Related papers: Distributed methods for synchronization of orthogo…
Using graphs to model irregular information domains is an effective approach to deal with some of the intricacies of contemporary (network) data. A key aspect is how the data, represented as graph signals, depend on the topology of the…
Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization,…
Quantifying the similarity between two graphs is a fundamental algorithmic problem at the heart of many data analysis tasks for graph-based data. In this paper, we study the computational complexity of a family of similarity measures based…
A natural generalization of the recognition problem for a geometric graph class is the problem of extending a representation of a subgraph to a representation of the whole graph. A related problem is to find representations for multiple…
We consider orthogonal transformations of arbitrary square matrices to a form where all diagonal entries are equal. In our main results we treat the simultaneous transformation of two matrices and the symplectic orthogonal transformation of…
Given a family of nearly commuting symmetric matrices, we consider the task of computing an orthogonal matrix that nearly diagonalizes every matrix in the family. In this paper, we propose and analyze randomized joint diagonalization (RJD)…
We analyze the convergence of gradient-based optimization algorithms that base their updates on delayed stochastic gradient information. The main application of our results is to the development of gradient-based distributed optimization…
Randomized algorithms for very large matrix problems have received a great deal of attention in recent years. Much of this work was motivated by problems in large-scale data analysis, and this work was performed by individuals from many…
The field of dynamic graph algorithms aims at achieving a thorough understanding of real-world networks whose topology evolves with time. Traditionally, the focus has been on the classic sequential, centralized setting where the main…
The concept of a random process has been recently extended to graph signals, whereby random graph processes are a class of multivariate stochastic processes whose coefficients are matrices with a \textit{graph-topological} structure. The…
We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…
Subgraph densities have been defined, and served as basic tools, both in the case of graphons (limits of dense graph sequences) and graphings (limits of bounded-degree graph sequences). While limit objects have been described for the…
Graphs are fundamental objects that find widespread applications across computer science and beyond. Graph Theory has yielded deep insights about structural properties of various families of graphs, which are leveraged in the design and…
In this paper, based on the assumption that the object boundaries (e.g., buildings) from the over-view data should coincide with footprints of fa\c{c}ade 3D points generated from street-view photogrammetric images, we aim to address this…
While algebrisation constitutes a powerful technique in the design and analysis of centralised algorithms, to date there have been hardly any applications of algebraic techniques in the context of distributed graph algorithms. This work is…
Dynamic graph clustering aims to detect and track time-varying clusters in dynamic graphs, revealing the evolutionary mechanisms of complex real-world dynamic systems. Matrix factorization-based methods are promising approaches for this…
The angular synchronization problem aims to accurately estimate (up to a constant additive phase) a set of unknown angles $\theta_1, \dots, \theta_n\in[0, 2\pi)$ from $m$ noisy measurements of their offsets $\theta_i-\theta_j \;\mbox{mod}…
Simultaneous embedding is concerned with simultaneously representing a series of graphs sharing some or all vertices. This forms the basis for the visualization of dynamic graphs and thus is an important field of research. Recently there…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
Graph signal processing (GSP) provides a powerful framework for analyzing signals arising in a variety of domains. In many applications of GSP, multiple network structures are available, each of which captures different aspects of the same…