Random Projection for Linear Twin Support Vector Machine

Abstract

Twin support vector machine (TSVM) is widely applied in a multitude of aspects. It works faster than SVM, since it solves a pair of smaller-sized quadratic programming problems rather than a larger one. Random projection (RP) is an oblivious feature extraction and dimension reduction method. This paper proposes a novel algorithm, named random projection for twin support vector machine (RP-TSVM), which inherits the high precision and fast solving speed of TSVM bounded with high efficiency and data-independent property of RP. We give two proofs on the geometry of TSVM under random projection. The first is that the sum of squared distances from the hyper-plane to points of one class in TSVM is almost unchanged with high probability, which insure the accuracy of RP-TSVM. The second is that the minimum enclosing ball in the feature space is preserved to within  - relative error, ensuring comparable generalization as in the original space. Numerical experiments demonstrate the theoretical discoveries. And the computational experimental results also show that the accuracy of the proposed RP-TSVM is higher than RP-SVM. What’s more, when solving large scale problems, the proposed algorithm performs almost at least twenty times faster than