Output-sensitive algorithms for computing nearest-neighbour decision boundaries

David Bremner, Erik Demaine, Jeff Erickson, John Iacono, Stefan Langerman, Pat Morin, Godfried Toussaint

    Research output: Contribution to journalArticle

    Abstract

    Given a set R of red points and a set B of blue points, the nearest-neighbour decision rule classifies a new point q as red (respectively, blue) if the closest point to q in R∪B comes from R (respectively, B). This rule implicitly partitions space into a red set and a blue set that are separated by a red-blue decision boundary. In this paper we develop output-sensitive algorithms for computing this decision boundary for point sets on the line and in ℝ 2. Both algorithms run in time O(n log k), where k is the number of points that contribute to the decision boundary. This running time is the best possible when parameterizing with respect to n and k.

    Original languageEnglish (US)
    Pages (from-to)451-461
    Number of pages11
    JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume2748
    StatePublished - 2003

    Fingerprint

    Nearest Neighbor
    Computing
    Output
    Decision Rules
    Point Sets
    Classify
    Partition
    Line

    ASJC Scopus subject areas

    • Computer Science(all)
    • Biochemistry, Genetics and Molecular Biology(all)
    • Theoretical Computer Science

    Cite this

    Output-sensitive algorithms for computing nearest-neighbour decision boundaries. / Bremner, David; Demaine, Erik; Erickson, Jeff; Iacono, John; Langerman, Stefan; Morin, Pat; Toussaint, Godfried.

    In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 2748, 2003, p. 451-461.

    Research output: Contribution to journalArticle

    Bremner, David ; Demaine, Erik ; Erickson, Jeff ; Iacono, John ; Langerman, Stefan ; Morin, Pat ; Toussaint, Godfried. / Output-sensitive algorithms for computing nearest-neighbour decision boundaries. In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 2003 ; Vol. 2748. pp. 451-461.
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    AU - Toussaint, Godfried

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