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DTSTART:20181028T030000
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DTSTART:20180325T020000
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RDATE:20190331T020000
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UID:calendar.13533.field_data.0@www.diag.uniroma1.it
DTSTAMP:20240302T080555Z
CREATED:20181004T222103Z
DESCRIPTION:Spectral clustering algorithms find clusters in a given network
by exploiting properties of the eigenvectors of matrices associated with
the network. As a first step\, one computes a spectral embedding\, that is
a mapping of nodes to points in a low-dimensional real space\; then one u
ses geometric clustering algorithms such as k-means to cluster the points
corresponding to the nodes.Such algorithms work so well that\, in certain
applications unrelated to network analysis\, such as image segmentation\,
it is useful to associate a network to the data\, and then apply spectral
clustering to the network. In addition to its application to clustering\,
spectral embeddings are a valuable tool for dimension-reduction and data v
isualization.The performance of spectral clustering algorithms has been ju
stified rigorously when applied to networks coming from certain probabilis
tic generative models.A more recent development\, which is the focus of th
is lecture\, is a worst-case analysis of spectral clustering\, showing tha
t\, for every graph that exhibits a certain cluster structure\, such struc
ture can be found by geometric algorithms applied to a spectral embedding.
Such results generalize the graph Cheegerâ€™s inequality (a classical result
in spectral graph theory)\, and they have additional applications in comp
utational complexity theory and in pure mathematics.Bio: Luca Trevisan is
a professor of electrical engineering and computer sciences at U.C. Berkel
ey and a senior scientist at the Simons Institute for the Theory of Comput
ing. Luca studied at the Sapienza University of Rome\, he was a post-doc a
t MIT and at DIMACS\, and he was on the faculty of Columbia University\, U
.C. Berkeley\, and Stanford\, before returning to Berkeley in 2014.Luca's
research is in theoretical computer science\, and it is focused on computa
tional complexity and graph algorithms.Luca received the STOC'97 Danny Lew
in (best student paper) award\, the 2000 Oberwolfach Prize\, and the 2000
Sloan Fellowship. He was an invited speaker at the 2006 International Cong
ress of Mathematicians.
DTSTART;TZID=Europe/Paris:20181018T120000
DTEND;TZID=Europe/Paris:20181018T120000
LAST-MODIFIED:20191008T082735Z
LOCATION:Aula Magna DIAG\, via Ariosto 25
SUMMARY:Luca Trevisan (Univ. Berkeley) : A Theory of Spectral Clustering -
Luca Trevisan\, U.C. Berkeley and Simons Institute for the Theory of Compu
ting
URL;TYPE=URI:http://www.diag.uniroma1.it/node/13533
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