Collaborative Research: CDS&E-MSS: Community detection via covariance structures

加权网络是这样一种网络，在该网络中，节点之间的每条边都被分配了权重，或者换句话说，被分配了数值。与边为二进制的未加权网络不同，加权网络提供有关节点之间连接的重要性、强度或强度的附加信息。该项目旨在开发专门为分析加权网络数据而设计的新的社区检测工具，主要侧重于在生物信息学和生物科学中的应用。目标是通过利用代表加权网络的协方差或相关矩阵来识别高度相关的基因模块。通过应用一种系统的、计算高效的和理论上严格的方法，该项目旨在有效地解决这个问题，促进其在各种生物学背景下的应用，如癌症研究和脑成像数据分析。这个项目的一个重要方面是它为学生提供了在统计学、数据科学和生物信息学方面获得宝贵研究经验的机会。PIS计划让本科生和研究生参与并指导他们与这个项目相关的研究。该项目首先提出了一种通过协方差结构进行社区检测的新方法。具体地说，该项目侧重于块结构协方差模型(BCM)及其变体，例如异质块协方差模型(HBCM)。在BCM下，数据服从多变量正态分布，协方差矩阵根据社区标签被组织成块。当与其他特征形成连接时，HBCM结合了不同的参数来考虑单个变量的特征。其次，该项目不仅提供了多种社区检测方法，而且为研究加权网络提供了一个系统的框架。该框架为社区检测研究开辟了新的途径。此外，BCM/HBCM框架允许在理论和实践中评估各种非参数方法和准则函数。此外，该项目开发了新的方法来克服新研究主题中固有的计算和理论挑战。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

A weighted network is a network in which each edge between nodes is assigned a weight or, in other words, a numerical value. In contrast to an unweighted network where edges are binary, a weighted network provides additional information about the importance, strength, or intensity of the connections between nodes. This project aims to develop novel community detection tools specifically designed for the analysis of weighted network data, with a primary focus on applications in bioinformatics and biological science. The goal is to identify modules of highly correlated genes by utilizing the covariance or correlation matrix that represents a weighted network. By applying a systematic, computationally efficient, and theoretically rigorous approach, this project aims to effectively address this problem, facilitating its application in various biological contexts such as cancer research and brain imaging data analysis. A significant aspect of this project is the opportunity it provides to students to gain valuable research experiences in statistics, data science, and bioinformatics. The PIs plan to involve and mentor both undergraduate and graduate students in their research related to this project.The project first presents a novel approach to community detection via covariance structures. Specifically, the project focuses on the block-structured covariance model (BCM) and its variants, such as the heterogeneous block covariance model (HBCM). Under the BCM, data follows a multivariate normal distribution, with the covariance matrix organized into blocks based on community labels. The HBCM incorporates heterogeneous parameters to account for the characteristics of individual variables when forming connections with other features. Second, this project provides not only multiple community detection methods but also a systematic framework for studying weighted networks. This framework opens up new avenues for community detection research. Additionally, the BCM/HBCM framework enables the evaluation of various nonparametric methods and criterion functions, both theoretically and practically. Moreover, the project develops novel methods to overcome computational and theoretical challenges inherent in the new research topic.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.