K-Means clustering based Extreme Learning ANFIS with improved interpretability for regression problems

Abstract

In this paper, a novel network called K-Means clustering based Extreme Learning ANFIS (KMELANFIS) with improved interpretability for regression problems is presented. Grid input space partitioning results in the exponential rise in the number of rules in Fuzzy Inference System (FIS) with an increase in the number of features, thus reducing the interpretability of the network and increasing the computational burden. In the proposed network, input partitioning is done using K-means clustering algorithm to avoid the computational complexity arising due to the large number of rules generated for problems with high input dimensionality. The cluster centers resulting from the clustering of input–output space are used for initializing the membership function parameters. Based on the similarity index between adjacent membership functions, the similar membership functions are merged, and membership function parameters are tuned to improve the distinguishability of membership functions. Extreme learning machine (ELM) technique is incorporated to compute the consequent parameters thus avoiding the computational complexity of the backpropagation algorithm used in the training of ANFIS network. For performance comparison, simulations for function approximation and real world benchmark regression problems are done for ANFIS, ELANFIS, LSSVR, and KMELANFIS networks. KMELANFIS network has improved interpretability with decent accuracy, lesser numbers of rules and parameters, and has faster training for most of the examples. Regularized KMELANFIS network have better accuracy and larger training time compared to KMELANFIS network.