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As graphs scale to billions of nodes and edges, graph Machine Learning workloads are constrained by the cost of multi-hop traversals over exponentially growing neighborhoods. While various system-level and algorithmic optimizations have…
We develop a framework for graph sparsification and sketching, based on a new tool, short cycle decomposition -- a decomposition of an unweighted graph into an edge-disjoint collection of short cycles, plus few extra edges. A simple…
Traffic flow forecasting is a critical spatio-temporal data mining task with wide-ranging applications in intelligent route planning and dynamic traffic management. Recent advancements in deep learning, particularly through Graph Neural…
We study random graphs with possibly different edge probabilities in the challenging sparse regime of bounded expected degrees. Unlike in the dense case, neither the graph adjacency matrix nor its Laplacian concentrate around their…
Analyzing massive data sets has been one of the key motivations for studying streaming algorithms. In recent years, there has been significant progress in analysing distributions in a streaming setting, but the progress on graph problems…
Graph-based recommendation systems are effective at modeling collaborative patterns but often suffer from two limitations: overreliance on low-pass filtering, which suppresses user-specific signals, and omission of sequential dynamics in…
In this work, we are interested in adaptive and distributed estimation of graph filters from streaming data. We formulate this problem as a consensus estimation problem over graphs, which can be addressed with diffusion LMS strategies. Most…
Jumping connections enable Graph Convolutional Networks (GCNs) to overcome over-smoothing, while graph sparsification reduces computational demands by selecting a sub-matrix of the graph adjacency matrix during neighborhood aggregation.…
A graph convolutional network (GCN) employs a graph filtering kernel tailored for data with irregular structures. However, simply stacking more GCN layers does not improve performance; instead, the output converges to an uninformative…
We study stochastic graph optimization problems in a novel distributed setting. As in the standard centralized setting, a random subgraph $G^*$ of a known base graph $G$ is realized by including each edge $e$ independently with a known…
Graph Neural Networks (GNNs) are the subject of intense focus by the machine learning community for problems involving relational reasoning. GNNs can be broadly divided into spatial and spectral approaches. Spatial approaches use a form of…
We consider effective preconditioners for solving Laplacians of general weighted graphs. Theoretically, spectral sparsifiers (SSs) provide preconditioners of optimal computational complexity. However, they are not easy to use for real-world…
Boundary detection has long been a fundamental tool for image processing and computer vision, supporting the analysis of static and time-varying data. In this work, we built upon the theory of Graph Signal Processing to propose a novel…
Spectral sparsification is a technique that is used to reduce the number of non-zero entries in a positive semidefinite matrix with little changes to its spectrum. In particular, the main application of spectral sparsification is to…
Uncertain graphs are prevalent in several applications including communications systems, biological databases and social networks. The ever increasing size of the underlying data renders both graph storage and query processing extremely…
Graphs possess exotic features like variable size and absence of natural ordering of the nodes that make them difficult to analyze and compare. To circumvent this problem and learn on graphs, graph feature representation is required. A good…
This work presents inGRASS, a novel algorithm designed for incremental spectral sparsification of large undirected graphs. The proposed inGRASS algorithm is highly scalable and parallel-friendly, having a nearly-linear time complexity for…
We present LaplaceGNN, a novel self-supervised graph learning framework that bypasses the need for negative sampling by leveraging spectral bootstrapping techniques. Our method integrates Laplacian-based signals into the learning process,…
Real-world data is often represented through the relationships between data samples, forming a graph structure. In many applications, it is necessary to learn this graph structure from the observed data. Current graph learning research has…
For any undirected and weighted graph $G=(V,E,w)$ with $n$ vertices and $m$ edges, we call a sparse subgraph $H$ of $G$, with proper reweighting of the edges, a $(1+\varepsilon)$-spectral sparsifier if \[…