Related papers: Drawing Big Graphs using Spectral Sparsification
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…
The spectral theory of graphs provides a bridge between classical signal processing and the nascent field of graph signal processing. In this paper, a spectral graph analogy to Heisenberg's celebrated uncertainty principle is developed.…
Random graph models are used to describe the complex structure of real-world networks in diverse fields of knowledge. Studying their behavior and fitting properties are still critical challenges, that in general, require model specific…
Graph neural networks (GNNs) have attracted considerable attention from the research community. It is well established that GNNs are usually roughly divided into spatial and spectral methods. Despite that spectral GNNs play an important…
The Kadison-Singer Conjecture, as proved by Marcus, Spielman, and Srivastava (MSS) [Ann. Math. 182, 327-350 (2015)], has been informally thought of as a strengthening of Batson, Spielman, and Srivastava's theorem that every undirected graph…
Image classification is a challenging problem for computer in reality. Large numbers of methods can achieve satisfying performances with sufficient labeled images. However, labeled images are still highly limited for certain image…
We initiate the study of dynamic algorithms for graph sparsification problems and obtain fully dynamic algorithms, allowing both edge insertions and edge deletions, that take polylogarithmic time after each update in the graph. Our three…
We prove that every graph has a spectral sparsifier with a number of edges linear in its number of vertices. As linear-sized spectral sparsifiers of complete graphs are expanders, our sparsifiers of arbitrary graphs can be viewed as…
Online social network services provide a platform for human social interactions. Nowadays, many kinds of online interactions generate large-scale social network data. Network analysis helps to mine knowledge and pattern from the…
Detailed network models of social, biological and other complex systems are often dense, which increases their computational complexity in simulations and analysis. To address this challenge, graph sparsification is used to remove edges…
We introduce a new measure of complexity (called spectral complexity) for directed graphs. We start with splitting of the directed graph into its recurrent and non-recurrent parts. We define the spectral complexity metric in terms of the…
As large-scale graphs become increasingly more prevalent, it poses significant computational challenges to process, extract and analyze large graph data. Graph coarsening is one popular technique to reduce the size of a graph while…
The recent surge in contrast-based graph self-supervised learning has prominently featured an intensified exploration of spectral cues. Spectral augmentation, which involves modifying a graph's spectral properties such as eigenvalues or…
Graph comparison is a fundamental operation in data mining and information retrieval. Due to the combinatorial nature of graphs, it is hard to balance the expressiveness of the similarity measure and its scalability. Spectral analysis…
Graph Neural Networks (GNNs) have achieved state-of-the-art performance in solving graph classification tasks. However, most GNN architectures aggregate information from all nodes and edges in a graph, regardless of their relevance to the…
In this paper, we revisit spectral sparsification for sums of arbitrary positive semidefinite (PSD) matrices. Concretely, for any collection of PSD matrices $\mathcal{A} = \{A_1, A_2, \ldots, A_r\} \subset \mathbb{R}^{n \times n}$, given…
Spectral graph convolutional networks are generalizations of standard convolutional networks for graph-structured data using the Laplacian operator. A common misconception is the instability of spectral filters, i.e. the impossibility to…
We study the problem of compressing a weighted graph $G$ on $n$ vertices, building a "sketch" $H$ of $G$, so that given any vector $x \in \mathbb{R}^n$, the value $x^T L_G x$ can be approximated up to a multiplicative $1+\epsilon$ factor…
As real-world graphs expand in size, larger GNN models with billions of parameters are deployed. High parameter count in such models makes training and inference on graphs expensive and challenging. To reduce the computational and memory…
We introduce an unsupervised graph embedding that trades off local node similarity and connectivity, and global structure. The embedding is based on a generalized graph Laplacian, whose eigenvectors compactly capture both network structure…