Linear Unbalanced Optimal Transport

Matthew Thorpe
University of Cambridge
Tuesday, January 21, 2020 - 1:25pm to 2:25pm
Lind 305

Optimal transport is a powerful tool for measuring the distances between
signals. However, the most common choice is to use the Wasserstein
distance where one is required to treat the signal as a probability
measure. This places restrictive conditions on the signals and although
ad-hoc renormalisation can be applied to sets of unnormalised measures
this can often dampen features of the signal. The second disadvantage is
that despite recent advances, computing optimal transport distances for
large sets is still difficult. In this talk I will focus on the
Hellinger--Kantorovich distance, which can be applied between any pair
of non-negative measures. I will describe how the distance can be
linearised and embedded into a Euclidean space. The Euclidean distance
in the embedded space is approximately the Wasserstein distance in the
original space. This method, in particular, allows for the application
of off-the-shelf data analysis tools such as principal component
analysis.

This is joint work with Bernhard Schmitzer (TU Munich).

Matthew is a research fellow in the Cantab Capital Institute for the
Mathematics of Information at the University of Cambridge. Prior to that
he was a postdoctoral associate at Carnegie Mellon University and a PhD
student at the University of Warwick. From this coming March he will be
a lecturer (US equivalent Assistant Professor) in Applied Mathematics at
the University of Manchester.