Kernels, Pre-images and Optimization

Chapter

Abstract

In the last decade, kernel-based learning has become a state-of-the-art technology in Machine Learning. We briefly review kernel PCAKernel principal component analysis (kPCA) (kPCA) and the pre-image problem that occurs in kPCA. Subsequently, we discuss a novel direction where kernel-based models are used for property optimization. For this purpose, a stable estimation of the model’s gradient is essential and non-trivial to achieve. The appropriate use of pre-image projections is key to successful gradient-based optimization—as will be shown for toy and real-world problems from quantum chemistry and physics.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Chemistry, Department of PhysicsUniversity of CaliforniaIrvineUSA
  2. 2.idalab GmbHBerlinGermany
  3. 3.Machine Learning GroupTechnical University of BerlinBerlinGermany
  4. 4.Department of Brain and Cognitive EngineeringKorea UniversitySeoulKorea

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