CIF: Small: Multiview Graph Learning with Applications to Single Cell Gene Expression Networks

现代数据分析涉及大量的结构化数据，其中的结构承载着有关数据性质的关键信息。实体之间的关系，如特征或数据样本，通常用图形结构来描述。虽然许多现实世界的数据本质上是图结构的，例如社交和交通网络，但仍然有大量的应用程序在其中图拓扑并不容易获得。例如，生物应用中的基因调控或大脑中的神经元连接通常不被观察到。推断潜在结构是这类数据的一项基本任务。现有的大多数关于图学习的工作都集中在学习单一的图结构上，假设观察到的数据样本之间的关系是齐次的。然而，在许多实际应用中，数据样本之间存在不同形式的交互，例如跨多种细胞类型的单细胞RNA测序(scRNA-seq)。本项目旨在解决异质数据的多视点图学习问题，重点是从scRNA序列中推断基因调控网络(GRN)。本项目将引入一个从异质数据中学习图形结构的多视点框架。首先，将介绍一种学习带符号图的新方法。带符号图在生物网络中是常见的，其中正边和负边分别对应于激活关系和抑制关系。该框架将通过图信号核来考虑节点间相互作用的非线性特性。其次，将考虑两种情况下的多视图图学习的综合框架：i)相同数据的多个视图和ii)具有未知聚类信息的异类数据。在第一种情况下，将开发一种联合学习方法，其中既学习个体图又学习共识图。在第二种情况下，将经典谱聚类与图信号平滑相结合，建立了用于联合聚类和多视点图学习的统一框架。图学习算法将解决基因调控网络推理中遇到的一些挑战，如基因表达数据的非高斯性、非线性，由于细胞周期异质性导致的基因表达的变化，以及由于单个细胞中低数量的mRNA而导致的高度稀疏性。该项目将为不同层次的学生提供跨学科培训。这些研究成果将被纳入一门新的在线研究生课程，作为对数据科学日益增长的兴趣的一部分。最后，拟议的研究将被纳入针对K-12女性学生的推广工作，并通过出版物、研讨会和代码共享向更广泛的研究社区传播。这一奖项反映了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。

Modern data analysis involves large sets of structured data, where the structure carries critical information about the nature of the data. The relationships between entities, such as features or data samples, are usually described by a graph structure. While many real-world data are intrinsically graph-structured, e.g. social and traffic networks, there are still a large number of applications where the graph topology is not readily available. For instance, gene regulations in biological applications or neuronal connections in the brain are not usually observed. Inferring the underlying structure is an essential task for such data. Most of the existing work on graph learning focuses on learning a single graph structure, assuming that the relations between the observed data samples are homogeneous. However, in many real-world applications, there are different forms of interactions between data samples, such as single-cell RNA sequencing (scRNA-seq) across multiple cell types. This project aims to address the multi-view graph-learning problem for heterogeneous data with a focus on gene regulatory network (GRN) inference from scRNA-seq.This project will introduce a multi-view framework to learn graphical structures from heterogeneous data. First, a new approach for learning signed graphs will be introduced. Signed graphs are commonly encountered in biological networks, where the positive and negative edges correspond to activating and inhibitory relationships, respectively. This framework will take the nonlinear nature of interactions between nodes into account through graph signal kernels. Second, a comprehensive framework for multi-view graph learning in two settings will be considered: i) multiple views of the same data and ii) heterogeneous data with unknown cluster information. In the first case, a joint learning approach where both individual graphs and a consensus graph are learned will be developed. In the second case, a unified framework that merges classical spectral clustering with graph signal smoothness will be developed for joint clustering and multi-view graph learning. The graph-learning algorithms will address some of the challenges encountered in gene regulatory network inference, such as non-Gaussian, nonlinear nature of gene expression data, changes in gene expression due to cell-cycle heterogeneity, and high sparsity due to low amounts of mRNA in individual cells. This project will provide interdisciplinary training to a diverse population of students at all levels. The research outcomes will be incorporated into a new online graduate course as part of the growing interest in data science. Finally, the proposed research will be incorporated into outreach efforts targeting K-12 female students and disseminated to the broader research community through publications, workshops and code sharing.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.