Abstract The classification of normally distributed data in a high-dimensional setting when variables are more numerous than observations is considered. Under the assumption that the inverse covariance matrices (the precision matrices) are the same over all groups, the method of the linear discriminant analysis (LDA) is adapted by including a sparse estimate of these matrices. Furthermore, a variable selection procedure is developed based on the graph associated to the estimated precision matrix. For that, a discriminant capacity is defined for each connected component of the graph, and variables of the most discriminant components are kept. The adapted LDA and the variable selection procedure are both evaluated on synthetic data, and applied to real data from PET brain images for the classification of patients with Alzheimer’s disease.

中文翻译：

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用于高维分类的具有变量选择的自适应线性判别分析，以及在医学数据中的应用

摘要 当变量多于观测值时，考虑在高维设置中对正态分布数据进行分类。在所有组的逆协方差矩阵（精度矩阵）都相同的假设下，线性判别分析 (LDA) 的方法通过包括这些矩阵的稀疏估计来适应。此外，基于与估计精度矩阵相关联的图形开发了变量选择程序。为此，为图中的每个连通分量定义了一个判别能力，并保留了最具判别能力的分量的变量。调整后的 LDA 和变量选择程序都在合成数据上进行评估，并应用于来自 PET 大脑图像的真实数据，以对阿尔茨海默病患者进行分类。