## GMap: Visualizing Graphs and Clusters as Maps (2009)

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Citations: | 12 - 9 self |

### BibTeX

@MISC{Gansner09gmap:visualizing,

author = {Emden Gansner and Stephen Kobourov and Yifan Hu},

title = {GMap: Visualizing Graphs and Clusters as Maps},

year = {2009}

}

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### Abstract

Information visualization is essential in making sense out of large data sets. Often, high-dimensional data are visualized as a collection of points in 2-dimensional space through dimensionality reduction techniques. However, these traditional methods often do not capture well the underlying structural information, clustering, and neighborhoods. In this paper, we describe GMap, a practical tool for visualizing relational data with geographic-like maps. We illustrate the effectiveness of this approach with examples from several domains. All the maps referenced in this paper can be found in www.research.att.com/˜yifanhu/GMap.

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Citation Context ...ulation). The map of science [5] uses vertex coloring in a graph drawing to provide an overview of the scientific landscape, based on citations of journal articles. Treemaps [30], squarified treemaps =-=[7]-=- and the more recent newsmaps [33] represent hierarchical information by means of space-filling tilings, allocating area proportional to some metric. Representing imagined places on a map as if they w... |

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66 | Graph Drawing by Stress Majorization
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Citation Context ... is still popular today (e.g., the New York Times red-blue maps of the US, showing the presidential election results in 2000 and 2004 with states drawn proportional to population). The map of science =-=[5]-=- uses vertex coloring in a graph drawing to provide an overview of the scientific landscape, based on citations of journal articles. Treemaps [30], squarified treemaps [7] and the more recent newsmaps... |

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Citation Context ...ons have also been considered. For example, treemaps [30] use a recursive space filling approach to represent trees. There is also a large body of work on representing planar graphs as contact graphs =-=[8, 14, 22]-=-, where vertices are embodied by geometrical objects and edges are shown by two objects touching in some specified fashion. Koebe’s theorem [18] shows that all planar graphs can be represented by touc... |

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Citation Context ...of interest in UML 1 All the images in this paper are available in high-resolution form at www.research.att.com/ ∼ yifanhu/MAPS.Figure 1: A map of books related to “1984” from Amazon.com diagram. In =-=[9]-=-, “bubblesets,” based on isocontours, are used to depict multiple relations among a set of objects. Simonetto et al. [35] automatically generate Euler diagrams which provide one of the standard ways, ... |

29 |
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Citation Context ...step in our GMap algorithm is to embed the graph in the plane. Possible embedding algorithms include principal component analysis [17], multidimensional scaling (MDS) [20], a force-directed algorithm =-=[12]-=-, or non-linear dimensionality reduction such as LLE [29] and Isomap [31]. The second step is a cluster analysis of the underlying graph or the embedded pointset from step one. In this step, it is imp... |

25 | Two improved algorithms for envelope and wavefront reduction
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Citation Context ...ong the edges is wellstudied. For example, in the context of minimum bandwidth or wavefront reduction ordering for sparse matrices, it is known that the problem is NP-hard, and a number of heuristics =-=[16, 21]-=- were proposed. One such heuristic is to order vertices using the Fiedler vector. Motivated by this approach, we approximate (1) by max ∑ wi, j(ci − c j) 2 , subject to ∑ c 2 k {i, j}∈Ec k∈Vc = 1 (2) ... |

22 |
The rectangular statistical cartogram
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Citation Context ...an space. Examples of the second kind of problem are found in cartograms, where the goal is to redraw a map so that the country areas are proportional to some metric, an idea which dates back to 1934 =-=[28]-=- and is still popular today (e.g., the New York Times red-blue maps of the US, showing the presidential election results in 2000 and 2004 with states drawn proportional to population). The map of scie... |

18 | 2006. Visualization of areas of interest in software architecture diagrams
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Citation Context ...so that the overall outline of the point set often follows that shape. Also related is work on visualizing subsets of a set of items using geometric regions to indicate the grouping. Byelas and Telea =-=[8]-=- use deformed convex hulls to highlight areas of interest in UML 1 All the images in this paper are available in high-resolution form at www.research.att.com/ ∼ yifanhu/MAPS.Figure 1: A map of books ... |

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Citation Context ...hu/MAPS.Figure 1: A map of books related to “1984” from Amazon.com diagram. In [9], “bubblesets,” based on isocontours, are used to depict multiple relations among a set of objects. Simonetto et al. =-=[35]-=- automatically generate Euler diagrams which provide one of the standard ways, along with Venn diagrams, for visualizing subset relationships. Apart from differences in the algorithms used to generate... |

16 |
On floor-plan of plane graphs
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Citation Context ...ons have also been considered. For example, treemaps [30] use a recursive space filling approach to represent trees. There is also a large body of work on representing planar graphs as contact graphs =-=[8, 14, 22]-=-, where vertices are embodied by geometrical objects and edges are shown by two objects touching in some specified fashion. Koebe’s theorem [18] shows that all planar graphs can be represented by touc... |

