Nonlinear Small Sample Data Regression with a New Rational-Quadratic Minkowski Kernel for Tobacco Laser Perforation Process Tar Reduction Estimation.

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This paper investigates the nonlinear relationship between tobacco harmful content tar reduction and laser perforation parameters. To find a model to demonstrate the relationship between the laser perforation parameters and the cigarette tar reduction level, an online platform based on Python Streamlit was built to collect and publish related data. After the initial analysis of the collected experimental data, the quadratic nonlinear regression model demonstrates a significant fit to the experimental data. However, although the nonlinear regression has much higher accuracy than the linear regression plane, the prediction normalized root mean squared error (NRMSE) is still high, over 10%, which indicates that the regression relationship is more complex than the simple quadratic function expression. On the other hand, the sample dataset used for modeling is very limited, which restricts its exploration and the development of a model comparable to those built with big data. To address this challenge for small sample size data in modeling this complex nonlinear relationship, a novel rational-quadratic Minkowski (RM)-based kernel was designed. This RM-kernel model acquires higher accuracy than other kernels in both SVM and Gaussian process regression. Furthermore, this new kernel also shows less sensitivity to hyperparameter change, the greater ability to capture complex relationships, and more flexibility than the RBF kernel and RQ kernel. Subsequently, the kernel-based RM regression model was successfully implemented for laser perforation parameter selection, yielding consistent results that align with human sensory test data.