Designing RBFNs Structure Using Similarity-Based and Kernel-Based Fuzzy C-Means Clustering Algorithms

Abstract

The RBF networks belong to a set of artificial neural network architectures. RBF networks have been successfully applied for solving various data mining tasks including classification, and regression. Successful implementation of the RBF network depends on numerous factors among which, the crucial is its structure. The decision on the network structure has to be taken at the network initialization stage. It requires calculating or inducing the number of centroids, and their respective locations. The above problem is known to be NP-hard, and hence, not easily solvable. The traditional approach for deciding on the number of hidden units is based on applying the k-means algorithm for calculating cluster centroids. Unfortunately, the procedure guarantees neither a satisfactory accuracy nor the required generalization level of the RBF network under development. To alleviate the problem for cluster determination, i.e. number of centroids, we propose the similarity-based algorithm (SCA) for the RBF networks initialization, as well as an alternative method for initializing RBFNs using the kernel-based fuzzy clustering algorithm (KFCM-K). In both cases, the number of resulting centroids and their initial locations are provided automatically. The next step involves applying the optimization procedure resulting in the selection of the final centroids' location. The procedure is integrated with the output weights determination. Since the discussed optimization problem is computationally difficult it has been decided to apply the agent-based population learning algorithm (PLA) which belongs to the class of metaheuristics. A comparative study of approaches based on SCA and KFCM-K is included in the paper. Their effectiveness is demonstrated experimentally using artificial and real benchmark datasets. The results of the computational experiment have shown that both proposed approaches for designing RBFNs perform significantly better than other algorithms used for this task.

Keywords

• Radial basis function network (RBFN)
• RBFN initialization
• classification
• clustering
• multi-agent system