Related papers: Relations Between Adjacency and Modularity Graph P…
In this paper, we present a new metric distance for comparing two large graphs to find similarities and differences between them based on one of the most important graph structural properties, which is Node Adjacency Information, for all…
Convex clustering is a recent stable alternative to hierarchical clustering. It formulates the recovery of progressively coalescing clusters as a regularized convex problem. While convex clustering was originally designed for handling…
Correlation clustering is a widely studied framework for clustering based on pairwise similarity and dissimilarity scores, but its best approximation algorithms rely on impractical linear programming relaxations. We present faster…
The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the…
We study the blind centrality ranking problem, where our goal is to infer the eigenvector centrality ranking of nodes solely from nodal observations, i.e., without information about the topology of the network. We formalize these nodal…
Designing efficient, effective, and consistent metric clustering algorithms is a significant challenge attracting growing attention. Traditional approaches focus on the stability of cluster centers; unfortunately, this neglects the…
As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to…
Eigenvector continuation is a computational method that finds the extremal eigenvalues and eigenvectors of a Hamiltonian matrix with one or more control parameters. It does this by projection onto a subspace of eigenvectors corresponding to…
We introduce a concept of similarity between vertices of directed graphs. Let G_A and G_B be two directed graphs. We define a similarity matrix whose (i, j)-th real entry expresses how similar vertex j (in G_A) is to vertex i (in G_B. The…
Correlation clustering is a central topic in unsupervised learning, with many applications in ML and data mining. In correlation clustering, one receives as input a signed graph and the goal is to partition it to minimize the number of…
Edge expansion is a parameter indicating how well-connected a graph is. It is useful for designing robust networks, analysing random walks or information flow through a network and is an important notion in theoretical computer science.…
Existing graph matching methods typically assume that there are similar structures between graphs and they are matchable. However, these assumptions do not align with real-world applications. This work addresses a more realistic scenario…
Constructing the adjacency graph is fundamental to graph-based clustering. Graph learning in kernel space has shown impressive performance on a number of benchmark data sets. However, its performance is largely determined by the chosen…
Underpinning the success of deep learning is effective regularizations that allow a variety of priors in data to be modeled. For example, robustness to adversarial perturbations, and correlations between multiple modalities. However, most…
Random graphs defined by an occurrence probability that is invariant under node aggregation have been identified recently in the context of network renormalization. The invariance property requires that edges are drawn with a specific…
We show that correlation matrices with particular average and variance of the correlation coefficients have a notably restricted spectral structure. Applying geometric methods, we derive lower bounds for the largest eigenvalue and the…
Cluster synchronization in synthetic networks of coupled chaotic oscillators is investigated. It is found that despite the asymmetric nature of the network structure, a subset of the oscillators can be synchronized as a cluster while the…
Graphs are often used to model relationships between entities. The identification and visualization of clusters in graphs enable insight discovery in many application areas, such as life sciences and social sciences. Force-directed graph…
We consider a large class of random geometric graphs constructed from samples $\mathcal{X}_n = \{X_1,X_2,\ldots,X_n\}$ of independent, identically distributed observations of an underlying probability measure $\nu$ on a bounded domain…
Graph clustering has many important applications in computing, but due to growing sizes of graphs, even traditionally fast clustering methods such as spectral partitioning can be computationally expensive for real-world graphs of interest.…