Exploiting Supervised Principal Component Analysis for Efficient High-Dimensional Kriging Modeling

High-dimensional Kriging modeling is widely used in engineering and scientific fields. However, as the input dimensionality increases, computational complexity rises dramatically, and the number of required training samples grows exponentially. To address these challenges, this paper proposes a novel high-dimensional Kriging modeling methodology, the SPCAK method, which integrates supervised principal component analysis (SPCA) with Kriging surrogate models to efficiently handle high-dimensional problems. The core innovation of the SPCAK method is the use of a Hilbert–Schmidt independence criterion (HSIC)–driven SPCA dimensionality reduction technique. This technique projects original high-dimensional space onto a low-dimensional orthogonal subspace while incorporating the nonlinear relationship between the high-dimensional input matrix and the response vector into the dimensionality reduction process. This approach is particularly advantageous for high-dimensional Kriging modeling, as it not only captures nonlinear relationships but also preserves critical information between inputs and outputs through supervised learning. As a result, it significantly reduces computational complexity while enhancing model accuracy. Experimental results show that the modeling performance is optimal when reducing the dimensionality of problems ranging from 20 to 80 dimensions to 3 dimensions. The effectiveness of the method under varying numbers of sampling points is validated through eight classical test functions. Additionally, the method is applied to a case study predicting rice fresh weight. The findings demonstrate that SPCAK outperforms the original Kriging and KPLS3 methods in terms of modeling accuracy, substantially reduces modeling time, and exhibits significant advantages in addressing high-dimensional problems.