Related papers: Path-Based Distance for Street Map Comparison
Recent years have witnessed a tremendous growth using topological summaries, especially the persistence diagrams (encoding the so-called persistent homology) for analyzing complex shapes. Intuitively, persistent homology maps a potentially…
We consider the following problem : we have a high-resolution street network of a given city, and low-resolution measurements of traffic within this city. We want to associate to each measurement the set of streets corresponding to the…
In many real-world applications data come as discrete metric spaces sampled around 1-dimensional filamentary structures that can be seen as metric graphs. In this paper we address the metric reconstruction problem of such filamentary…
Random geometric graphs are a popular choice for a latent points generative model for networks. Their definition is based on a sample of $n$ points $X_1,X_2,\cdots,X_n$ on the Euclidean sphere~$\mathbb{S}^{d-1}$ which represents the latent…
Recent urbanization has coincided with the enrichment of geotagged data, such as street view and point-of-interest (POI). Region embedding enhanced by the richer data modalities has enabled researchers and city administrators to understand…
Network embedding maps the nodes of a given network into a low-dimensional space such that the semantic similarities among the nodes can be effectively inferred. Most existing approaches use inner-product of node embedding to measure the…
Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph.…
The space of graphs is often characterised by a non-trivial geometry, which complicates learning and inference in practical applications. A common approach is to use embedding techniques to represent graphs as points in a conventional…
Map matching is a common preprocessing step for analysing vehicle trajectories. In the theory community, the most popular approach for map matching is to compute a path on the road network that is the most spatially similar to the…
The graph edit distance is used for comparing graphs in various domains. Due to its high computational complexity it is primarily approximated. Widely-used heuristics search for an optimal assignment of vertices based on the distance…
Graph similarity computation aims to predict a similarity score between one pair of graphs to facilitate downstream applications, such as finding the most similar chemical compounds similar to a query compound or Fewshot 3D Action…
We study a map matching problem, the task of finding in an embedded graph a path that has low distance to a given curve in R^2. The Fr\'echet distance is a common measure for this problem. Efficient methods exist to compute the best path…
Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not…
Mapper graphs are widely used tools in topological data analysis and visualization. They can be understood as discrete approximations of Reeb graphs, providing insight into the shape and connectivity of complex data. Given a…
The application of the network approach to the urban case poses several questions in terms of how to deal with metric distances, what kind of graph representation to use, what kind of measures to investigate, how to deepen the correlation…
We introduce a measure of {\em greedy connectivity} for geographical networks (graphs embedded in space) and where the search for connecting paths relies only on local information, such as a node's location and that of its neighbors.…
An embedding is a mapping from a set of nodes of a network into a real vector space. Embeddings can have various aims like capturing the underlying graph topology and structure, node-to-node relationship, or other relevant information about…
Graph matching aims to establish correspondences between vertices of graphs such that both the node and edge attributes agree. Various learning-based methods were recently proposed for finding correspondences between image key points based…
Graphs are used in almost every scientific discipline to express relations among a set of objects. Algorithms that compare graphs, and output a closeness score, or a correspondence among their nodes, are thus extremely important. Despite…
Consider a finite directed graph without cycles in which the arrows are weighted. We present an algorithm for the computation of a new distance, called path-length-weighted distance, which has proven useful for graph analysis in the context…