Alzheimer's Disease is a devastating neurological disorder that is increasingly affecting the elderly population. Early and accurate detection of Alzheimer's is crucial for providing effective treatment and support for patients and their families. In this study, we present a novel approach for detecting four different stages of Alzheimer's disease from MRI scan images based on inertia tensor analysis and machine learning. From each available MRI scan image for different classes of Dementia, we first compute a very simple 2 x 2 matrix, using the techniques of forming a moment of inertia tensor, which is largely used in different physical problems. Using the properties of the obtained inertia tensor and their eigenvalues, along with some other machine learning techniques, we were able to significantly classify the different types of Dementia. This process provides a new and unique approach to identifying and classifying different types of images using machine learning, with a classification accuracy of (90%) achieved. Our proposed method not only has the potential to be more cost-effective than current methods but also provides a new physical insight into the disease by reducing the dimension of the image matrix. The results of our study highlight the potential of this approach for advancing the field of Alzheimer's disease detection and improving patient outcomes.

翻译：阿尔茨海默病是一种严重神经退行性疾病，其发病率在老年人群中持续上升。对该病的早期准确诊断对于为患者及其家庭提供有效治疗与支持至关重要。本研究提出一种基于惯性张量分析和机器学习的创新方法，通过MRI扫描图像检测阿尔茨海默病的四个不同阶段。针对不同痴呆类别的每张MRI扫描图像，我们首先利用惯性张量构建技术（该技术广泛用于各类物理问题）计算出一个极为简化的2×2矩阵。通过所获惯性张量的特性及其特征值，结合其他机器学习技术，我们实现了对各类痴呆症的有效分类。该方法提供了一种全新且独特的图像分类识别思路，在机器学习分类中达到90%的准确率。相较于现有方法，我们提出的方案不仅具有更优的成本效益，还通过降维图像矩阵为疾病机制提供了新的物理视角。研究结果凸显了该方法在推动阿尔茨海默病检测领域发展及改善患者预后方面的巨大潜力。