Related papers: Mathematical Foundations of the GraphBLAS

We present a general graph-based modeling abstraction for optimization that we call an OptiGraph. Under this abstraction, any optimization problem is treated as a hierarchical hypergraph in which nodes represent optimization subproblems and…

Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not…

Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques…

The value of graph-based big data can be unlocked by exploring the topology and metrics of the networks they represent, and the computational approaches to this exploration take on many forms. The use-case of performing global computations…

Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i)…

In many ways, graphs are the main modality of data we receive from nature. This is due to the fact that most of the patterns we see, both in natural and artificial systems, are elegantly representable using the language of graph structures.…

Graph is powerful for representing various types of real-world data. The topology (edges' presence) and edges' features of a graph decides the message passing mechanism among vertices within the graph. While most existing approaches only…

Graph databases have become essential tools for managing complex and interconnected data, which is common in areas like social networks, bioinformatics, and recommendation systems. Unlike traditional relational databases, graph databases…

Graphlets are induced subgraphs of a large network and are important for understanding and modeling complex networks. Despite their practical importance, graphlets have been severely limited to applications and domains with relatively small…

Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including…

Important graph mining problems such as Clustering are computationally demanding. To significantly accelerate these problems, we propose ProbGraph: a graph representation that enables simple and fast approximate parallel graph mining with…

On the Euclidean domains of classical signal processing, linking of signal samples to the underlying coordinate structure is straightforward. While graph adjacency matrices totally define the quantitative associations among the underlying…

Data processing systems impose multiple views on data as it is processed by the system. These views include spreadsheets, databases, matrices, and graphs. Associative arrays unify and simplify these different approaches into a common…

Filters are fundamental in extracting information from data. For time series and image data that reside on Euclidean domains, filters are the crux of many signal processing and machine learning techniques, including convolutional neural…

Large multimodal models (LMMs) have exhibited proficiencies across many visual tasks. Although numerous well-known benchmarks exist to evaluate model performance, they increasingly have insufficient headroom. As such, there is a pressing…

Finding vertex-to-vertex correspondences in real-world graphs is a challenging task with applications in a wide variety of domains. Structural matching based on graphs connectivities has attracted considerable attention, while the…

Networks or graphs are widely used across the sciences to represent relationships of many kinds. igraph (https://igraph.org) is a general-purpose software library for graph construction, analysis, and visualisation, combining fast and…

Graphs are essential representations of many real-world data such as social networks. Recent years have witnessed the increasing efforts made to extend the neural network models to graph-structured data. These methods, which are usually…

Sparse matrix computations are ubiquitous in scientific computing. With the recent interest in scientific machine learning, it is natural to ask how sparse matrix computations can leverage neural networks (NN). Unfortunately, multi-layer…

In the Matrix approach to graph transformation we represent simple digraphs and rules with Boolean matrices and vectors, and the rewriting is expressed using Boolean operators only. In previous works, we developed analysis techniques…