相关论文: Solving Jigsaw Puzzles By the Graph Connection Lap…

Graph disaggregation is a technique used to address the high cost of computation for power law graphs on parallel processors. The few high-degree vertices are broken into multiple small-degree vertices, in order to allow for more efficient…

We consider apictorial edge-matching puzzles, in which the goal is to arrange a collection of puzzle pieces with colored edges so that the colors match along the edges of adjacent pieces. We devise an algebraic representation for this…

Spectral geometric methods have brought revolutionary changes to the field of geometry processing. Of particular interest is the study of the Laplacian spectrum as a compact, isometry and permutation-invariant representation of a shape.…

In this paper, we explore methods of complicating self-supervised tasks for representation learning. That is, we do severe damage to data and encourage a network to recover them. First, we complicate each of three powerful self-supervised…

Boundary detection has long been a fundamental tool for image processing and computer vision, supporting the analysis of static and time-varying data. In this work, we built upon the theory of Graph Signal Processing to propose a novel…

Relaxation processes driven by a Laplacian matrix can be found in many real-world big-data systems, for example, in search engines on the World-Wide-Web and the dynamic load balancing protocols in mesh networks. To numerically implement…

The Laplacian matrix and its pseudo-inverse for a strongly connected directed graph is fundamental in computing many properties of a directed graph. Examples include random-walk centrality and betweenness measures, average hitting and…

A divide-and-conquer based approach for computing the Moore-Penrose pseudo-inverse of the combinatorial Laplacian matrix $(\bb L^+)$ of a simple, undirected graph is proposed. % The nature of the underlying sub-problems is studied in detail…

The graph reconstruction conjecture states that all graphs on at least three vertices are determined up to isomorphism by their deck. In this paper, a general framework for this problem is proposed to simply explain the reconstruction of…

In this note, we study Laplacians on graphs for which connectivity within certain subgraphs tends to infinity. Our main focus are graphs sharing a common node set on which edge weights within certain clusters grow to infinity. As…

We present a simple spectral approach to the well-studied constrained clustering problem. It captures constrained clustering as a generalized eigenvalue problem with graph Laplacians. The algorithm works in nearly-linear time and provides…

Due to the limited resources and the scale of the graphs in modern datasets, we often get to observe a sampled subgraph of a larger original graph of interest, whether it is the worldwide web that has been crawled or social connections that…

We propose a novel distributed algorithm to cluster graphs. The algorithm recovers the solution obtained from spectral clustering without the need for expensive eigenvalue/vector computations. We prove that, by propagating waves through the…

The aim of this paper is to propose a novel framework to infer the sheaf Laplacian, including the topology of a graph and the restriction maps, from a set of data observed over the nodes of a graph. The proposed method is based on sheaf…

Generic deep learning (DL) networks for image restoration like denoising and interpolation lack mathematical interpretability, require voluminous training data to tune a large parameter set, and are fragile in the face of covariate shift.…

The graph partition problem is the problem of partitioning the vertex set of a graph into a fixed number of sets of given sizes such that the sum of weights of edges joining different sets is optimized. In this paper we simplify a known…

In graph signal processing, data samples are associated to vertices on a graph, while edge weights represent similarities between those samples. We propose a convex optimization problem to learn sparse well connected graphs from data. We…

This paper investigates the use of methods from partial differential equations and the Calculus of variations to study learning problems that are regularized using graph Laplacians. Graph Laplacians are a powerful, flexible method for…

For a connected weighted hypergraph, we give a randomized almost-linear-time solver for the Poisson problem for the cut-based hypergraph Laplacian in the natural input size $P=\sum_{e\in E}|e|$, the sum of hyperedge sizes. For every fixed…

The angular synchronization problem of estimating a set of unknown angles from their known noisy pairwise differences arises in various applications. It can be reformulated as a optimization problem on graphs involving the graph Laplacian…