An Adaptive Radial Basis Function Neural Network Glowworm Swarm Optimization for Time-Series Forecasting
It is well noted that statistical approaches to forecasting of time series have been going on since the start of the twentieth century. Advances in the field of computing, motivated researchers to develop new models based on Machine Learning. The Artificial Neural Network models (ANN) are known to construct good and useful approximations for sequence dependencies variables. The past three decades have witnessed active research using a class of ANN, the Radial Basis Function Neural Networks, to forecast time series.Many techniques for forecasting time series using Radial Basis Function Neural Networks (RBFNN) have been proposed and developed in literature. The major challenges in RBFNN lie in the optimization of its full parameters: the number and location of cluster centres, the number of neurons in the hidden layer as well as the output weights. To address these challenges, this study adapted the Clustering Analysis based on Glowworm Swarm Optimization (CGSO) algorithm to obtain a modified Clustering Analysis based on Glowworm Swarm Optimization (CGSOm) algorithm for solving the clustering problem. Adaptation was achieved by incorporating a mechanism that determines the sensor range of the CGSO efficiently and automatically, modifying the initialization method, and introducing a function that measures the cluster error during the iteration phase. For the weight optimization, the Bioluminescence Swarm Optimization algorithm (BSO) was adopted, making it the first time it will be applied in training the weights of the RBFNN. Algorithm as well as software development, and graphical simulation in this work are implemented using functional programming paradigm. The algorithms implemented include the CGSO, CGSOm, BSO, Conjugate Gradient Descent (CGD), Gradient Descent (GD) and Particle Swarm Optimization algorithm (PSO). Using seven well known datasets in literature, the first set of results compared the effectiveness of the CGSOm with the following five well-known clustering algorithms: CGSO, K-means, average linking agglomerative Hierarchical Clustering (HC), Further First (FF), and Learning Vector Quantization(LVQ). Experimental results indicate that the CGSOm gave best entropy and purity values in four out of the seven datasets clustered (57%); CGSO gave best results in two datasets (28.5%); and HC gave best result in one dataset (14.5%). With respect to the weight training, stock price and currencexchange rate data were used to train the combinations of models developed (based on Kmeans, CGSO, CGSOm and GD, CGD, PSO, BSO). The results obtained from the training showed that the CGSOm-CGD RBFNN gave best forecasting accuracy by yielding lowest error values; followed by the CGSOm-BSO RBFNN that gave relatively similar error. Hence, two new training methodologies for time series forecasting resulted from this study; they are the CGSOm-BSO RBFNN and the CGSOm-CGD RBFNN. Validation of the proposed approaches was done in comparison with other RBFNN models: Auto Regressive-Radial Basis Function tuned using Genetic Algorithm and Evolving Radial Basis Function Neural Network, using same data. The results obtained showed that CGSOm-BSO RBFNN and the CGSOm-CGD RBFNN yielded lowest error values.