15 |
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Citation Context ...that two authors are connected with an edge if they have written at least one joint paper in the first ten years of the symposium. Even when drawn with a high-quality scalable forcedirected algorithm =-=[15]-=- and after applying a node-overlap removal step, the resulting graph looks more like a hairball than anything else; see Fig. 5. On the other hand, the corresponding map, as shown in Fig. 6, seems much... |

15 | A multilevel algorithm for wavefront reduction
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Citation Context ...ong the edges is wellstudied. For example, in the context of minimum bandwidth or wavefront reduction ordering for sparse matrices, it is known that the problem is NP-hard, and a number of heuristics =-=[16, 21]-=- were proposed. One such heuristic is to order vertices using the Fiedler vector. Motivated by this approach, we approximate (1) by max ∑ wi, j(ci − c j) 2 , subject to ∑ c 2 k {i, j}∈Ec k∈Vc = 1 (2) ... |

15 |
Modularity clustering is force-directed layout. Physical Review, E 79 (2), 026102. 404 Nooy W., Mrvar A., and Batagelj V. 2011. Exploratory social network analysis with pajek
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Citation Context ... between clusters. On the other hand, with an embedding derived from a force-directed algorithm [12], a modularity based clustering [26] could be a better fit. The two algorithms are strongly related =-=[27]-=- and therefore we can expect vertices that are in the same cluster to also be physically close to each other in the embedding. In the third step the two-dimensional embedding together with the cluster... |

14 | Compact floor-planning via orderly spanning trees
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Citation Context ...ons have also been considered. For example, treemaps [30] use a recursive space filling approach to represent trees. There is also a large body of work on representing planar graphs as contact graphs =-=[8, 14, 22]-=-, where vertices are embodied by geometrical objects and edges are shown by two objects touching in some specified fashion. Koebe’s theorem [18] shows that all planar graphs can be represented by touc... |

14 | Methods for Realistic Landscape Imaging
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Citation Context ... therefore overall outline of the point set often follows that shape. Generating synthetic geography has a large literature, connected to its use in computer games and movies. Most of the work (e.g., =-=[23, 25]-=-) relies on variations of a fractal model. These techniques could provide additional photorealism, and may be used in future extention of our work. 3 THE GMAP ALGORITHM The input to our algorithm is a... |

9 | Optimal polygonal representation of planar graphs
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Citation Context ... maps also can have lakes, islands, and peninsulas, similar to those found in real geographic maps. 1 2 RELATED WORK There is a large body of work on contact polygonal representation of planar graphs =-=[11, 16, 19, 23]-=-. While some theoretical problems from this area are related to our work, the emphasis in this paper is not on the strict preservation of adjacency information, but on a practical approach to visualiz... |

8 |
ColorBrewer - selecting good color schemes for maps. www.colorbrewer.org
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Citation Context ...everal disjoint regions we must use the same color for all regions to avoid ambiguity. Thus, four colors (or even five or six) are not enough. In GMap we start with a coloring scheme from ColorBrewer =-=[6]-=-, which typically has 5 easy to differentiate base colors, and generate as many colors as the number of countries by blending the base colors. As a result our color space is linear and discrete. Becau... |

6 | C.: Putting recommendations on the map - visualizing clusters and relations
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Citation Context ...kLand observed that the “gateway” to Fringistan is Rand’s Atlas Shrugged. We plan to perform formal user studies of the interaction with graphs and maps, in the context of visualizing recommendations =-=[17]-=-. There are practical and theoretical obstacles to obtaining “perfect” maps, that is, maps that do not omit or distort the underlying information. However, a similar drawback plagues any 2dimensional ... |

4 | M.T.: Choosing colors for geometric graphs via color space embeddings
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Citation Context ...not connected countries having very similar colors by making the country graph a complete graph, and assigning edge weights to be the inverse of the distance between two countries. Dillencourt et al. =-=[9]-=- investigated the case where all colors in the color spectrum are available. They proposed a force-directed model aimed at selecting |Vc| colors as far apart as possible in the color space. However in... |

4 |
Gmap: Drawing graphs and clusters as map
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Citation Context ... and clustering information so that we can create the map representation and make it aesthetically appealing. Our presentation is narrative and informal. We refer the interested reader to the article =-=[5]-=- for technical details and more references. Making the map Given the placement of the points from the first step, and their clustering from the second, we want to create a map, with inner boundaries s... |

2 |
A fractal-based relaxation algorithm for shape from terrain image
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Citation Context ... therefore overall outline of the point set often follows that shape. Generating synthetic geography has a large literature, connected to its use in computer games and movies. Most of the work (e.g., =-=[23, 25]-=-) relies on variations of a fractal model. These techniques could provide additional photorealism, and may be used in future extention of our work. 3 THE GMAP ALGORITHM The input to our algorithm is a... |

2 |
The Shaping of Middle-Earth
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Citation Context ...ing tilings, allocating area proportional to some metric. Representing imagined places on a map as if they were real countries also has a long history, e.g., the 1930’s Map of Middle Earth by Tolkien =-=[32]-=- and the Bücherlandes map by Woelfle from the same period [1]. More recent popular maps include xkcd’s Map of Online Communities [4]. While most such maps are generated in an ad hoc manner and are not... |