Abstract-We propose an exact framework for online learning with a family of indefinite (not positive) kernels. As we study the case of nonpositive kernels, we first show how to extend kernel principal component analysis (KPCA) from a reproducing kernel Hilbert space to Krein space. We then formulate an incremental KPCA in Krein space that does not require the calculation of preimages and therefore is both efficient and exact. Our approach has been motivated by the application of visual tracking for which we wish to employ a robust gradient-based kernel. We use the proposed nonlinear appearance model learned online via KPCA in Krein space for visual tracking in many popular and difficult tracking scenarios. We also show applications of our kernel framework for the problem of face recognition. Index Terms-Gradient-based kernel, online kernel learning, principal component analysis with indefinite kernels, recognition, robust tracking.
Liwicki et al. REF formulated an incremental kernel PCA in Krein space to learn a nonlinear subspace representation for tracking.
Efficient Online Subspace Learning With an Indefinite Kernel for Visual Tracking and Recognition
IEEE Transactions on Neural Networks and Learning Systems
IEEE Transactions on Neural Networks and Learning Systems
Medicine Computer Science