Tensor decomposition methods for multi-omics immunology data analysis

项目摘要/摘要 免疫图谱研究的复杂性继续增加，多组设计包含更多的 时间、组织和空间侧写等维度变得越来越常见。无人监督 降维已经成为一种广泛使用和有价值的方法，用于提取和理解 以前研究中的主要变异来源，但流行的方法，如主成分分析 (PCA)和非负矩阵分解(NMF)不能支持这些数据复杂性的增加，也不能 现有的多组体嵌入方法，这些方法是为静态数据集设计的。至关重要的是，算法必须 集成了最先进的免疫图谱多组学固有的复杂数据结构的开发 包括额外维度(例如，时间或空间)以捕捉多分辨率分量的研究 疫苗接种和感染。 这个项目的目标是开发基于张量框架的算法--张量框架是矩阵的扩展 超越了两个维度。张量自然地表示复杂的数据，而不会在任何变量上展平，张量 分解可以识别多指标的变异模式，类似于更高维度的主成分分析或非主成分分析。 张量分解方法在应用数学界是一个活跃的研究领域，但 对于免疫简档数据的应用开发不足，当前的方法面临着严重的挑战 防止它们被直接应用于免疫学研究。该项目将计算机化 免疫学和应用数学研究人员加强和发展张量的新方法 分解，以使它们有益于免疫学社区。目标1将重新构造张量 将问题分解为正则化的NMF问题，从而允许为矩阵分析开发的工具 将用于张量数据，并将进一步扩展新算法以处理具有 时间或空间成分。目标2将直接改进张量分解方法，开发 张量分解质量的新度量，并通过将多体嵌入方法扩展到张量中 空间中使用了一种新的张量代数。生成的算法将能够生成关联的组件 数据可以包括多维和多维(例如，时间、空间、组织等)。设计。这些 可以分析成分与临床特征和结果的关联，从而发现新的 生物机制。拟议的项目将产生一套补充算法，将有助于 免疫学社区了解复杂的致病和治疗/疫苗接种过程 日益复杂的研究设计正变得常见于免疫图谱研究。

PROJECT SUMMARY/ABSTRACT Immune profiling studies continue to increase in complexity, with multi-omic designs that encompass additional dimensions such as time, tissue, and spatial profiling becoming more commonplace. Unsupervised dimensionality reduction has been a widely used and valuable approach for extracting and understanding the major sources of variation in previous studies, but popular methods such as Principal Components Analysis (PCA) and Non-negative Matrix Factorization (NMF) cannot support these increases in data complexity, nor can existing multi-omic embedding methods, which are designed for static datasets. It is critical that algorithms be developed that incorporate the complex data structures inherent in state-of-the-art immune profiling multi-omics studies that include additional dimensions (e.g., time or space) in order to capture multi-resolution components of vaccination and infection. The goal of this project is to develop algorithms based on tensor frameworks - which are extensions of matrices beyond two dimensions. Tensors naturally represent complex data without flattening on any variable, and tensor decompositions can identify multi-index patterns of variation, analogous to PCA or NMF in higher dimensions. Tensor decomposition methodology is an active area of research in the applied mathematics community, but is under-developed for application to immune profiling data, and current methods face critical challenges that prevent them from being directly applied in immunology studies. This project brings together computational immunology and applied mathematics researchers to strengthen and develop novel approaches of tensor decomposition in order to make them beneficial to the immunology community. Aim 1 will reframe a tensor decomposition problem into a regularized NMF problem, thereby allowing tools developed for matrix analysis to be used on tensor data, and furthermore will extend the new algorithm to handle multi-omics data that has a temporal or spatial component. Aim 2 will directly improve tensor decomposition approaches by developing novel metrics for tensor decomposition quality, and by extending a multi-omic embedding method into the tensor space using a novel tensor-algebra. The resulting algorithm will be able to generate components associated with data that can include both multi-omic and multi-dimensional (e.g. time, space, tissue, etc.) designs. These components can be analyzed for association with clinical features and outcomes, allowing for discovery of novel biological mechanisms. The proposed project will result in a suite of complementary algorithms that will aid the immunology community in understanding complex pathogenic and treatment/vaccination processes using the increasingly complex study designs that are becoming common to immune profiling studies.