Multiclass classification based on extended support vector data description.

We propose two variations of the support vector data description (SVDD) with negative samples (NSVDD) that learn a closed spherically shaped boundary around a set of samples in the target class by involving different forms of slack vectors, including the two-norm NSVDD and nu-NSVDD. We extend the NSVDDs to solve the multiclass classification problems based on the distances between the samples and the centers of the learned spherically shaped boundaries in a kernel-defined feature space by using a combination of linear discriminant analysis (LDA) and nearest-neighbor (NN) rule. Extensive simulations are developed with one real-world data set on the automatic monitoring of roller bearings with vibration signals and eight benchmark data sets for both binary and multiclass classification. The benchmark testing results show that our proposed methods provide lower classification error rates and smaller standard deviations with the cross-validation procedure. The two-norm NSVDD with the LDA-NN rule recorded a test accuracy of 100.0% for the binary fault detection of roller bearings and 99.9% for the multiclass classification of roller bearings under six conditions.