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    This study introduces an exact online learning framework using indefinite kernels. The novel approach extends kernel principal component analysis (KPCA) to Krein space for efficient visual tracking and face recognition.

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    Area of Science:

    • Machine Learning
    • Computer Vision
    • Kernel Methods

    Background:

    • Online learning with indefinite kernels presents challenges.
    • Kernel Principal Component Analysis (KPCA) is typically limited to positive definite kernels.
    • Extending KPCA to nonpositive kernels is crucial for broader applications.

    Purpose of the Study:

    • To develop an exact framework for online learning with indefinite kernels.
    • To extend KPCA to Krein space for handling nonpositive kernels.
    • To enable efficient and exact online learning for applications like visual tracking and face recognition.

    Main Methods:

    • Extension of KPCA from Reproducing Kernel Hilbert Space to Krein space.
    • Formulation of an incremental KPCA in Krein space.
    • Development of a nonlinear appearance model learned online via KPCA in Krein space.

    Main Results:

    • An exact framework for online learning with indefinite kernels is established.
    • The proposed incremental KPCA in Krein space is efficient and exact, avoiding preimage calculations.
    • Successful application of the framework to visual tracking in challenging scenarios and face recognition tasks.

    Conclusions:

    • The proposed Krein space KPCA offers an efficient and exact solution for online learning with indefinite kernels.
    • This framework significantly advances the capabilities of kernel methods in machine learning.
    • The approach demonstrates strong performance in practical computer vision applications such as visual tracking and face recognition.