Related papers: Transport based Graph Kernels
Most graph kernels are an instance of the class of $\mathcal{R}$-Convolution kernels, which measure the similarity of objects by comparing their substructures. Despite their empirical success, most graph kernels use a naive aggregation of…
In graph analysis, a classic task consists in computing similarity measures between (groups of) nodes. In latent space random graphs, nodes are associated to unknown latent variables. One may then seek to compute distances directly in the…
Measuring similarity between complex objects is a fundamental task in many scientific fields. When objects are represented as graphs, graph similarity/distance measures offer a powerful framework for quantifying structural resemblance.…
Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph…
Tracking of moving objects is crucial to security systems and networks. Given a graph $G$, terminal vertices $s$ and $t$, and an integer $k$, the \textsc{Tracking Paths} problem asks whether there exists at most $k$ vertices, which if…
We analytically study proximity and distance properties of various kernels and similarity measures on graphs. This helps to understand the mathematical nature of such measures and can potentially be useful for recommending the adoption of…
Networks are widely used to model real-world systems and uncover their topological features. Network properties such as the degree distribution and shortest path length have been computed in numerous real-world networks, and most of them…
In this paper, we develop a new graph kernel, namely the Hierarchical Transitive-Aligned kernel, by transitively aligning the vertices between graphs through a family of hierarchical prototype graphs. Comparing to most existing…
We develop a statistical inference method for an optimal transport map between distributions on real numbers with uniform confidence bands. The concept of optimal transport (OT) is used to measure distances between distributions, and OT…
The current best practice for computing optimal transport (OT) is via entropy regularization and Sinkhorn iterations. This algorithm runs in quadratic time as it requires the full pairwise cost matrix, which is prohibitively expensive for…
The availability of graph data with node attributes that can be either discrete or real-valued is constantly increasing. While existing kernel methods are effective techniques for dealing with graphs having discrete node labels, their…
The graphlet kernel is a classical method in graph classification. It however suffers from a high computation cost due to the isomorphism test it includes. As a generic proxy, and in general at the cost of losing some information, this test…
In this paper we present a simple but powerful subgraph sampling primitive that is applicable in a variety of computational models including dynamic graph streams (where the input graph is defined by a sequence of edge/hyperedge insertions…
With the recent rise in the amount of structured data available, there has been considerable interest in methods for machine learning with graphs. Many of these approaches have been kernel methods, which focus on measuring the similarity…
We propose a learning framework for graph kernels, which is theoretically grounded on regularizing optimal transport. This framework provides a novel optimal transport distance metric, namely Regularized Wasserstein (RW) discrepancy, which…
One of the major challenges in applications related to social networks, computational biology, collaboration networks etc., is to efficiently search for similar patterns in their underlying graphs. These graphs are typically noisy and…
We investigate finding a map $g$ within a function class $G$ that minimises an Optimal Transport (OT) cost between a target measure $\nu$ and the image by $g$ of a source measure $\mu$. This is relevant when an OT map from $\mu$ to $\nu$…
Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and…
We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem. Then we propose a novel distance between two graphs, named…
(Directed) graphs with node attributes are a common type of data in various applications and there is a vast literature on developing metrics and efficient algorithms for comparing them. Recently, in the graph learning and optimization…