LSSVM - Least Squares Support Vector Machine

LSSVM (Least Squares Support Vector Machine) is a variant of traditional Support Vector Machines (SVM) that transforms the optimization problem into solving linear equations by introducing a least squares loss function, thereby reducing computational complexity. The core concept replaces inequality constraints in conventional SVM with equality constraints, simplifying the optimization process.

The main program typically involves the following key steps: Data Preparation: Load training datasets and perform standardization/normalization to ensure features are within similar numerical ranges (e.g., using z-score normalization or min-max scaling). Parameter Configuration: Select kernel functions (such as Gaussian RBF kernel or linear kernel) and set hyperparameters (including regularization coefficient and kernel width parameters). Equation Construction: Build linear equation systems based on training data, transforming the optimization problem into matrix operations through Lagrange multiplier methods. Model Solving: Solve linear equations to obtain support vectors and bias terms, determining the decision function for classification or regression tasks. Prediction and Evaluation: Perform classification or regression predictions on new samples, and validate model performance using metrics like accuracy, mean squared error, or R-squared values.

Compared to traditional SVM, LSSVM is more suitable for large-scale datasets and offers faster training speeds, though it may be more sensitive to noise. Practical applications require careful parameter tuning to prevent overfitting, often implemented through cross-validation techniques.