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

Area of Science:

• Tobacco research
• Materials science
• Data science

Background:

• Understanding the relationship between laser perforation parameters and cigarette tar reduction is crucial for product development.
• Existing models struggle with the complex nonlinearities and limited data inherent in this field.

Purpose of the Study:

• To develop a robust model for predicting cigarette tar reduction based on laser perforation parameters.
• To address the challenges of small sample sizes and complex nonlinear relationships in regression modeling.

Main Methods:

• An online platform using Python Streamlit was developed for data collection and analysis.
• Quadratic nonlinear regression was initially employed, followed by the design of a novel rational-quadratic Minkowski (RM)-based kernel.
• Support Vector Machines (SVM) and Gaussian Process Regression (GPR) were utilized with the new RM-kernel.

Main Results:

• Quadratic regression showed significant fit but high prediction error (NRMSE > 10%).
• The novel RM-kernel demonstrated superior accuracy and flexibility compared to RBF and RQ kernels in SVM and GPR.
• The RM-kernel model achieved higher accuracy and robustness, capturing complex relationships effectively.

Conclusions:

• The RM-kernel regression model offers a significant advancement for predicting tar reduction with limited data.
• This approach successfully guides laser perforation parameter selection, aligning with human sensory data.