Detection of Alzheimer's Disease using Explainable Machine Learning and Mathematical Models.

Purpose: 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.

Methodology: 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.

Results: 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%.

Conclusions: 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.