Scalable Methods for Classification of Heterogeneous High-Dimensional Data

最近的技术进步使生物医学领域中大规模高维数据的常规收集成为可能。例如，在癌症研究中，通常使用多个高通量技术平台来测量基因型、基因表达水平和甲基化水平。分析这类数据的主要挑战之一是确定可用于将受试者归类为已知癌症亚型的关键生物学测量。虽然在开发计算高效的分类方法以应对这一挑战方面取得了重大进展，但现有方法没有充分考虑到跨癌症亚型的异质性和跨技术平台的混合类型的测量(二进制/计数/连续)。因此，现有的方法可能无法识别相关的生物模式。该项目的目标是开发新的分类方法，明确考虑到测量的类型和异质性。虽然主要的重点是方法论，但将高度优先考虑计算和软件开发，以鼓励传播和确保领域科学家的易用性。正则化线性判别方法由于其可解释性和计算效率，常用于同时分类和变量选择。然而，这些方法依赖于组协方差矩阵相等和测量值正态的不切实际的假设。该项目旨在解决目前判别方法中存在的局限性，有三个目标：(1)制定计算效率高的二次分类规则，进行变量选择；(2)将判别分析框架推广到非正态测量；(3)为同一组受试者收集的来自多个技术平台的混合类型数据开发一个分类框架。关键的方法创新是将稀疏的低阶奇异值分解与线性判别分析的几何解释相结合，前者能够提高计算效率，后者允许通过重新定义判别空间来构建非线性分类规则。

Recent technological advances have enabled routine collection of large-scale high-dimensional data in the biomedical fields. For example, in cancer research it is common to use multiple high-throughput technology platforms to measure genotype, gene expression levels, and methylation levels. One of the main challenges in the analysis of such data is the identification of key biological measurements that can be used to classify the subject into a known cancer subtype. While significant progress has been made in the development of computationally efficient classification methods to address this challenge, existing methods do not adequately take into account the heterogeneity across the cancer subtypes and the mixed types of measurements (binary/count/continuous) across technology platforms. As such, existing methods may fail to identify relevant biological patterns. The goal of this project is to develop new classification methods that explicitly take into account the type and heterogeneity of measurements. While the primary focus is on methodology, high priority will be given to computational considerations and software development to encourage dissemination and ensure ease of use for domain scientists. Regularized linear discriminant methods are commonly used for simultaneous classification and variable selection due to their interpretability and computational efficiency. These methods, however, rely on unrealistic assumptions of equality of group-covariance matrices and normality of measurements. This project aims to address the limitations present in current discriminant approaches, and has three objectives: (1) to develop computationally efficient quadratic classification rules that perform variable selection; (2) to generalize the discriminant analysis framework to non-normal measurements; (3) to develop a classification framework for mixed type data coming from multiple technology platforms collected on the same set of subjects. The key methodological innovation is the combination of sparse low-rank singular value decomposition, which enables computational efficiency, with geometric interpretation of linear discriminant analysis, which allows for the construction of nonlinear classification rules by redefining the space for discrimination.