Optimal transport · graphs · time series
The mathematics of moving piles of sand.
A probability distribution is a pile of sand with unit mass. Optimal transport asks how to move one pile onto another as cheaply as possible, and the answer turns out to be a geometry. This site collects research that puts that geometry to work: finding structure in time series, and averaging and decomposing distributions that live on graphs.
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Try it: barycentric coding on a graph
λ = (, , )
Linear mixture Σ λiνi
spread
Transport barycenter νλ
spread
Circle area is proportional to mass, on the same scale in both graphs. Spread is the root-mean-square distance of the mass from its own center, measured in grid steps.
An interactive demo highlighting the geometry of barycentric coding of measures on graphs.
Talk · slides in your browser
A Barycentric Coding Model for Measures on Graphs
FSU Topology & Geometry Seminar
Papers & code
Preprints and open-source packages
Change point detection for time series, and barycenters of measures on graphs.
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Nice to meet you too.