Related papers: Tagged barcodes for the topological analysis of gr…
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…
A topological approach to the study of genetic recombination, based on persistent homology, was introduced by Chan, Carlsson, and Rabad\'an in 2013. This associates a sequence of signatures called barcodes to genomic data sampled from an…
This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information. We model a directed graph as a finite set of observations from a diffusion on a manifold endowed with a vector field.…
In this paper, we propose a scalable and highly efficient index structure for the reachability problem over graphs. We build on the well-known node interval labeling scheme where the set of vertices reachable from a particular node is…
Extended persistence is a technique from topological data analysis to obtain global multiscale topological information from a graph. This includes information about connected components and cycles that are captured by the so-called…
The interface between stochastic analysis and machine learning is a rapidly evolving field, with path signatures - iterated integrals that provide faithful, hierarchical representations of paths - offering a principled and universal feature…
Although topological considerations amongst multiple labels have been previously investigated in the context of continuous max-flow image segmentation, similar investigations have yet to be made about shape considerations in a general and…
We give formulas, in terms of graph theoretical invariants, for the minimum distance and the generalized Hamming weights of the linear code generated by the rows of the incidence matrix of a signed graph over a finite field, and for those…
Graphs face challenges when dealing with massive datasets. They are essential tools for modeling interconnected data and often become computationally expensive. Graph embedding techniques, on the other hand, provide an efficient approach.…
Graph embedding has become an increasingly important technique for analyzing graph-structured data. By representing nodes in a graph as vectors in a low-dimensional space, graph embedding enables efficient graph processing and analysis…
In recent years, arrays of atomic ions in a linear RF trap have proven to be a particularly successful platform for quantum simulation. However, a wide range of quantum models and phenomena have, so far, remained beyond the reach of such…
The transducer model trained based on sequence-level criterion requires a lot of memory due to the generation of the large probability matrix. We proposed a lightweight transducer model based on frame-level criterion, which uses the results…
We introduce a novel class of explicit feature maps based on topological indices that represent each graph by a compact feature vector, enabling fast and interpretable graph classification. Using radial basis function kernels on these…
Representation learning for graphs enables the application of standard machine learning algorithms and data analysis tools to graph data. Replacing discrete unordered objects such as graph nodes by real-valued vectors is at the heart of…
Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques…
Morse complexes and Morse-Smale complexes are topological descriptors popular in topology-based visualization. Comparing these complexes plays an important role in their applications in feature correspondences, feature tracking, symmetry…
Local geometrical features of a porous material such as the shape and size of a pore or the curvature of a solid ligament often affect the macroscopic properties of the material, and their characterization is necessary to fully understand…
In this paper we propose a new approach to detect clusters in undirected graphs with attributed vertices. We incorporate structural and attribute similarities between the vertices in an augmented graph by creating additional vertices and…
Graded rings provide a natural algebraic framework for encoding symmetry via decompositions into homogeneous components indexed by a group, together with multiplication rules reflecting the group operation. Among graded rings, strongly…
A metric tensor for Riemann manifold Monte Carlo particularly suited for non-linear Bayesian hierarchical models is proposed. The metric tensor is built from symmetric positive semidefinite log-density gradient covariance (LGC) matrices,…