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

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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.