Tensor decomposition methods for multi-omics immunology data analysis

项目总结/摘要 免疫分析研究的复杂性继续增加，多组学设计包括额外的免疫分析。 诸如时间、组织和空间轮廓的维度变得越来越普遍。无监督 降维是一种广泛使用的和有价值的方法，用于提取和理解 主要来源的变化，在以前的研究，但流行的方法，如主成分分析 (PCA)非负矩阵分解（NMF）不能支持这些数据复杂性的增加， 现有的多组学嵌入方法，这是专为静态数据集。关键是算法必须 开发了一种结合了最先进的免疫分析多组学中固有的复杂数据结构的 包括附加维度的研究（例如，时间或空间），以便捕获多分辨率分量 接种疫苗和感染。 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 超越二维。张量自然地表示复杂数据，而不会对任何变量进行平坦化， 分解可以识别变化的多指数模式，类似于更高维度中的PCA或NMF。 张量分解方法是应用数学界的一个活跃的研究领域， 免疫分析数据的应用开发不足，目前的方法面临着严峻的挑战， 阻止它们直接应用于免疫学研究。该项目将计算 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。Aim 1将重构张量 分解问题转化为正则化的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 时间或空间分量。Aim 2将通过开发直接改进张量分解方法 张量分解质量的新度量，并通过将多组学嵌入方法扩展到张量中， 空间使用一种新的张量代数。由此产生的算法将能够生成相关的组件 具有可以包括多组学和多维（例如，时间、空间、组织等）的数据。的设计.这些 可以分析组分与临床特征和结果的关联，允许发现新的 生物机制。拟议的项目将产生一套互补的算法，这将有助于 免疫学社区在理解复杂的病原和治疗/疫苗接种过程中使用的 越来越复杂的研究设计在免疫分析研究中变得越来越普遍。

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.