Product Graph Learning from Multi-domain Data with Sparsity and Rank Constraints

In this paper, we focus on learning product graphs from multi-domain data. We assume that the product graph is formed by the Cartesian product of two smaller graphs, which we refer to as graph factors. We pose the product graph learning problem as the problem of estimating the graph factor Laplacian matrices. To capture local interactions in data, we seek sparse graph factors and assume a smoothness model for data. We propose an efficient iterative solver for learning sparse product graphs from data. We then extend this solver to infer multi-component graph factors with applications to product graph clustering by imposing rank constraints on the graph Laplacian matrices. Although working with smaller graph factors is computationally more attractive, not all graphs may readily admit an exact Cartesian product factorization. To this end, we propose efficient algorithms to approximate a graph by a nearest Cartesian product of two smaller graphs. The efficacy of the developed framework is demonstrated using several numerical experiments on synthetic data and real data.

Dr-COVID: Graph Neural Networks for SARS-CoV-2 Drug Repurposing

The 2019 novel coronavirus (SARS-CoV-2) pandemic has resulted in more than a million deaths, high morbidities, and economic distress worldwide. There is an urgent need to identify medications that would treat and prevent novel diseases like the 2019 coronavirus disease (COVID-19). Drug repurposing is a promising strategy to discover new medical indications of the existing approved drugs due to several advantages in terms of the costs, safety factors, and quick results compared to new drug design and discovery. In this work, we explore computational data-driven methods for drug repurposing and propose a dedicated graph neural network (GNN) based drug repurposing model, called Dr-COVID. Although we analyze the predicted drugs in detail for COVID-19, the model is generic and can be used for any novel diseases. We construct a four-layered heterogeneous graph to model the complex interactions between drugs, diseases, genes, and anatomies. We pose drug repurposing as a link prediction problem. Specifically, we design an encoder based on the scalable inceptive graph neural network (SIGN) to generate embeddings for all the nodes in the four-layered graph and propose a quadratic norm scorer as a decoder to predict treatment for a disease. We provide a detailed analysis of the 150 potential drugs (such as Dexamethasone, Ivermectin) predicted by Dr-COVID for COVID-19 from different pharmacological classes (e.g., corticosteroids, antivirals, antiparasitic). Out of these 150 drugs, 46 drugs are currently in clinical trials. Dr-COVID is evaluated in terms of its prediction performance and its ability to rank the known treatment drugs for diseases as high as possible. For a majority of the diseases, Dr-COVID ranks the actual treatment drug in the top 15.

Multiview Variational Graph Autoencoders for Canonical Correlation Analysis

We present a novel multiview canonical correlation analysis model based on a variational approach. This is the first nonlinear model that takes into account the available graph-based geometric constraints while being scalable for processing large scale datasets with multiple views. It is based on an autoencoder architecture with graph convolutional neural network layers. We experiment with our approach on classification, clustering, and recommendation tasks on real datasets. The algorithm is competitive with state-of-the-art multiview representation learning techniques.

Graph Learning for Clustering Multi-view Data

In this paper, we focus on graph learning from multi-view data of shared entities for clustering. We can explain interactions between the entities in multi-view data using a multi-layer graph with a common vertex set representing the shared entities. The edges on different layers capture the relationships of the entities. Assuming a smoothness data model, we estimate the graph Laplacian matrices of the individual graph layers by constraining their ranks to obtain multi-component graph layers for clustering. We also learn low-dimensional node embeddings, common to all the views, that assimilate the complementary information present in the views. We propose an efficient solver based on alternating minimization to solve the proposed multi-layer multi-component graph learning problem. Numerical experiments on synthetic and real datasets demonstrate that the proposed algorithm outperforms state-of-the-art multi-view clustering techniques.

Learning Sparse Graphs Under Smoothness Prior

In this paper, we are interested in learning the underlying graph structure behind training data. Solving this basic problem is essential to carry out any graph signal processing or machine learning task. To realize this, we assume that the data is smooth with respect to the graph topology, and we parameterize the graph topology using an edge sampling function. That is, the graph Laplacian is expressed in terms of a sparse edge selection vector, which provides an explicit handle to control the sparsity level of the graph. We solve the sparse graph learning problem given some training data in both the noiseless and noisy settings. Given the true smooth data, the posed sparse graph learning problem can be solved optimally and is based on simple rank ordering. Given the noisy data, we show that the joint sparse graph learning and denoising problem can be simplified to designing only the sparse edge selection vector, which can be solved using convex optimization.