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Graph sparsification is to approximate an arbitrary graph by a sparse graph and is useful in many applications, such as simplification of social networks, least squares problems, numerical solution of symmetric positive definite linear…
In this work, we establish theoretical and practical connections between vertex indexing for sparse graph/network compression and matrix ordering for sparse matrix-vector multiplication and variable elimination. We present a fundamental…
We propose a Greedy strategy to solve the problem of Graph Cut, called GGC. It starts from the state where each data sample is regarded as a cluster and dynamically merges the two clusters which reduces the value of the global objective…
Clustering a graph means identifying internally dense subgraphs which are only sparsely interconnected. Formalizations of this notion lead to measures that quantify the quality of a clustering and to algorithms that actually find…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…
To better understand the overlapping modular organization of large networks with respect to flow, here we introduce the map equation for overlapping modules. In this information-theoretic framework, we use the correspondence between…
In recent years, Graph Convolutional Networks (GCNs) have gained popularity for their exceptional ability to process graph-structured data. Existing GCN-based approaches typically employ a shallow model architecture due to the…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
Graph summarization via node grouping is a popular method to build concise graph representations by grouping nodes from the original graph into supernodes and encoding edges into superedges such that the loss of adjacency information is…
Given a graph G and the desired size k in bits, how can we summarize G within k bits, while minimizing the information loss? Large-scale graphs have become omnipresent, posing considerable computational challenges. Analyzing such large…
For various purposes and, in particular, in the context of data compression, a graph can be examined at three levels. Its structure can be described as the unlabeled version of the graph; then the labeling of its structure can be added; and…
Graph coarsening is a widely used dimensionality reduction technique for approaching large-scale graph machine learning problems. Given a large graph, graph coarsening aims to learn a smaller-tractable graph while preserving the properties…
We continue the line of research on graph compression started with WebGraph, but we move our focus to the compression of social networks in a proper sense (e.g., LiveJournal): the approaches that have been used for a long time to compress…
Graph neural networks (GNNs) have achieved great success on various tasks and fields that require relational modeling. GNNs aggregate node features using the graph structure as inductive biases resulting in flexible and powerful models.…
To cope with the complexity of large networks, a number of dimensionality reduction techniques for graphs have been developed. However, the extent to which information is lost or preserved when these techniques are employed has not yet been…
Representing patterns as labeled graphs is becoming increasingly common in the broad field of computational intelligence. Accordingly, a wide repertoire of pattern recognition tools, such as classifiers and knowledge discovery procedures,…
The design of good heuristics or approximation algorithms for NP-hard combinatorial optimization problems often requires significant specialized knowledge and trial-and-error. Can we automate this challenging, tedious process, and learn the…
Graph pattern matching, which aims to discover structural patterns in graphs, is considered one of the most fundamental graph mining problems in many real applications. Despite previous efforts, existing systems face two main challenges.…
We consider the problem of sampling from data defined on the nodes of a weighted graph, where the edge weights capture the data correlation structure. As shown recently, using spectral graph theory one can define a cut-off frequency for the…
Spatial graphs are particular graphs for which the nodes are localized in space (e.g., public transport network, molecules, branching biological structures). In this work, we consider the problem of spatial graph reduction, that aims to…