TY - JOUR

T1 - Visualizing Proportions and Dissimilarities by Space-filling Maps

T2 - A Large Neighborhood Search Approach

AU - Carrizosa, Emilio

AU - Guerrero, Vanesa

AU - Romero Morales, Dolores

PY - 2017/2

Y1 - 2017/2

N2 - In this paper we address the problem of visualizing a set of individuals, which have attached a statistical value given as a proportion, and a dissimilarity measure. Each individual is represented as a region within the unit square, in such a way that the area of the regions represent the proportions and the distances between them represent the dissimilarities. To enhance the interpretability of the representation, the regions are required to satisfy two properties. First, they must form a partition of the unit square, namely, the portions in which it is divided must cover its area without overlapping. Second, the portions must be made of a connected union of rectangles which verify the so-called box-connectivity constraints, yielding a visualization map called Space-filling Box-connected Map (SBM). The construction of an SBM is formally stated as a mathematical optimization problem, which is solved heuristically by using the Large Neighborhood Search technique. The methodology proposed in this paper is applied to three real-world datasets: the first one concerning financial markets in Europe and Asia, the second one about the letters in the English alphabet, and finally the provinces of The Netherlands as a geographical application.

AB - In this paper we address the problem of visualizing a set of individuals, which have attached a statistical value given as a proportion, and a dissimilarity measure. Each individual is represented as a region within the unit square, in such a way that the area of the regions represent the proportions and the distances between them represent the dissimilarities. To enhance the interpretability of the representation, the regions are required to satisfy two properties. First, they must form a partition of the unit square, namely, the portions in which it is divided must cover its area without overlapping. Second, the portions must be made of a connected union of rectangles which verify the so-called box-connectivity constraints, yielding a visualization map called Space-filling Box-connected Map (SBM). The construction of an SBM is formally stated as a mathematical optimization problem, which is solved heuristically by using the Large Neighborhood Search technique. The methodology proposed in this paper is applied to three real-world datasets: the first one concerning financial markets in Europe and Asia, the second one about the letters in the English alphabet, and finally the provinces of The Netherlands as a geographical application.

KW - Large Neighborhood Search

KW - Dissimilarities

KW - Proportions

KW - Box-connectivity

KW - Data Visualization

KW - Data Visualization

KW - Box-connectivity

KW - Proportions

KW - Dissimilarities

KW - Large Neighborhood Search

U2 - 10.1016/j.cor.2016.09.018

DO - 10.1016/j.cor.2016.09.018

M3 - Journal article

SN - 0305-0548

VL - 78

SP - 369

EP - 380

JO - Computers & Operations Research

JF - Computers & Operations Research

ER -