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CATEGORIES:Lecture / Talk / Workshop
DESCRIPTION:Catherine Babecki\, Caltech\n\nAbstract: We propose an approac
h to graph sparsification based on the idea of preserving the smallest k ei
genvalues and eigenvectors of the Graph Laplacian. This is motivated by the
fact that small eigenvalues and their associated eigenvectors tend to be m
ore informative of the global structure and geometry of the graph than larg
er eigenvalues and their eigenvectors. The set of all weighted subgraphs of
a graph G that have the same first k eigenvalues (and eigenvectors) as G i
s the intersection of a polyhedron with a cone of positive semidefinite mat
rices. We discuss the geometry of these sets and deduce the natural scale o
f k. Various families of graphs illustrate our construction.
DTEND:20240221T230000Z
DTSTAMP:20241103T160051Z
DTSTART:20240221T220000Z
GEO:34.022409;-118.291027
LOCATION:Kaprielian Hall (KAP)\, 414
SEQUENCE:0
SUMMARY:Combinatorics Seminar: Spectrahedral Geometry of Graph Sparsifiers
UID:tag:localist.com\,2008:EventInstance_45642282344082
URL:https://calendar.usc.edu/event/combinatorics_seminar_spectrahedral_geom
etry_of_graph_sparsifiers
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