Multi-task Support Vector Machine Classifier with Generalized Huber Loss

Compared to single-task learning (STL), multi-task learning (MTL) achieves a better generalization by exploiting domain-specific information implicit in the training signals of several related tasks. The adaptation of MTL to support vector machines (SVMs) is a rather successful example. Inspired by the recently published generalized Huber loss SVM (GHSVM) and regularized multi-task learning (RMTL), we propose a novel generalized Huber loss multi-task support vector machine including linear and non-linear cases for binary classification, named as MTL-GHSVM. The new method extends the GHSVM from single-task to multi-task learning, and the application of Huber loss to MTL-SVM is innovative to the best of our knowledge. The proposed method has two main advantages: on the one hand, compared with SVMs with hinge loss and GHSVM, our MTL-GHSVM using the differentiable generalized Huber loss has better generalization performance; on the other hand, it adopts functional iteration to find the optimal solution, and does not need to solve a quadratic programming problem (QPP), which can significantly reduce the computational cost. Numerical experiments have been conducted on fifteen real datasets, and the results demonstrate the effectiveness of the proposed multi-task classification algorithm compared with the state-of-the-art algorithms.