The fuzzy Laplacianclassifier

We develop a novel classifier in a kernel feature space, which can be used to handle the class imbalanced problem in the presence of noise and outliers. In many applications, each input point may not be fully assigned to one of two classes or multiclasses. Based on the Laplacian classifier (LC), we applied a fuzzy membership to each input point and reformulate LC so that different input points can make different contributions to the learning process. We called the proposed method the fuzzy Laplacian classifier (FLC). We thoroughly evaluated the proposed FLC method on two simulation data examples and ten real-world data examples and compare its performance with support vector machine (SVM), fuzzy support vector machine (FSVM), fuzzy support vector machines for class imbalance learning (FSVM-CIL) and LC. Based on the overall results obtained in the experiments, we can conclude that the proposed FLC method can not only result in better classification results than SVM, FSVM, FSVM-CIL and LC for the imbalanced data sets in the presence of noise or outliers, but also emphasize more to classify the least probableclass.