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SUMMARY:Geometric Structure of graph Laplacian embeddings - Nicolas Garcia
  Trillos\, Brown University
DTSTART:20180614T140000Z
DTEND:20180614T150000Z
UID:TALK105679@talks.cam.ac.uk
CONTACT:Matthew Thorpe
DESCRIPTION:In this talk I will address theoretical questions related to t
 he task of data clustering (unsupervised learning) and in particular about
  a concrete and popular methodology known as  spectral clustering. In spec
 tral clustering the idea is to first use the spectrum of a graph Laplacian
  associated to a point cloud to construct an embedding of the cloud into s
 ome Euclidean space\; after the embedding step\, an algorithm like k-means
  is used to obtain the desired clusters. Despite the popularity of the met
 hod and its intuitive understanding by practitioners\, only very few rigor
 ous mathematical results aiming to justify its use are available. During m
 y talk I intend to give answers to the following theoretical questions: Wh
 at is the geometry of these graph Laplacian embeddings as the number of da
 ta points goes to infinity\, and what is special about them that makes spe
 ctral clustering a successful methodology? I will also discuss some of the
  computational consequences of the theoretical results that I will present
 . \n \nA variety of mathematical tools from optimal transport\, spectral g
 eometry\, meta stability\, and probability makes the analysis possible. Th
 e talk is based on joint work with Bamdad Hosseini (Caltech) and Franca Ho
 ffman (Caltech).
LOCATION:MR 14
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