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The inference and training stages of Graph Neural Networks (GNNs) are often dominated by the time required to compute a long sequence of matrix multiplications between the sparse graph adjacency matrix and its embedding. To accelerate these…
The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…
We revisit the probabilistic construction of sparse random matrices where each column has a fixed number of nonzeros whose row indices are drawn uniformly at random with replacement. These matrices have a one-to-one correspondence with the…
We study the localization of a cluster of activated vertices in a graph, from adaptively designed compressive measurements. We propose a hierarchical partitioning of the graph that groups the activated vertices into few partitions, so that…
We study the family of intersection graphs of low density objects in low dimensional Euclidean space. This family is quite general, and includes planar graphs. We prove that such graphs have small separators. Next, we present efficient…
This paper addresses matrix approximation problems for matrices that are large, sparse and/or that are representations of large graphs. To tackle these problems, we consider algorithms that are based primarily on coarsening techniques,…
Artificial neural networks are prone to being fooled by carefully perturbed inputs which cause an egregious misclassification. These \textit{adversarial} attacks have been the focus of extensive research. Likewise, there has been an…
Finding the graphs that are most similar to a query graph in a large database is a common task with various applications. A widely-used similarity measure is the graph edit distance, which provides an intuitive notion of similarity and…
Sparse graphs built by sparse representation has been demonstrated to be effective in clustering high-dimensional data. Albeit the compelling empirical performance, the vanilla sparse graph ignores the geometric information of the data by…
Neighborhood selection is a widely used method used for estimating the support set of sparse precision matrices, which helps determine the conditional dependence structure in undirected graphical models. However, reporting only point…
Statistical analysis of large and sparse graphs is a challenging problem in data science due to the high dimensionality and nonlinearity of the problem. This paper presents a fast and scalable algorithm for partitioning such graphs into…
This paper proposes a compression framework for adjacency matrices of weighted graphs based on graph filter banks. Adjacency matrices are widely used mathematical representations of graphs and are used in various applications in signal…
The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…
Nowadays, data is represented by vectors. Retrieving those vectors, among millions and billions, that are similar to a given query is a ubiquitous problem, known as similarity search, of relevance for a wide range of applications.…
We pursue a study of the Generalized Demand Matching problem, a common generalization of the $b$-Matching and Knapsack problems. Here, we are given a graph with vertex capacities, edge profits, and asymmetric demands on the edges. The goal…
In the paper, we consider the problem of link prediction in time-evolving graphs. We assume that certain graph features, such as the node degree, follow a vector autoregressive (VAR) model and we propose to use this information to improve…
In graph sparsification, the goal has almost always been of {global} nature: compress a graph into a smaller subgraph ({sparsifier}) that maintains certain features of the original graph. Algorithms can then run on the sparsifier, which in…
Graph Sparsification aims at compressing large graphs into smaller ones while preserving important characteristics of the input graph. In this work we study Vertex Sparsifiers, i.e., sparsifiers whose goal is to reduce the number of…
Local graph clustering is an important algorithmic technique for analysing massive graphs, and has been widely applied in many research fields of data science. While the objective of most (local) graph clustering algorithms is to find a…
Graph sparsification is a powerful tool to approximate an arbitrary graph and has been used in machine learning over homogeneous graphs. In heterogeneous graphs such as knowledge graphs, however, sparsification has not been systematically…