5 papers
Unbalanced Optimal Transport Dictionary Learning for Unsupervised Hyperspectral Image Clustering
Joshua Lentz, Nicholas Karris, Alex Cloninger +1
Hyperspectral images capture vast amounts of high-dimensional spectral information about a scene, making labeling an intensive task that is resistant to out-of-the-box statistical…
Optimal Transport, Timesteppers, Newton-Krylov Methods and Steady States of Collective Particle Dynamics
Hannes Vandecasteele, Nicholas Karris, Alexander Cloninger +1
Timesteppers constitute a powerful tool in modern computational science and engineering. Although they are typically used to advance the system forward in time, they can also be vi…
Which Way from B to A: The role of embedding geometry in image interpolation for Stable Diffusion
Nicholas Karris, Luke Durell, Javier Flores +1
It can be shown that Stable Diffusion has a permutation-invariance property with respect to the rows of Contrastive Language-Image Pretraining (CLIP) embedding matrices. This inspi…
Linearized Optimal Transport pyLOT Library: A Toolkit for Machine Learning on Point Clouds
Jun Linwu, Varun Khurana, Nicholas Karris +1
The pyLOT library offers a Python implementation of linearized optimal transport (LOT) techniques and methods to use in downstream tasks. The pipeline embeds probability distributi…
Using Linearized Optimal Transport to Predict the Evolution of Stochastic Particle Systems
Nicholas Karris, Evangelos A. Nikitopoulos, Ioannis G. Kevrekidis +2
We develop an Euler-type method to predict the evolution of a time-dependent probability measure without explicitly learning an operator that governs its evolution. We use lineariz…