Bicompletions of distance matrices

Dusko Pavlovic

    Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

    1 Citation (Scopus)
    11 Downloads (Pure)

    Abstract

    In the practice of information extraction, the input data are usually arranged into pattern matrices, and analyzed by the methods of linear algebra and statistics, such as principal component analysis. In some applications, the tacit assumptions of these methods lead to wrong results. The usual reason is that the matrix composition of linear algebra presents information as flowing in waves, whereas it sometimes flows in particles, which seek the shortest paths. This wave-particle duality in computation and information processing has been originally observed by Abramsky. In this paper we pursue a particle view of information, formalized in distance spaces, which generalize metric spaces, but are slightly less general than Lawvere’s generalized metric spaces. In this framework, the task of extracting the ‘principal components’ from a given matrix of data boils down to a bicompletion, in the sense of enriched category theory. We describe the bicompletion construction for distance matrices. The practical goal that motivates this research is to develop a method to estimate the hardness of attack constructions in security.
    Original languageEnglish
    Title of host publicationComputation, Logic, games, and Quantum Foundations. The Many Facets of Samson Abramsky
    Subtitle of host publicationEssays Dedicated to Samson Abramsky on the Occasion of His 60th Birthday
    EditorsBob Coecke, Luke Ong, Prakash Panangaden
    Place of PublicationBerlin
    PublisherSpringer
    Pages291-310
    Number of pages20
    ISBN (Electronic)978-3-642-38164-5
    ISBN (Print)978-3-642-38163-8
    DOIs
    Publication statusPublished - Mar 2013

    Publication series

    NameLecture Notes in Computer Science
    PublisherSpringer
    Volume7860
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Keywords

    • Distance matrix
    • Weighted limit
    • Distance space
    • Kolmogorov complexity
    • Denotational semantic

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