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Visualizing proportions and dissimilarities by space-filling maps: a large neighborhood search approach

机译:通过填满地图可视化比例和差异:一种大型邻域搜索方法

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摘要

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. Toenhance 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). Theconstruction 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.
机译:在本文中,我们解决了可视化一组个人的问题,这些个人已附加了按比例给出的统计值和不相似性度量。每个个体都表示为单位正方形内的一个区域,以使区域的面积表示比例,它们之间的距离表示不相似。为了增强表示的可解释性,要求区域满足两个属性。首先,它们必须形成单位正方形的分隔,即,分隔单位的部分必须覆盖其区域且不重叠。其次,这些部分必须由相互连接的矩形联合体组成,以验证所谓的盒连接性约束,并生成可视化图,称为空间填充盒连接图(SBM)。 SBM的构造被正式表示为一个数学优化问题,可以通过使用大邻域搜索技术来启发式解决。本文提出的方法适用于三个真实世界的数据集:第一个涉及欧洲和亚洲的金融市场,第二个涉及英语字母中的字母,最后一个是荷兰在地理上的应用。

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