Learning Similarity with Operator-valued Large-margin Classifier

A method is introduced to learn and represent similarity with lin-ear operators in kernel induced Hilbert spaces. Transferring well estab-lished error bounds for vector valued large-margin classi\u85ers to the set-ting of Hilbert-Schmidt operators leads to dimension free bounds on a risk functional for linear representations and motivates a regularized ob-jective functional. Minimization of this objective is e¤ected 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.