Multi-output regression aims at learning a mapping from a multivariate input feature space to a multivariate output space. Despite its potential usefulness, the standard formulation of the least-squares support vector regression machine (LS-SVR) [1][2] cannot cope with the multi-output case. The usual procedure is to train multiple independent LS-SVR, thus disregarding the underlying (potentially nonlinear) cross relatedness among different outputs.

To address this problem, inspired by the multi-task learning methods (such as [3]), Xu et. al. [4] proprosed a novel approach, Multi-output LS-SVR (MLS-SVR), in multi-output setting. MLSSVR is a MATLAB implementation of MLS-SVR with the more efficient training algorithm in [4].

MATLAB

https://github.com/pzczxs/MLSSVR

If you find this toolbox useful, please cite MLS-SVR as follows:

• Shuo Xu, Xin An, Xiaodong Qiao, Lijun Zhu, and Lin Li, 2013. Multi-Output Least-Squares Support Vector Regression Machines. Pattern Recognition Letters, Vol. 34, No. 9, pp. 1078-1084. PDF

1. C. Saunders, A. Gammerman, and V. Vovk, 1998. Ridge Regression Learning Algorithm in Dual Variables. Proceedings of the 15th International Conference on Machine Learning (ICML), pp. 515-521.
2. Johan A. K. Suyken, Tony van Gestel, Jos de Brabanter, Bart de Moor, and Joos Vandewalle, 2002. Least-Squares Support Vector Machines. World Scientific Pub. Co.
3. Theodoros Evgeniou and Massimiliano Pontil, 2004. Regularized Multi-Task Learning. Proceedings of the 10th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), pp. 109-117.
4. Shuo Xu, Xin An, Xiaodong Qiao, Lijun Zhu, and Lin Li, 2013. [Multi-Output Least-Squares Support Vector Regression Machines](http://doi.org/10.1016/j.patrec.2013.01.015). Pattern Recognition Letters, Vol. 34, No. 9, pp. 1078-1084.