Multiple types of data measured on a common set of subjects arise in many areas. Numerous empirical studies have found that integrative analysis of such data can result in better statistical performance in terms of prediction and feature selection. However, the advantages of integrative analysis have mostly been demonstrated empirically. In the context of two-class classification, we propose an integrative linear discriminant analysis method and establish a theoretical guarantee that it achieves a smaller classification error than running linear discriminant analysis on each data type individually. We address the issues of outliers and missing values, frequently encountered in integrative analysis, and illustrate our method through simulations and a neuroimaging study of Alzheimer's disease.

中文翻译：

---

具有保证错误率改进的综合线性判别分析

在许多领域都出现了对一组共同主题进行测量的多种类型的数据。许多实证研究发现，对此类数据进行综合分析可以在预测和特征选择方面产生更好的统计性能。然而，整合分析的优势大多是通过经验证明的。在两类分类的背景下，我们提出了一种综合线性判别分析方法，并建立了一个理论保证，即它比对每种数据类型单独运行线性判别分析实现更小的分类误差。我们解决了在综合分析中经常遇到的异常值和缺失值问题，并通过模拟和阿尔茨海默病的神经影像学研究来说明我们的方法。