Kernel-Based Partial Least Squares Algorithm

In this article, we introduce a kernel-based algorithm—the Partial Least Squares (PLS) method. This algorithm is particularly useful for solving regression problems, where the kernel function enables nonlinear transformation of the original data to achieve better fitting performance. During implementation, the algorithm employs nonlinear iterative techniques to optimize the solution. The iterative process involves calculating latent variables through eigenvalue decomposition or singular value decomposition, with key functions like kernel matrix computation and score vector updates being executed in each iteration. Common kernel functions include polynomial and radial basis function (RBF) kernels, which map the data to higher-dimensional feature spaces. Through this algorithm, we can gain deeper insights into data patterns and make more accurate predictions and decisions, with the iterative optimization continuously refining the model parameters until convergence criteria are met.