multidimensional scaling

A Multi-Objective approach to visualize proportions and similarities between individuals by rectangular maps

  • Emilio Carrizosa
  • Dolores Romero Morales
  • Vanesa Guerrero
    • Categories Applications - OR and Management Sciences Tags , , ,

    In this paper we address the problem of visualizing the proportions and the similarities attached to a set of individuals. We represent this information using a rectangular map, i.e., a subdivision of a rectangle into rectangular portions so that each portion is associated with one individual, their areas reflect the proportions, and the closeness between … Read more

    Six mathematical gems from the history of Distance Geometry

  • Carlile Lavor
  • Leo Liberti
    • Categories Combinatorial Optimization, Global Optimization, Linear, Cone and Semidefinite Programming Tags , , ,

    This is a partial account of the fascinating history of Distance Geometry. We make no claim to completeness, but we do promise a dazzling display of beautiful, elementary mathematics. We prove Heron’s formula, Cauchy’s theorem on the rigidity of polyhedra, Cayley’s generalization of Heron’s formula to higher dimensions, Menger’s characterization of abstract semi-metric spaces, a … Read more