Model selection for least squares support vector regressions based on small-world strategy

Model selection plays a key role in the application of support vector machine (SVM). In this paper, a method of model selection based on the small-world strategy is proposed for least squares support vector regression (LS-SVR). In this method, the model selection is treated as a single-objective global optimization problem in which generalization performance measure performs as fitness function. To get better optimization performance, the main idea of depending more heavily on dense local connections in small-world phenomenon is considered, and a new small-world optimization algorithm based on tabu search, called the tabu-based small-world optimization (TSWO), is proposed by employing tabu search to construct local search operator. Therefore, the hyper-parameters with best generalization performance can be chosen as the global optimum based on the powerful search ability of TSWO. Experiments on six complex multimodal functions are conducted, demonstrating that TSWO performs better in avoiding premature of the population in comparison with the genetic algorithm (GA) and particle swarm optimization (PSO). Moreover, the effectiveness of leave-one-out bound of LS-SVM on regression problems is tested on noisy sinc function and benchmark data sets, and the numerical results show that the model selection using TSWO can almost obtain smaller generalization errors than using GA and PSO with three generalization performance measures adopted.

Research highlights
► A new decimal-coding small-world algorithm based on tabu search is proposed, which has good global search ability.
► The effectiveness of leave-one-out bound of LS-SVR is tested, which suggests LOO bound qualifies as generalization measure for regression problems.
► A new model selection algorithm for LS-SVR based on small-world strategy is proposed, which can obtain better generalization performance than using other search strategies.