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CATEGORIES:Applied and Computational Analysis
SUMMARY:Geometric Structure of graph Laplacian embeddings
- Nicolas Garcia Trillos\, Brown University
DTSTART;TZID=Europe/London:20180614T150000
DTEND;TZID=Europe/London:20180614T160000
UID:TALK105679AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/105679
DESCRIPTION:In this talk I will address theoretical questions
related to the task of data clustering (unsupervis
ed learning) and in particular about a concrete an
d popular methodology known as spectral clusterin
g. In spectral clustering the idea is to first use
the spectrum of a graph Laplacian associated to a
point cloud to construct an embedding of the clou
d into some Euclidean space\; after the embedding
step\, an algorithm like k-means is used to obtain
the desired clusters. Despite the popularity of t
he method and its intuitive understanding by pract
itioners\, only very few rigorous mathematical res
ults aiming to justify its use are available. Duri
ng my talk I intend to give answers to the followi
ng theoretical questions: What is the geometry of
these graph Laplacian embeddings as the number of
data points goes to infinity\, and what is special
about them that makes spectral clustering a succe
ssful methodology? I will also discuss some of the
computational consequences of the theoretical res
ults that I will present. \n \nA variety of mathem
atical tools from optimal transport\, spectral geo
metry\, meta stability\, and probability makes the
analysis possible. The talk is based on joint wor
k with Bamdad Hosseini (Caltech) and Franca Hoffma
n (Caltech).
LOCATION:MR 14
CONTACT:Matthew Thorpe
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