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Sparse Approximate Solutions to Max-Plus Equations

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Discrete Geometry and Mathematical Morphology (DGMM 2021)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12708))

Abstract

In this work, we study the problem of finding approximate, with minimum support set, solutions to matrix max-plus equations, which we call sparse approximate solutions. We show how one can obtain such solutions efficiently and in polynomial time for any \(\ell _p\) approximation error. Subsequently, we propose a method for pruning morphological neural networks, based on the developed theory.

P. Maragos—The work of P. Maragos was co-financed by the European Regional Development Fund of the European Union and Greek national funds through the Operational Program Competitiveness, Entrepreneurship and Innovation, under the call RESEARCH–CREATE–INNOVATE (Project: “e-Prevention”, code: T1EDK-02890).

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Notes

  1. 1.

    The new, truncated, error function remains supermodular; see [16].

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Tsilivis, N., Tsiamis, A., Maragos, P. (2021). Sparse Approximate Solutions to Max-Plus Equations. In: Lindblad, J., Malmberg, F., Sladoje, N. (eds) Discrete Geometry and Mathematical Morphology. DGMM 2021. Lecture Notes in Computer Science(), vol 12708. Springer, Cham. https://doi.org/10.1007/978-3-030-76657-3_39

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  • DOI: https://doi.org/10.1007/978-3-030-76657-3_39

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