Finding the Principal Points of a Random Variable

Emilio Carrizosa, E Conde, A Castaño, Dolores Romero Morales

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

The p-principal points of a random variable X with finite second moment are those p points in ${\mathbb R}$ minimizing the expected squared distance from X to the closest point. Although the determination of principal points involves in general the resolution of a multiextremal optimization problem, existing procedures in the literature provide just a local optimum. In this paper we show that standard Global Optimization techniques can be applied.
The p-principal points of a random variable X with finite second moment are those p points in ${\mathbb R}$ minimizing the expected squared distance from X to the closest point. Although the determination of principal points involves in general the resolution of a multiextremal optimization problem, existing procedures in the literature provide just a local optimum. In this paper we show that standard Global Optimization techniques can be applied.
LanguageEnglish
JournalR A I R O - Operations Research
Volume35
Issue number3
Pages315-328
ISSN0399-0559
DOIs
StatePublished - 2001
Externally publishedYes

Keywords

    Cite this

    Carrizosa, Emilio ; Conde, E ; Castaño, A ; Morales, Dolores Romero. / Finding the Principal Points of a Random Variable. In: R A I R O - Operations Research. 2001 ; Vol. 35, No. 3. pp. 315-328
    @article{9b9cd4fc84f14f6baa252e2882be128c,
    title = "Finding the Principal Points of a Random Variable",
    abstract = "The p-principal points of a random variable X with finite second moment are those p points in ${\mathbb R}$ minimizing the expected squared distance from X to the closest point. Although the determination of principal points involves in general the resolution of a multiextremal optimization problem, existing procedures in the literature provide just a local optimum. In this paper we show that standard Global Optimization techniques can be applied.",
    keywords = "Principal points, D.C. functions, Branch and bound",
    author = "Emilio Carrizosa and E Conde and A Casta{\~n}o and Morales, {Dolores Romero}",
    year = "2001",
    doi = "10.1051/ro:2001117",
    language = "English",
    volume = "35",
    pages = "315--328",
    journal = "R A I R O - Operations Research",
    issn = "0399-0559",
    publisher = "EDP Sciences",
    number = "3",

    }

    Carrizosa, E, Conde, E, Castaño, A & Morales, DR 2001, 'Finding the Principal Points of a Random Variable' R A I R O - Operations Research, vol. 35, no. 3, pp. 315-328. DOI: 10.1051/ro:2001117

    Finding the Principal Points of a Random Variable. / Carrizosa, Emilio; Conde, E; Castaño, A; Morales, Dolores Romero.

    In: R A I R O - Operations Research, Vol. 35, No. 3, 2001, p. 315-328.

    Research output: Contribution to journalJournal articleResearchpeer-review

    TY - JOUR

    T1 - Finding the Principal Points of a Random Variable

    AU - Carrizosa,Emilio

    AU - Conde,E

    AU - Castaño,A

    AU - Morales,Dolores Romero

    PY - 2001

    Y1 - 2001

    N2 - The p-principal points of a random variable X with finite second moment are those p points in ${\mathbb R}$ minimizing the expected squared distance from X to the closest point. Although the determination of principal points involves in general the resolution of a multiextremal optimization problem, existing procedures in the literature provide just a local optimum. In this paper we show that standard Global Optimization techniques can be applied.

    AB - The p-principal points of a random variable X with finite second moment are those p points in ${\mathbb R}$ minimizing the expected squared distance from X to the closest point. Although the determination of principal points involves in general the resolution of a multiextremal optimization problem, existing procedures in the literature provide just a local optimum. In this paper we show that standard Global Optimization techniques can be applied.

    KW - Principal points

    KW - D.C. functions

    KW - Branch and bound

    U2 - 10.1051/ro:2001117

    DO - 10.1051/ro:2001117

    M3 - Journal article

    VL - 35

    SP - 315

    EP - 328

    JO - R A I R O - Operations Research

    T2 - R A I R O - Operations Research

    JF - R A I R O - Operations Research

    SN - 0399-0559

    IS - 3

    ER -

    Carrizosa E, Conde E, Castaño A, Morales DR. Finding the Principal Points of a Random Variable. R A I R O - Operations Research. 2001;35(3):315-328. Available from, DOI: 10.1051/ro:2001117