ПОЛУЧЕНИЕ РАЗРЕЖЕННЫХ РЕШЕНИЙ МЕТОДОМ LS SVM ЧЕРЕЗ ПОСТРОЕНИЕ ВЫБОРКИ С ПОМОЩЬЮ МЕТОДОВ ОПТИМАЛЬНОГО ПЛАНИРОВАНИЯ И ВНЕШНИХ КРИТЕРИЕВ КАЧЕСТВА МОДЕЛЕЙ

Abstract

PURPOSE. The paper deals with the methods of obtaining sparse solutions based on the least square support vector machines (LS SVM). METHODS. The sample is split into the training and test parts in order to obtain a sparse solution. A sequential algorithm is given to receive the training and test parts of the observation sample using the method of D -optimal experiment design as applied to the LS SVM method. We also present the sequential algorithms of sample splitting into parts using the consistency criterion. To testify the operation efficiency of the proposed sample splitting method a computational experiment is conducted where the solution accuracy by LS SVM is improved through adjusting of the scale of the Gaussian kernel function. This parameter of the kernel function is selected by minimizing the prediction error on the sample test part. Finally, the accuracy of the obtained solutions is tested by the mean-square error. RESULTS AND THEIR DISCUSSION. The computational experiment was performed on simulated data. A nonlinear dependence on the input factor was selected to be a data generating model. The variance of noise (noise level) was determined as the percentage of the signal strength. Three methods of sample splitting into the training and test parts including replacement, rejection and inclusion of points into the training part have been compared. The cross-validation method has been used to select the parameters of the LS SVM algorithm. CONCLUSIONS. The results of conducted computational experiments have shown that a sparse solution by the LS-SVM method can be obtained through the use of the sample split into parts using the D -optimal experiment design.