Novel Multi-output Support Vector Regression Model via Double Regularization

Multi-output regression estimation aims at mining a vector-valued function from multi-dimensional input vector to multi-dimensional output vector. However, the output variables may be correlative. It is desirable to develop a multi-dimensional regression model taking advantage of the possible correlations. Therefore, this paper proposes a novel multi-output support vector regression model via double regularization. For each output variable, we first introduce an influential level vector with the dimensionality equal to the one of the input vector, in order to characterize the correlation between this variable and other output variables. As a second regularization term, 2-norms of all influential level vectors are then added into the objective function. Each influential level vector is also considered in constraints of our model. Finally, experimental comparisons demonstrate that our proposed model in this paper has a better generalization performance as well as a better robustness.