MATLAB Implementation of LIBSVM Parameter Optimization

In machine learning applications using LIBSVM for regression analysis, selecting appropriate parameters C (penalty coefficient) and g (kernel function parameter) is crucial for model performance. Here we present the methodology and implementation approach for this optimization process.

First, define the parameter search space. The grid search method is typically employed to traverse predetermined ranges for C and g parameters. For instance, C values can range from 2^-5 to 2^15 while g values span from 2^-15 to 2^3. Using logarithmic scaling for parameter division is more rational as it better covers potential optimal parameter values. In MATLAB implementation, this can be achieved using logspace() or creating geometric sequences with power operations.

Second, employ cross-validation to evaluate model performance. The k-fold cross-validation method (commonly 5-fold or 10-fold) is widely adopted. Cross-validation reduces randomness from data splitting and ensures stable model evaluation. After training the model on each training fold, compute performance metrics such as Mean Squared Error (MSE) or R-squared (R2) on the validation set to assess each parameter combination. The MATLAB implementation typically involves using cvpartition() for data splitting and maintaining separate training/validation indices.

Finally, select the optimal parameter combination. After testing all possible C and g combinations, compare validation set performances across different parameters to identify the combination that minimizes model error or maximizes accuracy. It's recommended to record validation results for each parameter set for subsequent analysis. This can be implemented using nested loops with results stored in a matrix or table structure.

The parameter optimization process can be implemented through loop structures that systematically test different C and g combinations. To improve computational efficiency, consider incorporating parallel computing (using parfor loops) or optimized search strategies like heuristic algorithms. However, grid search remains the most intuitive and reliable method when dealing with a small number of parameters. The MATLAB code typically involves nested for-loops with svmtrain() calls within each iteration.

This systematic approach enables finding optimal parameter combinations for LIBSVM regression problems, thereby enhancing model prediction accuracy and generalization capability. The complete implementation includes parameter grid generation, cross-validation setup, model training/evaluation loops, and result comparison logic.