Motivation Elucidating the topology of gene regulatory networks (GRNs) from large single-cell RNA sequencing (scRNAseq) datasets, while effectively capturing its inherent cell-cycle heterogeneity and dropouts, is currently one of the most pressing problems in computational systems biology. Recently, graph learning (GL) approaches based on graph signal processing (GSP) have been developed to infer graph topology from signals defined on graphs. However, existing GL methods are not suitable for learning signed graphs, a characteristic feature of GRNs, which are capable of accounting for both activating and inhibitory relationships in the gene network. They are also incapable of handling high proportion of zero values present in the single cell datasets. Results To this end, we propose a novel signed GL approach, scSGL, that learns GRNs based on the assumption of smoothness and non-smoothness of gene expressions over activating and inhibitory edges, respectively. scSGL is then extended with kernels to account for non-linearity of co-expression and for effective handling of highly occurring zero values. The proposed approach is formulated as a non-convex optimization problem and solved using an efficient ADMM framework. Performance assessment using simulated datasets demonstrates the superior performance of kernelized scSGL over existing state of the art methods in GRN recovery. The performance of scSGL is further investigated using human and mouse embryonic datasets. Availability and Implementation The scSGL code and analysis scripts are available on https://github.com/Single-Cell-Graph-Learning/scSGL. Supplementary information Supplementary data are available at Bioinformatics online.
Networks are useful representations of many systems with interacting entities, such as social, biological and physical systems. Characterizing the meso-scale organization, i.e. the community structure, is an important problem in network science. Community detection aims to partition the network into sets of nodes that are densely connected internally but sparsely connected to other dense sets of nodes. Current work on community detection mostly focuses on static networks. However, many real world networks are dynamic, i.e. their structure and properties change with time, requiring methods for dynamic community detection. In this paper, we propose a new stochastic block model (SBM) for modeling the evolution of community membership. Unlike existing SBMs, the proposed model allows each community to evolve at a different rate. This new model is used to derive a maximum a posteriori estimator for community detection, which can be written as a constrained spectral clustering problem. In particular, the transition probabilities for each community modify the graph adjacency matrix at each time point. This formulation provides a relationship between statistical network inference and spectral clustering for dynamic networks. The proposed method is evaluated on both simulated and real dynamic networks.
Characterizing the underlying topology of gene regulatory networks is one of the fundamental problems of systems biology. Ongoing developments in high throughput sequencing technologies has made it possible to capture the expression of thousands of genes at the single cell resolution. However, inherent cellular heterogeneity and high sparsity of the single cell datasets render void the application of regular Gaussian assumptions for constructing gene regulatory networks. Additionally, most algorithms aimed at single cell gene regulatory network reconstruction, estimate a single network ignoring group-level (cell-type) information present within the datasets. To better characterize single cell gene regulatory networks under different but related conditions we propose the joint estimation of multiple networks using multiview graph learning (mvGL). The proposed method is developed based on recent works in graph signal processing (GSP) for graph learning, where graph signals are assumed to be smooth over the unknown graph structure. Graphs corresponding to the different datasets are regularized to be similar to each other through a learned consensus graph. We further kernelize mvGL with the kernel selected to suit the structure of single cell data. An efficient algorithm based on prox-linear block coordinate descent is used to optimize mvGL. We study the performance of mvGL using synthetic data generated with a diverse set of parameters. We further show that mvGL successfully identifies well-established regulators in a mouse embryonic stem cell differentiation study and a cancer clinical study of medulloblastoma.
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