Zobrazeno 1 - 10
of 93
pro vyhledávání: '"Fasy, Brittany Terese"'
Autor:
Fajstrup, Lisbeth, Fasy, Brittany Terese, Li, Wenwen, Mezrag, Lydia, Rask, Tatum, Tombari, Francesca, Urbančič, Živa
The Gromov--Hausdorff distance measures the similarity between two metric spaces by isometrically embedding them into an ambient metric space. In this work, we introduce an analogue of this distance for metric spaces endowed with directed structures.
Externí odkaz:
http://arxiv.org/abs/2408.14394
Merge trees are a valuable tool in the scientific visualization of scalar fields; however, current methods for merge tree comparisons are computationally expensive, primarily due to the exhaustive matching between tree nodes. To address this challeng
Externí odkaz:
http://arxiv.org/abs/2404.05879
Recent developments in shape reconstruction and comparison call for the use of many different (topological) descriptor types, such as persistence diagrams and Euler characteristic functions. We establish a framework to quantitatively compare the stre
Externí odkaz:
http://arxiv.org/abs/2402.13632
We introduce the manifold density function, which is an intrinsic method to validate manifold learning techniques. Our approach adapts and extends Ripley's $K$-function, and categorizes in an unsupervised setting the extent to which an output of a ma
Externí odkaz:
http://arxiv.org/abs/2402.09529
This paper presents the first approach to visualize the importance of topological features that define classes of data. Topological features, with their ability to abstract the fundamental structure of complex data, are an integral component of visua
Externí odkaz:
http://arxiv.org/abs/2309.13185
Publikováno v:
Proc. 18th Algorithms and Data Structures Symposium. 605-619, 2023
Let $\gamma$ be a generic closed curve in the plane. Samuel Blank, in his 1967 Ph.D. thesis, determined if $\gamma$ is self-overlapping by geometrically constructing a combinatorial word from $\gamma$. More recently, Zipei Nie, in an unpublished manu
Externí odkaz:
http://arxiv.org/abs/2309.02383
The weighted Euler characteristic transform (WECT) is a new tool for extracting shape information from data equipped with a weight function. Image data may benefit from the WECT where the intensity of the pixels are used to define the weight function
Externí odkaz:
http://arxiv.org/abs/2307.13940
Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of persistence dia
Externí odkaz:
http://arxiv.org/abs/2212.13206
Autor:
Fasy, Brittany Terese, Patel, Amit
Publikováno v:
Foundations of Data Science, 2024
The combinatorial interpretation of the persistence diagram as a M\"obius inversion was recently shown to be functorial. We employ this discovery to recast the Persistent Homology Transform of a geometric complex as a representation of a cellulation
Externí odkaz:
http://arxiv.org/abs/2208.05243
Autor:
Cisewski-Kehe, Jessi, Fasy, Brittany Terese, Hellwing, Wojciech, Lovell, Mark R., Drozda, Pawel, Wu, Mike
The spatial distribution of galaxies at sufficiently small scales will encode information about the identity of the dark matter. We develop a novel description of the halo distribution using persistent homology summaries, in which collections of poin
Externí odkaz:
http://arxiv.org/abs/2204.00443