Multi-category ternion support vector machine

Abstract

This paper proposes a three-class classifier termed as ‘Ternion support vector machine’ (TerSVM) and its tree based multi-category classification approach termed as ‘Multi-category ternion support vector machine’ (M-TerSVM). The proposed classifier, TerSVM, is motivated by twin multi-class support vector classification (Twin-KSVC) and evaluates the data patterns for three outputs (+1,−1,0). Twin-KSVC has very high computational complexity, which makes it infeasible for real-world problems. Our proposed classifier, TerSVM, overcomes this limitation, as it formulates three unconstrained minimization problems (UMPs), instead of quadratic programming problems as solved by Twin-KSVC. The UMPs of TerSVM are solved as systems of linear equations which determine three proximal nonparallel hyperplanes. TerSVM can also be used as a binary classifier. This work also proposes a multi-category classification algorithm, M-TerSVM, that extents our three-class classifier (TerSVM) into multi-category framework. For a K-class problem, M-TerSVM constructs a classifier model in the form of a ternion tree of height ⌊K∕2⌋, where the data is partitioned into three groups at each level. Our algorithm uses a novel procedure to identify a reduced training set which improves its learning time. Numerical experiments performed on synthetic and benchmark datasets indicate that M-TerSVM outperforms other classical multi-category approaches like one-against-all and Twin-KSVC, in terms of generalization ability and learning time. This paper proposes the application of M-TerSVM for handwritten digit recognition and color image classification.