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One-Against-All Halfplane Dichotomies

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Structural, Syntactic, and Statistical Pattern Recognition (S+SSPR 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13813))

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Abstract

Given M vectors in N-dimensional attribute space, it is much easier to find M hyperplanes that separate each of the vectors from all the others than to solve M arbitrary linear dichotomies with approximately equal class memberships. An explanation of the rapid growth with M and N of the number of separable one-against-all linear halfplane dichotomies is proposed in terms of convex polyhedra in a hyperspherical shell. The counterintuitive surge is illustrated by averaged results on pseudo-random integer arrays obtained by Linear Programming and Neural Networks. Although the initial motivation arose from seemingly arbitrary rankings of scientists and universities, this project is not directed at any application.

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Authors and Affiliations

  1. Rensselaer Polytechnic Institute, Troy, N.Y., 12180, USA

    George Nagy & Mukkai Krishnamoorthy

Authors
  1. George Nagy
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  2. Mukkai Krishnamoorthy
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Correspondence to George Nagy .

Editor information

Editors and Affiliations

  1. Concordia University, Montreal, QC, Canada

    Adam Krzyzak

  2. Concordia University, Montreal, QC, Canada

    Ching Y. Suen

  3. Ca Foscari University of Venice, Venezia, Italy

    Andrea Torsello

  4. Concordia University, Montreal, QC, Canada

    Nicola Nobile

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Nagy, G., Krishnamoorthy, M. (2022). One-Against-All Halfplane Dichotomies. In: Krzyzak, A., Suen, C.Y., Torsello, A., Nobile, N. (eds) Structural, Syntactic, and Statistical Pattern Recognition. S+SSPR 2022. Lecture Notes in Computer Science, vol 13813. Springer, Cham. https://doi.org/10.1007/978-3-031-23028-8_19

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  • DOI: https://doi.org/10.1007/978-3-031-23028-8_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-23027-1

  • Online ISBN: 978-3-031-23028-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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