A nonparallel support vector machine for a classification problem with universum learning

Universum samples, defined as samples not belonging to any class for a classification problem of interest, have been useful in supervised learning. Here we design a new nonparallel support vector machine (U-NSVM) that can exploit prior knowledge embedded in the universum to construct a more robust classifier for training. To this end, U-NSVM maximizes the two margins associated with the two closest neighboring classes, which is combined by two nonparallel hyperplanes. Therefore, U-NSVM has better flexibility and can yield a more reasonable classifier in most cases. In addition, our method includes fewer parameters than U-SVM, so is easier to implement. Experiments demonstrate that U-NSVM outperforms the traditional SVM and U-SVM.