Related papers: A Topological Distance between Multi-fields based …
We introduce a principled way of computing the Wasserstein distance between two distributions in a federated manner. Namely, we show how to estimate the Wasserstein distance between two samples stored and kept on different devices/clients…
Given trajectories with gaps, we investigate methods to tighten spatial bounds on areas (e.g., nodes in a spatial network) where possible rendezvous activity could have occurred. The problem is important for reducing the onerous amount of…
We introduce a construction and an algorithm, both based on Topological Data Analysis (TDA), to tackle the problem of the isomorphism check of Orthogonal Arrays (OAs). Specifically, we associate to any binary OA a persistence diagram, one…
Interleaving distances are used widely in Topological Data Analysis (TDA) as a tool for comparing topological signatures of datasets. The theory of interleaving distances has been extended through various category-theoretic constructions,…
To investigate the topological structure of planar polygon decomposition on trapezoids, which is formed by height functions. We use the oriented Reeb graph of the function with a marked vertex. We describe all possible optimal Reeb graphs…
Manifold reconstruction has been extensively studied for the last decade or so, especially in two and three dimensions. Recently, significant improvements were made in higher dimensions, leading to new methods to reconstruct large classes…
In topological data analysis (TDA), one often studies the shape of data by constructing a filtered topological space, whose structure is then examined using persistent homology. However, a single filtered space often does not adequately…
By assigning a probability measure via the spectrum of the normalized Laplacian to each graph and using L^p Wasserstein distances between probability measures, we define the corresponding spectral distances d_p on the set of all graphs.…
A merge tree is a fundamental topological structure used to capture the sub-level set (and similarly, super-level set) topology in scalar data analysis. The interleaving distance is a theoretically sound, stable metric for comparing merge…
The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides important geometric and topological information about a space.…
We propose a hyperbolic set-to-set distance measure for computing dissimilarity between sets in hyperbolic space. While point-to-point distances in hyperbolic space effectively capture hierarchical relationships between data points, many…
Subgraph matching is a core task in graph analytics, widely used in domains such as biology, finance, and social networks. Existing top-k diversified methods typically focus on maximizing vertex coverage, but often return results in the…
Reeb graphs are an important tool for abstracting and representing the topological structure of a function defined on a manifold. We have identified three properties for faithfully representing Reeb graphs in a visualization: they should be…
We present an exact and efficient algorithm for computing the Reeb space of a bivariate PL map. The Reeb space is a topological structure that generalizes the Reeb graph to the setting of multiple scalar-valued functions defined over a…
Comparing images to recommend items from an image-inventory is a subject of continued interest. Added with the scalability of deep-learning architectures the once `manual' job of hand-crafting features have been largely alleviated, and…
The problem of comparing probability distributions is at the heart of many tasks in statistics and machine learning. Established comparison methods treat the standard setting that the distributions are supported in the same space. Recently,…
Persistence diagrams are objects that play a central role in topological data analysis. In the present article, we investigate the local and global geometric properties of spaces of persistence diagrams. In order to do this, we construct a…
Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at…
Multi-connected universe models with space identification scales smaller than the size of the observable universe produce topological images of cosmic sources. We generalise to locally hyperbolic spaces the crystallographic method, aimed to…
Over the past few years, symmetric positive definite (SPD) matrices have been receiving considerable attention from computer vision community. Though various distance measures have been proposed in the past for comparing SPD matrices, the…