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@ARTICLE{Grajewski:1010398,
      author       = {Grajewski, Matthias and Kleefeld, Andreas},
      title        = {{D}etecting and approximating decision boundaries in
                      low-dimensional spaces},
      journal      = {Numerical algorithms},
      volume       = {95},
      issn         = {1017-1398},
      publisher    = {Springer},
      reportid     = {FZJ-2023-03038},
      pages        = {1503-1537},
      year         = {2024},
      abstract     = {A method for detecting and approximating fault lines or
                      surfaces, respectively, or decision curves in two and three
                      dimensions with guaranteed accuracy is presented.
                      Reformulated as a classification problem, our method starts
                      from a set of scattered points along with the corresponding
                      classification algorithm to construct a representation of a
                      decision curve by points with prescribed maximal distance to
                      the true decision curve. Hereby, our algorithm ensures that
                      the representing point set covers the decision curve in its
                      entire extent and features local refinement based on the
                      geometric properties of the decision curve. We demonstrate
                      applications of our method to problems related to the
                      detection of faults, to multi-criteria decision aid and, in
                      combination with Kirsch’s factorization method, to solving
                      an inverse acoustic scattering problem. In all applications
                      we considered in this work, our method requires
                      significantly less pointwise classifications than previously
                      employed algorithms.},
      cin          = {JSC},
      ddc          = {510},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs)
                      and Research Groups (POF4-511)},
      pid          = {G:(DE-HGF)POF4-5112},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:001048063000004},
      doi          = {10.1007/s11075-023-01618-6},
      url          = {https://juser.fz-juelich.de/record/1010398},
}