## 1 Introduction  
Deep-learning techniques, including convolutional and recurrent neural networks, are being actively researched. Several related studies have reported successful results in many fields [1, 2, 3, 4, 5]. Nevertheless, the support vector machine (SVM)--one of the well-known machine learning techniques--still constitutes an option for the construction of classification systems [6, 7, 8]. The SVM has superior generalization ability compared with other classifiers and can be used in instances wherein the training data are not extensive [9, 10]. Additionally, the complexity of the SVM is also relatively lower than those of deep-learning techniques [11]. Correspondingly, SVM is an effective solution given the limited computational resources. However, the techniques using SVM rely on hyper-parameters to construct the kernel function and to penalize slack variables [12, 13]. The process used to select the appropriate hyper-parameters is essential to the design of the SVM classifier with a preferred performance. This hyper-parameter setting is called model selection (MS). Gradient-based methods comprise one of the categories of the MS. Gradient-based methods calculate the gradient of a specific generalization error function and use the gradient descent approach to determine the appropriate model [14, 15]. Various differentiable generalization error functions have been used in gradient-based methods, but the local minima problem and sensitivity to initialization are the major drawbacks of these methods [16]. Grid-search methods are alternative approaches that can be used for MS. These methods construct a grid on the hyper-parameters and evaluate each model that corresponds to each grid point to select the optimal SVM model [17; 18]. The grid-search-based methods are simple and are not prone to the local minima problem, but only the models that are based on fixed grid points can be tested for MS. To resolve this weakness and facilitate more flexibility for model searching, uniform design and evolutionary-algorithm-based methods have been introduced [19; 20]. A more detailed review on the recent MS methods can be found in [21]. There are some differences in the manner in which candidate SVM models are chosen for testing. The basic ideas of the grid search, uniform design, and evolutionary-algorithm-based methods are similar as these methods assess the various candidate SVM models and select the model with the optimum performance. In this respect, it is important to evaluate the performance of each SVM model precisely for MS, and selection criteria are used for the purpose. Generalization error obtained by leave-one-out cross validation (LOOCV) is a popular selection criterion used to evaluate the SVM models [22]. Herein, when the training set contains \(N\) data, LOOCV trains the SVM using \(N-1\) data and tests it with the remaining one datum to evaluate the classification error. The generalization error is calculated from the mean of the classification errors for the \(N\) sets of data. These generalization errors are then compared for each model, and the model with the lowest generalization error is selected in the MS step. The LOOCV is commonly known as an unbiased estimator of the generalization error but incurs a heavy computational load because the SVM is trained \(N\) times for each model. However, the K-fold cross validation (KCV) is associated with a smaller computational load, and generalization error calculated by the KCV has greater practical use to be considered as a suitable alternative selection criterion. In this method, the training data are divided into \(K\) segments, and the segments are individually cross validated. The generalization error is obtained as the average error from the \(K\) tests. The mean value of sensitivity and specificity can also be used as a selection criterion in the KCV [18].