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Kernel Based Implicit Graph Regularization of Structured Objects

Francois-Xavier Dupe &
Seebastien Bougleux &
Luc Brun &
Olivier Lezoray &
Abder Elmoataz.
Weighted Graph regularization provides a rich framework
which allow to regularize functions defined over the
vertice of a weighted graph. Until now, such a
framework has been only defined for real or
multivalued functions hereby restricting the
regularization framework to numerical objects. On
the other hand, several kernels have been defined on
structured objects such as strings or graphs. Using
definite positive kernels, each original object is
associated by the ``kernel trick'' to one element of
an Hilbert space. This paper proposes to extend the
weighted graph regularization framework to objects
implicitly defined by their kernel hereby performing
the regularization within the Hilbert space
associated to the kernel. This work opens the door
to the regularization of structured objects.