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abstract:
In many fields such as machine learning, computer vision and
exploratory data analysis, a major
goal is the the automatic and efficient
extraction of knowledge from
data. Many important methods in data analysis are based
on linear eigenproblems including well known applications such as
spectral clustering and principal component analysis.
As linear eigenproblems are quite limited in their modeling capabilities we shall in this
talk discuss nonlinear eigenproblems since they significantly
extend the modeling freedom. After
an introduction of the framework, we will present recent results on an
important application of
nonlinear eigenproblems, namely tight relaxations of balanced graph
cuts. Moreover we provide an efficient
algorithm - a generalization of the inverse power method - for the resulting nonconvex and nonsmooth optimization
problems. |
