Visualizing data as objects by DC (difference of convex) optimization

Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero

doi:10.1007/s10107-017-1156-1

Cited by 20 publications

(24 citation statements)

References 54 publications

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“…The location of the circles in the visualization region is guided by the weighted average of three In what follows, we formalize the definition of the three criteria, see also [7,10].…”

Section: The Visualization Modelmentioning

confidence: 99%

“…In this paper we use Mathematical Optimization techniques [7,10] to build a novel online visualization map that makes it possible to produce visualizations of news data as it develops over time. This online visualization in turn depends on Natural Language Processing for uncovering the semantic structure in the news data, by computing the importance and the relatedness of the words that occur.…”

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confidence: 99%

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On Building Online Visualization Maps for News Data Streams by Means of Mathematical Optimization

et al. 2018

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In this article we develop a novel online framework to visualize news data over a time horizon. First, we perform a Natural Language Processing analysis, wherein the words are extracted, and their attributes, namely the importance and the relatedness, are calculated. Second, we present a Mathematical Optimization model for the visualization problem and a numerical optimization approach. The model represents the words using circles, the time-varying area of which displays the importance of the words in each time period. Word location in the visualization region is guided by three criteria, namely, the accurate representation of semantic relatedness, the spread of the words in the visualization region to improve the quality of the visualization, and the visual stability over the time horizon. Our approach is flexible, allowing the user to interact with the display, as well as incremental and scalable. We show results for three case studies using data from Danish news sources.

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“…The location of the circles in the visualization region is guided by the weighted average of three In what follows, we formalize the definition of the three criteria, see also [7,10].…”

Section: The Visualization Modelmentioning

confidence: 99%

mentioning

confidence: 99%

On Building Online Visualization Maps for News Data Streams by Means of Mathematical Optimization

et al. 2018

Self Cite

View full text Add to dashboard Cite

show abstract

“…Constraints (4) and (5) establish the type of the variables. The box-connectivity in Definition 2, and required in (D2), is enforced through constraint (6). The box-connectivity of P r (x) is enforced by imposing that the box generated by each pair of non-adjacent cells belonging to P r (x) (two cells that do not share a common boundary) must contain also cells of P r (x), namely the intersection between such box (excluding its two generator cells) and the portion must be nonempty.…”

Section: The Mathematical Optimization Modelmentioning

confidence: 99%

“…Problems (α − SBM ) and (β − SBM ) enforce the box-connectivity of the portions P in the SBM through constraint (6). There exist several attempts in the literature which deal with the problem of modeling connectivity with integer programming, for instance using graph theory, [31,43], designing the connected portions according to fixed locations, [44], or considering nodecut sets, [8,58].…”

Section: A Tighter Modelmentioning

confidence: 99%

“…Treemaps are space-filling layouts which represent exactly the statistical values as the area of the rectangles but, in general, they fail to properly represent dissimilarities. Other attempts, such as [6,17,26,27,39,55], either disregard dissimilarities or proportions, or they are not space-filling visualization maps. In [5,20], space-filling rectangular maps are proposed, which take into consideration both dissimilarities and proportions.…”

Section: Introductionmentioning

confidence: 99%

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Visualizing proportions and dissimilarities by Space-filling maps: A Large Neighborhood Search approach

Carrizosa

Guerrero

Morales

2017

Computers & Operations Research

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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.

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Multiobjective Double Bundle Method for DC Optimization

Montonen

Joki

2020

Numerical Nonsmooth Optimization

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We discuss about the multiobjective double bundle method for nonsmooth multiobjective optimization where objective and constraint functions are presented as a difference of two convex (DC) functions. By utilizing a special technique called the improvement function, we are able to handle several objectives and constraints simultaneously. The method improves every objective at each iteration and the improvement function preserves DC property of the objectives and constraints. Once the improvement function is formed, we can approximate it by using a special cutting plane model capturing the convex and concave behaviour of a DC function. We solve the problem with a modified version of the single-objective double bundle method using the cutting plane model as a objective. The multiobjective double bundle method is proved to be finitely convergent to a weakly Pareto stationary solution under mild assumptions. Moreover, the applicability of the method is considered.

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Visualizing data as objects by DC (difference of convex) optimization

Cited by 20 publications

References 54 publications

On Building Online Visualization Maps for News Data Streams by Means of Mathematical Optimization

On Building Online Visualization Maps for News Data Streams by Means of Mathematical Optimization

Visualizing proportions and dissimilarities by Space-filling maps: A Large Neighborhood Search approach

Multiobjective Double Bundle Method for DC Optimization

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