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Graph representation learning aims to effectively encode high-dimensional sparse graph-structured data into low-dimensional dense vectors, which is a fundamental task that has been widely studied in a range of fields, including machine…
Graph neural networks (GNNs) work well when the graph structure is provided. However, this structure may not always be available in real-world applications. One solution to this problem is to infer a task-specific latent structure and then…
Spectral graph sparsification aims to find ultra-sparse subgraphs whose Laplacian matrix can well approximate the original Laplacian eigenvalues and eigenvectors. In recent years, spectral sparsification techniques have been extensively…
In this paper we present an iterative method, inspired by the inverse iteration with shift technique of finite linear algebra, designed to find the eigenvalues and eigenfunctions of the Laplacian with homogeneous Dirichlet boundary…
Dynamic graph representation learning is a task to learn node embeddings over dynamic networks, and has many important applications, including knowledge graphs, citation networks to social networks. Graphs of this type are usually…
This work deals with approximate solution of generalized eigenvalue problem with coefficient matrix that is an affine function of d-parameters. The coefficient matrix is assumed to be symmetric positive definite and spectrally equivalent to…
It is a key to construct a similarity graph in graph-oriented subspace learning and clustering. In a similarity graph, each vertex denotes a data point and the edge weight represents the similarity between two points. There are two popular…
Several fundamental tasks in data science rely on computing an extremal eigenspace of size $r \ll n$, where $n$ is the underlying problem dimension. For example, spectral clustering and PCA both require the computation of the leading…
The integration of graphs with Goal-conditioned Hierarchical Reinforcement Learning (GCHRL) has recently gained attention, as intermediate goals (subgoals) can be effectively sampled from graphs that naturally represent the overall task…
Self-supervised learning on graphs has recently drawn a lot of attention due to its independence from labels and its robustness in representation. Current studies on this topic mainly use static information such as graph structures but…
Regularization is often used in high-dimensional regression settings to generate a sparse model, which can save tremendous computing resources and identify predictors that are most strongly associated with the response. When the predictors…
We are interested in multilayer graph clustering, which aims at dividing the graph nodes into categories or communities. To do so, we propose to learn a clustering-friendly embedding of the graph nodes by solving an optimization problem…
Spectral methods which represent data points by eigenvectors of kernel matrices or graph Laplacian matrices have been a primary tool in unsupervised data analysis. In many application scenarios, parametrizing the spectral embedding by a…
Complex time-varying networks are prominent models for a wide variety of spatiotemporal phenomena. The functioning of networks depends crucially on their connectivity, yet reliable techniques for learning communities in time-evolving…
We propose a supervised learning approach for predicting an underlying graph from a set of graph signals. Our approach is based on linear regression. In the linear regression model, we predict edge-weights of a graph as the output, given a…
The random walker (RW) algorithm is used for both image segmentation and registration, and possesses several useful properties that make it popular in medical imaging, such as being globally optimizable, allowing user interaction, and…
Attempting to fully exploit the rich information of topological structure and node features for attributed graph, we introduce self-supervised learning mechanism to graph representation learning and propose a novel Self-supervised Consensus…
We show theoretically and empirically that the linear Transformer, when applied to graph data, can implement algorithms that solve canonical problems such as electric flow and eigenvector decomposition. The Transformer has access to…
Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately. Such explorations on Riemannian manifolds, on the other hand, are relatively new, limited, and challenging. This is because of the…
Accurate feature matching and correspondence in endoscopic images play a crucial role in various clinical applications, including patient follow-up and rapid anomaly localization through panoramic image generation. However, developing…