no code implementations • 29 Jun 2022 • Guillaume Huguet, D. S. Magruder, Alexander Tong, Oluwadamilola Fasina, Manik Kuchroo, Guy Wolf, Smita Krishnaswamy
In GAE the latent space distance between points is regularized to match a novel multiscale geodesic distance on the data manifold that we define.
no code implementations • 28 Mar 2022 • Guillaume Huguet, Alexander Tong, Bastian Rieck, Jessie Huang, Manik Kuchroo, Matthew Hirn, Guy Wolf, Smita Krishnaswamy
From a geometric perspective, we obtain convergence bounds based on the smallest transition probability and the radius of the data, whereas from a spectral perspective, our bounds are based on the eigenspectrum of the diffusion kernel.
no code implementations • 26 Jul 2021 • Alexander Tong, Guillaume Huguet, Dennis Shung, Amine Natik, Manik Kuchroo, Guillaume Lajoie, Guy Wolf, Smita Krishnaswamy
We propose to compare and organize such datasets of graph signals by using an earth mover's distance (EMD) with a geodesic cost over the underlying graph.
1 code implementation • 25 Feb 2021 • Alexander Tong, Guillaume Huguet, Amine Natik, Kincaid MacDonald, Manik Kuchroo, Ronald Coifman, Guy Wolf, Smita Krishnaswamy
Here, Diffusion EMD can derive distances between patients on the manifold of cells at least two orders of magnitude faster than equally accurate methods.
no code implementations • 12 Feb 2021 • Manik Kuchroo, Abhinav Godavarthi, Alexander Tong, Guy Wolf, Smita Krishnaswamy
We propose a method called integrated diffusion for combining multimodal datasets, or data gathered via several different measurements on the same system, to create a joint data diffusion operator.
1 code implementation • 10 Jul 2019 • Nathan Brugnone, Alex Gonopolskiy, Mark W. Moyle, Manik Kuchroo, David van Dijk, Kevin R. Moon, Daniel Colon-Ramos, Guy Wolf, Matthew J. Hirn, Smita Krishnaswamy
Here, we consider multiple levels of abstraction via a multiresolution geometry of data points at different granularities.