Fuzzy connectivity clustering with radial basis kernel functions

This method clusters data when the number of classes is unknown. We partition a data set with a Gaussian radial basis kernel function on pairs of feature vectors from a reduced sample to obtain a fuzzy connectivity matrix. The matrix entries are fuzzy truths that the row–column vector pairs belong to the same classes. To reduce the matrix size when the data set is large, we obtain a smaller set of representative vectors by first grouping the feature vectors into many small pre-clusters based on a new robust similarity measure. Then we use the pre-cluster centers as the reduced sample. We next map pairs of the centers via the kernel function to form the connectivity matrix entries of fuzzy values from which we determine the classes and the number of classes. Afterward, when an unknown feature vector is input for recognition, we find its nearest pre-cluster center and assign that centerʹs class to the unknown vector. We demonstrate the method first on a simple set of linearly nonseparable synthetic data to show how it works and then apply it to the well-known difficult iris data. We also apply it to the more substantial and noisy Wisconsin breast cancer data.