Visualizing proportions and dissimilarities by Space-filling maps: A Large Neighborhood Search approach. (February 2017)

• Record Type: Journal Article
• Authors: Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero
• Is Part Of: Computers & operations research. Volume 78(2017)
• Page Start: 369
• Page End: 380
• Publication Date: 2017-02
• Subjects: Data Visualization -- Box-connectivity -- Proportions -- Dissimilarities -- Large Neighborhood Search; Operations research -- Periodicals; Electronic digital computers -- Periodicals; 004.05
• DOI: 10.1016/j.cor.2016.09.018
• Languages: English
• ISSNs: 0305-0548

Abstract

Abstract: 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. Abstract : Highlights: We visualize the proportions and the dissimilarities attached to a set of individuals by using Space-filling Box-connected Maps (SBM), which are more flexible than the pie or fan charts. We propose a Mixed Integer Linear model to build SBMs. Large Neighborhood Search metaheuristic is shown to be capable of help visualizing complex sets. The methodology proposed in this paper is applicable to sets of different nature, as shown in our examples.