Related papers: A random walk on image patches

Learning a metric of natural image patches is an important tool for analyzing images. An efficient means is to train a deep network to map an image patch to a vector space, in which the Euclidean distance reflects patch similarity. Previous…

In this work we introduce a statistical framework in order to analyze the spatial redundancy in natural images. This notion of spatial redundancy must be defined locally and thus we give some examples of functions (auto-similarity and…

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…

Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…

Graph clustering is an important technique to understand the relationships between the vertices in a big graph. In this paper, we propose a novel random-walk-based graph clustering method. The proposed method restricts the reach of the…

Convolutional layers within graph neural networks operate by aggregating information about local neighbourhood structures; one common way to encode such substructures is through random walks. The distribution of these random walks evolves…

Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…

Recently, weighted patch representation has been widely studied for alleviating the impact of background information included in bounding box to improve visual tracking results. However, existing weighted patch representation models…

This paper is about the construction of displacement interpolations on a discrete metric graph. Our approach is based on the approximation of any optimal transport problem whose cost function is a distance on a discrete graph by a sequence…

We investigate searching efficiency of different kinds of random walk on complex networks which rely on local information and one-step memory. For the studied navigation strategies we obtained theoretical and numerical values for the graph…

We consider the problem of inferring meaningful spatial information in networks from incomplete information on the connection intensity between the nodes of the network. We consider two spatially distributed networks: a population migration…

We first explore methods for approximating the commute time and Katz score between a pair of nodes. These methods are based on the approach of matrices, moments, and quadrature developed in the numerical linear algebra community. They rely…

In this paper, we consider continuous-time quantum walks (CTQWs) on finite graphs determined by the Laplacian matrices. By introducing fully interconnected graph decomposition of given graphs, we show a decomposition method for the…

We present a method to approximate pairwise distance on a graph, having an amortized sub-linear complexity in its size. The proposed method follows the so called heat method due to Crane et al. The only additional input are the values of…

We present a new algorithm for community detection. The algorithm uses random walks to embed the graph in a space of measures, after which a modification of $k$-means in that space is applied. The algorithm is therefore fast and easily…

Graph neural networks (GNNs) achieve strong performance on graph learning tasks, but training on large-scale networks remains computationally challenging. Transferability results show that GNNs with fixed weights can generalize from smaller…

Socioeconomic segregation is considered one of the main factors behind the emergence of large-scale inequalities in urban areas, and its characterisation is an active area of research in urban studies. There are currently many available…

Walk on Spheres algorithms leverage properties of Brownian Motion to create Monte Carlo estimates of solutions to a class of elliptic partial differential equations. We propose a new caching strategy which leverages the continuity of paths…

Graphs are widely used in various fields of computer science. They have also found application in unrelated areas, leading to a diverse range of problems. These problems can be modeled as relationships between entities in various contexts,…

A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…