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pro vyhledávání: '"Bendich A"'
Autor:
Mousley, Jonathan M., Bendich, Paul
Topological Data Analysis (TDA) has been applied with success to solve problems across many scientific disciplines. However, in the setting of a point cloud $X$ sampled from a shape $\mathcal{S}$ of low intrinsic dimension embedded within high ambien
Externí odkaz:
http://arxiv.org/abs/2411.09797
For safety and robustness of AI systems, we introduce topological parallax as a theoretical and computational tool that compares a trained model to a reference dataset to determine whether they have similar multiscale geometric structure. Our proofs
Externí odkaz:
http://arxiv.org/abs/2306.11835
Autor:
Solomon, Elchanan, Bendich, Paul
In this paper, we consider topological featurizations of data defined over simplicial complexes, like images and labeled graphs, obtained by convolving this data with various filters before computing persistence. Viewing a convolution filter as a loc
Externí odkaz:
http://arxiv.org/abs/2208.02107
Autor:
Momtaz, David A., Pereira, Daniel E., Singh, Aaron, Gonuguntla, Rishi, Mittal, Mehul M., Torres, Beltran, Lee, Tiffany M., Dayhim, Fariba, Hosseinzadeh, Pooya, Bendich, Ilya
Publikováno v:
In The Journal of Arthroplasty January 2025 40(1):160-168
Autor:
Yinzhu Jin, Rory McDaniel, N. Joseph Tatro, Michael J. Catanzaro, Abraham D. Smith, Paul Bendich, Matthew B. Dwyer, P. Thomas Fletcher
Publikováno v:
Frontiers in Computer Science, Vol 6 (2024)
Many deep generative models, such as variational autoencoders (VAEs) and generative adversarial networks (GANs), learn an immersion mapping from a standard normal distribution in a low-dimensional latent space into a higher-dimensional data space. As
Externí odkaz:
https://doaj.org/article/27a48a21b24043779d3800b7b6875e1f
Autor:
Koplik, Gary, Borggren, Nathan, Voisin, Sam, Angeloro, Gabrielle, Hineman, Jay, Johnson, Tessa, Bendich, Paul
As Internet of Things (IoT) devices become both cheaper and more powerful, researchers are increasingly finding solutions to their scientific curiosities both financially and computationally feasible. When operating with restricted power or communica
Externí odkaz:
http://arxiv.org/abs/2206.07486
We propose a novel approach to dimensionality reduction combining techniques of metric geometry and distributed persistent homology, in the form of a gradient-descent based method called DIPOLE. DIPOLE is a dimensionality-reduction post-processing st
Externí odkaz:
http://arxiv.org/abs/2106.07613
What is the "right" topological invariant of a large point cloud X? Prior research has focused on estimating the full persistence diagram of X, a quantity that is very expensive to compute, unstable to outliers, and far from a sufficient statistic. W
Externí odkaz:
http://arxiv.org/abs/2101.12288
Topological statistics, in the form of persistence diagrams, are a class of shape descriptors that capture global structural information in data. The mapping from data structures to persistence diagrams is almost everywhere differentiable, allowing f
Externí odkaz:
http://arxiv.org/abs/2009.08496
Autor:
Solomon, Elchanan, Bendich, Paul
We introduce geometric and topological methods to develop a new framework for fusing multi-sensor time series. This framework consists of two steps: (1) a joint delay embedding, which reconstructs a high-dimensional state space in which our sensors c
Externí odkaz:
http://arxiv.org/abs/2002.11201