Related papers: Gromov-Wasserstein Bound between Reeb and Mapper G…
In the regime of two-sample comparison, tests based on a graph constructed on observations by utilizing similarity information among them is gaining attention due to their flexibility and good performances for high-dimensional/non-Euclidean…
The Reeb graph of a smooth function is a graph being a natural quotient space of the manifold of the domain and the space of all connected components of preimages. Such a combinatorial and topological object roughly and compactly represents…
Gromov-Wasserstein (GW) distances are combinations of Gromov-Hausdorff and Wasserstein distances that allow the comparison of two different metric measure spaces (mm-spaces). Due to their invariance under measure- and distance-preserving…
The random intersection graph model $\mathcal G(n,m,p)$ is considered. Due to substantial edge dependencies, studying even fundamental statistics such as the subgraph count is significantly more challenging than in the classical binomial…
Graphs are crucial for representing interrelated data and aiding predictive modeling by capturing complex relationships. Achieving high-quality graph representation is important for identifying linked patterns, leading to improvements in…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
The Gromov-Wasserstein (GW) problem, a variant of the classical optimal transport (OT) problem, has attracted growing interest in the machine learning and data science communities due to its ability to quantify similarity between measures…
A popular approach to semi-supervised learning proceeds by endowing the input data with a graph structure in order to extract geometric information and incorporate it into a Bayesian framework. We introduce new theory that gives appropriate…
We consider a Random Graph Model on $\mathbb{Z}^{d}$ that incorporates the interplay between the statistics of the graph and the underlying space where the vertices are located. Based on a graphical construction of the model as the…
The Gromov-Wasserstein (GW) problem provides a powerful framework for aligning heterogeneous datasets by matching their internal structures in a way that minimizes distortion. However, GW alignment is sensitive to data contamination by…
This is a note on the graphs of two smooth real-valued functions in the plane with no intersection and the natural map onto the region surrounded by them with the canonical projection to the line composed, yielding its Reeb space. The Reeb…
A half-square of a bipartite graph $B=(X,Y,E_B)$ has one color class of $B$ as vertex set, say $X$; two vertices are adjacent whenever they have a common neighbor in $Y$. If $G=(V,E_G)$ is the half-square of a planar bipartite graph…
Gromov-Wasserstein distance has found many applications in machine learning due to its ability to compare measures across metric spaces and its invariance to isometric transformations. However, in certain applications, this invariance…
Given two graphs, the graph matching problem is to align the two vertex sets so as to minimize the number of adjacency disagreements between the two graphs. The seeded graph matching problem is the graph matching problem when we are first…
Graph Edit Distance (GED) is a fundamental, albeit NP-hard, metric for structural graph similarity. Recent neural graph matching architectures approximate GED by first encoding graphs with a Graph Neural Network (GNN) and then applying…
We examine data-processing of Markov chains through the lens of information geometry. We first establish a theory of congruent Markov morphisms within the framework of stochastic matrices. Specifically, we introduce and justify the concept…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…
We propose a novel approach for comparing distributions whose supports do not necessarily lie on the same metric space. Unlike Gromov-Wasserstein (GW) distance which compares pairwise distances of elements from each distribution, we…
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.…