Essec\Faculty\Model\Contribution {#2205
  #_index: "academ_contributions"
  #_id: "13115"
  #_source: array:26 [
    "id" => "13115"
    "slug" => "on-the-combinatorics-of-the-2-class-classification-problem"
    "yearMonth" => "2019-02"
    "year" => "2019"
    "title" => "On the combinatorics of the 2-class classification problem"
    "description" => "CORRÊA, R., DELLE DONNE, D. et MARENCO, J. (2019). On the combinatorics of the 2-class classification problem. <i>Discrete Optimization</i>, 31(1), pp. 40-55."
    "authors" => array:3 [
      0 => array:3 [
        "name" => "DELLE DONNE Diego"
        "bid" => "B00788133"
        "slug" => "delle-donne-diego"
      ]
      1 => array:1 [
        "name" => "CORRÊA Ricardo"
      ]
      2 => array:1 [
        "name" => "MARENCO Javier"
      ]
    ]
    "ouvrage" => ""
    "keywords" => array:2 [
      0 => "Classification -Integer programming"
      1 => "Polyhedral combinatorics"
    ]
    "updatedAt" => "2023-01-27 01:00:44"
    "publicationUrl" => "https://doi.org/10.1016/j.disopt.2018.08.002"
    "publicationInfo" => array:3 [
      "pages" => "40-55"
      "volume" => "31"
      "number" => "1"
    ]
    "type" => array:2 [
      "fr" => "Articles"
      "en" => "Journal articles"
    ]
    "support_type" => array:2 [
      "fr" => "Revue scientifique"
      "en" => "Scientific journal"
    ]
    "countries" => array:2 [
      "fr" => null
      "en" => null
    ]
    "abstract" => array:2 [
      "fr" => "A set of points  is linearly separable if the convex hulls of  and  are disjoint, hence there exists a hyperplane separating  from . Such a hyperplane provides a method for classifying new points, according to which side of the hyperplane the new points lie. When such a linear separation is not possible, it may still be possible to partition  and  into prespecified numbers of groups, in such a way that every group from  is linearly separable from every group from . We may also discard some points as outliers, and seek to minimize the number of outliers necessary to find such a partition. Based on these ideas, Bertsimas and Shioda proposed the classification and regression by integer optimization (CRIO) method in 2007. In this work we explore the integer programming aspects of the classification part of CRIO, in particular theoretical properties of the associated formulation. We are able to find facet-inducing inequalities coming from the stable set polytope, hence showing that this classification problem has exploitable combinatorial properties."
      "en" => "A set of points  is linearly separable if the convex hulls of  and  are disjoint, hence there exists a hyperplane separating  from . Such a hyperplane provides a method for classifying new points, according to which side of the hyperplane the new points lie. When such a linear separation is not possible, it may still be possible to partition  and  into prespecified numbers of groups, in such a way that every group from  is linearly separable from every group from . We may also discard some points as outliers, and seek to minimize the number of outliers necessary to find such a partition. Based on these ideas, Bertsimas and Shioda proposed the classification and regression by integer optimization (CRIO) method in 2007. In this work we explore the integer programming aspects of the classification part of CRIO, in particular theoretical properties of the associated formulation. We are able to find facet-inducing inequalities coming from the stable set polytope, hence showing that this classification problem has exploitable combinatorial properties."
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
      "en" => "Information Systems, Decision Sciences and Statistics"
    ]
    "indexedAt" => "2024-04-25T14:22:01.000Z"
    "docTitle" => "On the combinatorics of the 2-class classification problem"
    "docSurtitle" => "Articles"
    "authorNames" => "<a href="/cv/delle-donne-diego">DELLE DONNE Diego</a>, CORRÊA Ricardo, MARENCO Javier"
    "docDescription" => "<span class="document-property-authors">DELLE DONNE Diego, CORRÊA Ricardo, MARENCO Javier</span><br><span class="document-property-authors_fields">Systèmes d’Information, Sciences de la Décision et Statistiques</span> | <span class="document-property-year">2019</span>"
    "keywordList" => "<a href="#">Classification -Integer programming</a>, <a href="#">Polyhedral combinatorics</a>"
    "docPreview" => "<b>On the combinatorics of the 2-class classification problem</b><br><span>2019-02 | Articles </span>"
    "docType" => "research"
    "publicationLink" => "<a href="https://doi.org/10.1016/j.disopt.2018.08.002" target="_blank">On the combinatorics of the 2-class classification problem</a>"
  ]
  +lang: "fr"
  +"_type": "_doc"
  +"_score": 8.511416
  +"parent": null
}