Kernel-Based Implicit Regularization of Structured Objects

Weighted graph regularization provides a rich framework that allows to regularize functions defined over the vertices 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 data. On the other hand, several kernels have been defined so far 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 a Hilbert space. As a consequence, 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. Keywords-kernel; graph-based regularization; total variation; classification; discrete structures

• Type: Conference
• Year: 2010
• Where: ICPR
• Authors: François-Xavier Dupé, Sébastien Bougleux, Luc Brun, Olivier Lezoray, Abderrahim Elmoataz
• Keywords: Computer Vision, Graph Regularization Framework, ICPR 2010, Regularization Framework, Weighted Graph Regularization