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UID:233@isdm.umontpellier.fr
DTSTART;TZID=Europe/Paris:20240613T140000
DTEND;TZID=Europe/Paris:20240613T140000
DTSTAMP:20260825T133911Z
URL:https://isdm.umontpellier.fr/events/the-procrustes-wasserstein-problem
 -aligning-embeddings-and-geometric-graphs/
SUMMARY:The Procrustes-Wasserstein problem: aligning embeddings and geometr
 ic graphs
DESCRIPTION:Room 03.124\, Building 5\, St Priest campus\n\nMachine Learning
  in Montpellier\, Theory &amp\; Practice\n\nThe Procrustes-Wasserstein pro
 blem consists in matching two high-dimensional point clouds in an unsuperv
 ised setting\, and has applications in natural language processing and com
 puter vision. This talk will first introduce and motivate this problem\, b
 efore considering a planted model with two random datasets $X\,Y$ that con
 sist of $n$ datapoints in $\\R^d$\, where $Y$ is a noisy version of $X$\, 
 up to an orthogonal transformation and a relabeling of the data points. Th
 is setting is related to the graph alignment problem in geometric models a
 s we will show. Focusing on the Euclidean transport cost between the point
  clouds as a measure of performance for the alignment\, we first establish
  information-theoretic results\, in the high ($d \\gg \\log n$) and low ($
 d \\ll \\log n$) dimensional regimes\, and provide geometrical and probabi
 listic insights to explain the dichotomy between these two regimes. We the
 n study computational aspects and propose intuitive algorithms to approxim
 ate solutions for this problem\, alternatively estimating the orthogonal t
 ransformation and the relabeling\, initialized via a convex relaxation.\n\
 nMachine Learning in Montpellier\, Theory &amp\; Practice
ATTACH;FMTTYPE=image/jpeg:https://isdm.umontpellier.fr/wp-content/uploads/
 2026/06/ml-mtp-gC78d5.png
CATEGORIES:ML MTP
LOCATION:Saint Priest Campus - Building 5 - Room 03.124\, 860 rue St Priest
 \, Montpellier\, 
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=860 rue St Priest\, Montpel
 lier\, ;X-APPLE-RADIUS=100;X-TITLE=Saint Priest Campus - Building 5 - Room
  03.124:geo:0,0
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