@phdthesis{5600,
  title = {Efficient and Invariant Regularisation with Application to Computer Graphics},
  abstract = {This thesis develops the theory and practise of reproducing kernel methods.
  Many functional inverse problems which arise in, for example, machine learning
  and computer graphics, have been treated with practical success using
  methods based on a reproducing kernel Hilbert space perspective. This perspective
  is often theoretically convenient, in that many functional analysis
  problems reduce to linear algebra problems in these spaces. Somewhat more
  complex is the case of conditionally positive definite kernels, and we provide
  an introduction to both cases, deriving in a particularly elementary manner
  some key results for the conditionally positive definite case.
  A common complaint of the practitioner is the long running time of these
  kernel based algorithms. We provide novel ways of alleviating these problems
  by essentially using a non-standard function basis which yields computational
  advantages. That said, by doing so we must also forego the aforementioned
  theoretical conveniences, and hence need some additional analysis
  which we provide in order to make the approach practicable. We demonstrate
  that the method leads to state of the art performance on the problem
  of surface reconstruction from points.
  We also provide some analysis of kernels invariant to transformations such
  as translation and dilation, and show that this indicates the value of learning
  algorithms which use conditionally positive definite kernels. Correspondingly,
  we provide a few approaches for making such algorithms practicable.
  We do this either by modifying the kernel, or directly solving problems with
  conditionally positive definite kernels, which had previously only been solved
  with positive definite kernels. We demonstrate the advantage of this approach,
  in particular by attaining state of the art classification performance
  with only one free parameter.},
  degree_type = {PhD},
  institution = {University of Queensland, Brisbane, Australia},
  school = {Biologische Kybernetik},
  month = jan,
  year = {2008},
  slug = {5600},
  author = {Walder, CJ.},
  month_numeric = {1}
}