Fuzzy connectivity clustering with radial basis kernel functions

– We use a Gaussian radial basis kernel function to map pairs of feature vectors from a sample into a fuzzy connectivity matrix whose entries are fuzzy truths that the 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 to form a smaller matrix. To this end we first group the feature vectors into many small pre-clusters based on summed feature-wise similarities, and then we use the pre-cluster centers as a reduced set of representatives. We next map the centers pair-wise to form the fuzzy connectivity matrix entries. When an unknown feature vector is input for classification, we find the nearest pre-cluster center and assign its 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 and difficult iris data and to the substantial and noisy Wisconsin breast cancer data.