Learning Similarity with Operator-valued Large-margin Classifiers

Andreas Maurer

A method is introduced to learn and represent similarity with linear operators in kernel induced Hilbert spaces. Transferring error bounds for vector valued large-margin classifiers to the setting of Hilbert-Schmidt operators leads to dimension free bounds on a risk functional for linear representations and motivates a regularized objective functional. Minimization of this objective is effected by a simple technique of stochastic gradient descent. The resulting representations are tested on transfer problems in image processing, involving plane and spatial geometric invariants, handwritten characters and face recognition.

Learning Similarity with Operator-valued Large-margin Classifiers

Abstract