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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\u2019s 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.<\/jats:p>","DOI":"10.1007\/s11075-023-01618-6","type":"journal-article","created":{"date-parts":[[2023,8,14]],"date-time":"2023-08-14T13:02:10Z","timestamp":1692018130000},"page":"1503-1537","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Detecting and approximating decision boundaries in low-dimensional spaces"],"prefix":"10.1007","volume":"95","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8115-7074","authenticated-orcid":false,"given":"Matthias","family":"Grajewski","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8324-821X","authenticated-orcid":false,"given":"Andreas","family":"Kleefeld","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,8,14]]},"reference":[{"key":"1618_CR1","doi-asserted-by":"publisher","unstructured":"Figueira, J.: Multiple criteria decision analysis: state of the art surveys. 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