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The least squares support vector regression (LS-SVR) is usually used for the modeling of single output system, but it is not well suitable for the actual multi-input-multi-output system. The paper aims at the modeling of multi-output systems by LS-SVR. The multi-output LS-SVR is derived in detail. To avoid the inversion of large matrix, the recursive algorithm of the parameters is given, which makes the online algorithm of LS-SVR practical. Since the computing time increases with the number of training samples, the sparseness is studied based on the pro-jection of online LS-SVR. The residual of projection less than a threshold is omitted, so that a lot of samples are kept out of the training set and the sparseness is obtained. The standard LS-SVR, nonsparse online LS-SVR and sparse online LS-SVR with different threshold are used for modeling the isomerization of C8 aromatics. The root-mean-square-error (RMSE), number of support vectors and running time of three algorithms are compared and the result indicates that the performance of sparse online LS-SVR is more favorable.
The least squares support vector regression (LS-SVR) is usually used for the modeling of single output system, but it is not well suitable for the actual multi-input-multi-output system. The paper aims at the modeling of multi-output systems by LS-SVR. The multi-output LS-SVR is derived in detail. To avoid the inversion of large matrix, the recursive algorithm of the parameters is given, which makes the online algorithm of LS-SVR practical. Since the computing time increases with the number of training samples, the sparseness is studied based on the pro-jection of online LS-SVR. The residual of projection less than a threshold is omitted, so that a lot of samples are kept out of the training set and the The standard LS-SVR, nonsparse online LS-SVR and sparse online LS-SVR with different threshold are used for modeling the isomerization of C8 aromatics. The root-mean-square-error and running time of three algorithms are compared and the result indicates that the performance of sparse online LS-SVR is more favorable.