An integrated adaptive fuzzy clustering model for pattern recognition

This dissertation presents the Integrated Adaptive Fuzzy Clustering (lAFC) model that overcomes the abovementioned problems. The lAFC model is a fuzzy neural network which incorporates a new fuzzy learning rule into a neural network structure, similar to the ART-1 neural network. The new learning rule incorporates fusion of a fuzzy membership value, the 7C-function [35] , and a function of the number of iterations into the incremental learning rule. The combination of the 7i-function and a function of the number of iterations guarantees weights to converge. The lAFC model introduces a new similarity measure that incorporates a fuzzy membership value into the Euclidean distance. The Euclidean distance and the Mahalanobis distance are commonly used as similarity measures. Even though the use of the Euclidean distance is convenient, it is best suited to hyper-spherical cluster shapes. The Mahalanobis distance accounts for some variations in cluster shape, but it works well for only hyper-ellipsoidal cluster shapes and is computationally burdensome. The new similarity measure considers not only the distance between the input data point and the centroid of a winning cluster but also the relative location of the input point to the existing cluster centroids as the degree of similarity. Thus, it gives more flexibility to the shape of clusters formed.

Chapter II describes current clustering and fuzzy clustering algorithms. Problems of current algorithms are also discussed. Chapter III provides an overview of current self-organizing neural networks for clustering. Chapter IV discusses current neuro-fuzzy clustering algorithms. Chapter V describes the new similarity measure and the lAFC model. Chapter VI presents the results of classification of real data sets by the lAFC model and compares the performance of the lAFC model with that of other recent neuro-fuzzy clustering and fuzzy clustering algorithms. Chapter VII concludes the dissertation.