Mahapatra Krishna, Selvakumar R
Department of Mathematics, Vellore Institute of Technology, Vellore, Tamil Nadu, India.
J Med Phys. 2025 Jan-Mar;50(1):131-139. doi: 10.4103/jmp.jmp_128_24. Epub 2025 Mar 24.
This study proposes a novel approach combining mathematical modeling and machine learning (ML) to classify four Alzheimer's disease (AD) stages from magnetic resonance imaging (MRI) scans.
We first mapped each MRI pixel value matrix to a 2 × 2 matrix, using the techniques of forming a moment of inertia (MI) tensor, commonly used in physics to measure the mass distribution. Using the properties of the obtained inertia tensor and their eigenvalues, along with ML techniques, we classify the different stages of AD.
In this study, we have compared the performance of an intuitive mathematical model integrated with a machine learning approach across various ML models. Among them, the Gaussian Naïve Bayes classifier achieves the highest accuracy of 95.45%.
Beyond improved accuracy, our method offers potential for computational efficiency due to dimensionality reduction and provides novel physical insights into AD through inertia tensor analysis.
本研究提出一种将数学建模与机器学习（ML）相结合的新方法，用于从磁共振成像（MRI）扫描中对阿尔茨海默病（AD）的四个阶段进行分类。
我们首先使用在物理学中常用于测量质量分布的形成惯性矩（MI）张量的技术，将每个MRI像素值矩阵映射为一个2×2矩阵。利用所得惯性张量的性质及其特征值，结合ML技术，我们对AD的不同阶段进行分类。
在本研究中，我们比较了在各种ML模型中集成机器学习方法的直观数学模型的性能。其中，高斯朴素贝叶斯分类器实现了最高准确率95.45%。
除了提高准确率外，我们的方法由于降维而具有计算效率潜力，并通过惯性张量分析为AD提供了新的物理见解。
