Improvements on νν-Twin Support Vector Machine

In this paper, we propose two novel binary classifiers termed as “Improvements on νν-Twin Support Vector Machine: Iνν-TWSVM and Iνν-TWSVM (Fast)” that are motivated by νν-Twin Support Vector Machine (νν-TWSVM). Similar to νν-TWSVM, Iνν-TWSVM determines two nonparallel hyperplanes such that they are closer to their respective classes and are at least ρρ distance away from the other class. The significant advantage of Iνν-TWSVM over νν-TWSVM is that Iνν-TWSVM solves one smaller-sized Quadratic Programming Problem (QPP) and one Unconstrained Minimization Problem (UMP); as compared to solving two related QPPs in νν-TWSVM. Further, Iνν-TWSVM (Fast) avoids solving a smaller sized QPP and transforms it as a unimodal function, which can be solved using line search methods and similar to Iνν-TWSVM, the other problem is solved as a UMP. Due to their novel formulation, the proposed classifiers are faster than νν-TWSVM and have comparable generalization ability. Iνν-TWSVM also implements structural risk minimization (SRM) principle by introducing a regularization term, along with minimizing the empirical risk. The other properties of Iνν-TWSVM, related to support vectors (SVs), are similar to that of νν-TWSVM. To test the efficacy of the proposed method, experiments have been conducted on a wide range of UCI and a skewed variation of NDC datasets. We have also given the application of Iνν-TWSVM as a binary classifier for pixel classification of color images.