANN were compared here with varying number of clusters and a trimming mechanism. Results suggest the superiority of cluster based NAR-ANN over the single NAR-ANN. Modular ANN approach with an optimum combination of the 14 models can be used for better results. The proposed cluster based NAR-ANN used in this paper is a novel generalization to NAR-ANN where the cluster effect is incorporated as a binary exogenous variable (NARX).