Visualizing Graphs and Clusters as Maps

Emden R. Gansner∗ Yifan Hu† AT&T Labs - Research, 180 Park Ave, Florham Park, NJ 07932 AT&T Labs - Research, 180 Park Ave, Florham Park, NJ 07932 Stephen G. Kobourov‡ University of Arizona, 1040 E 4th Street, Tucson, AZ 85721

ABSTRACT to understand the visualization of a biological experiment that was Information visualization is essential in making sense out of large created by a statistician. data sets. Often, high-dimensional data are visualized as a collec- When large data sets are drawn as point clouds or node-link tion of points in 2-dimensional space through dimensionality reduc- graphs, it is sometimes possible to observe a visual similarity to ge- tion techniques. However, these traditional methods often do not ographic maps. For example, several small connected components capture well the underlying structural information, clustering, and next to a much larger component suggest several small islands next neighborhoods. In this paper, we describe GMap, a practical algo- to a big continent. We took the next step in visualizing data directly rithmic framework for visualizing relational data with geographic- as a geographic map. A map representation is familiar and intuitive; like maps. We illustrate the effectiveness of this approach with ex- most people are very familiar with maps and nicely drawn maps of- amples from several domains. ten provide hours of enjoyable exploration. Many people take ad- vantage of this familiarity with maps and manually create map-like Keywords: Information Visualization; Clustering; Graph Draw- representations that portray relations among abstract concepts. We ing; Graph Coloring; Maps; Set Visualization. were interested in automating the process which begins with the data and ends with a drawing of a map. In this process there are INTRODUCTION two main competing goals: First, we would like to be faithful to the With the growth of the Internet and scientific and technological ad- data, by maintaining the inherent structure and relationships, with- vances, the world has seen an explosion in the generation and col- out adding or implying non-existent structure. Second, we would lection of data. This data is often relational, high-dimensional, or like the final result to look like a map, using standard cartographic both. With such a wealth of data comes the need to understand it, conventions. Our attempt to address these two goals led to a frame- analyze it, and use it. Visualization can play a key role in all of work for a map-based data representation that we call GMap. these steps, but especially so in the exploratory phase. Many useful techniques for visualizing abstract data sets have GMAP been considered in the past. Graphs made of nodes and links (or The GMap framework allows us to generate map-like represen- edges) are often used to capture the relationships between objects, tations from an abstract data set. Specifically, given a high- and graph drawing allows us to visualize such relationships. Typ- dimensional data set or a graph with edge weights (e.g., the sim- ically nodes are represented by points in two or three dimensional ilarity between books as determined by purchase behavior at Ama- space, and edges are represented by lines between the correspond- zon.com), it produces a drawing with a map-like look, with coun- ing vertices. For an example of a relational data set, consider the tries that enclose similar objects, outer boundaries that follow the Amazon.com graph, where books are nodes and there is an edge be- outline of the vertex set, and inner boundaries that have the twists tween two books if people who have bought one of the books also and turns found in real maps. A typical example is in Figure 1 buy the other. and shows just under 1000 books.1 Our maps also can have lakes, High-dimensional data sets, on the other hand, are often visual- islands, and peninsulas, similar to those found in real geographic ized as point clouds in two or three dimensional space. An example maps. is the listening pattern of users of the last.fm website. Each user can be represented by a long vector. The dimension of the vector is GMap is a framework in the true sense of the word, rather than a the same as the number of musicians available at the website, and specific algorithm. It consists of four main steps, the first two steps the value of each element is proportional to the number of times a can be achieved by a variety existing algorithms. For the last two user listens to the corresponding musician. In a point cloud visual- steps we propose new algorithms. ization, each point is a user and two points are close to each other In the first step we take as input a graph or high-dimensional if the two users have similar music taste. data set, and embed it into the plane. The statistics and scien- Unfortunately, these standard approaches of node-link diagrams tific modeling communities have extensively explored this prob- and point cloud representations often require considerable effort to lem and provide many ways of doing this. Possible embedding comprehend. If we desire to make the data accessible to people algorithms include principal component analysis, multidimensional outside the areas of computer science and statistics, providing more scaling (MDS), force-directed algorithms, or non-linear dimension- compelling drawings is an important task. This is certainly true for ality reductions such as Locally Linear Embedding and Isomap. the ordinary user who might be curious about the recommendations The second step takes this collection of points in the plane and made by Amazon.com, but is also true for the biologist who wishes aggregates them into clusters. Here, it is important to match the clustering algorithm to the embedding algorithm. For example, a ∗e-mail: [email protected] geometric clustering algorithm such as k-means may be suitable for †e-mail: [email protected] an embedding derived from MDS, as the latter tends to place similar ‡e-mail: [email protected]. Work done while this author was at points in the same geometric region with good separation between AT&T Labs. clusters. On the other hand, with an embedding derived from a

1Most of the images in this article are available in an interac- tive form at http://www.research.att.com/˜yifanhu/MAPS/ imap.html.

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Rock 'n' Roll: A The SeafarerNew Play

Figure 1: A map of books related to “1984” from Amazon.com

force-directed layout, a modularity based clustering [9] could be a Making the map better fit. The two algorithms are strongly related, and therefore we can expect vertices that are in the same cluster to also be physically Given the placement of the points from the first step, and their clus- close to each other in the embedding. tering from the second, we want to create a map, with inner bound- aries separating points not in the same cluster and outer bound- In the third step, we use the two-dimensional embedding to- aries preferably following the general outline of the point set. A gether with the clustering to create the actual map by delineating naive approach for creating the map is to form the Voronoi diagram country boundaries, carving continental outlines, and separating is- of the vertices based on the embedding information, together with lands from continents. This can be accomplished with the help of four points on the corners of the bounding box. This is illustrated plane partitioning techniques such as Voronoi diagrams, but with in Figure 2(a). Such maps often have sharp corners, and angular new algorithmic techniques to ensure realistic looking outer and in- outer boundaries. We can generate more natural outer boundaries ner boundaries. by adding random points to the current embedding. A random point is only accepted if its distance from any of the real points is more In the fourth and final step, we add additional graphical attributes than some preset threshold. Note that this step can be implemented to the drawing in order to enhance its clarity, to serve as keys to the efficiently using a suitable space decomposing data structure, such abstract data, or to simply make it more aesthetically appealing. as a quadtree. This leads to boundaries that follow the shape of This would involve assigning an appropriate set of colors to the the point set. In addition, the randomness of the points on the out- various regions. We propose a spectral algorithm that maximize skirts gives rise to some randomness of the outer boundaries, thus color difference between neighboring countries. In addition, we making them more map-like, as seen in Figure 2(b). Furthermore, could add mountains to the map or overlay it with a heat map to depending on the value of the threshold, this step can also result indicate scalar values associated with geographic positions. in the creation of lakes and fjords in areas where vertices are far While the first two steps have been the subject of hundreds of apart from each other. Nevertheless, some inner boundaries remain papers, the last two steps in this process are new. With this in mind, artificially straight. in the next sections we describe how we put together the embedding At this point, we still note the undesirable feature that the “coun- and clustering information so that we can create the map represen- tries” all have roughly the same area (Figure 2(b)), whereas we tation and make it aesthetically appealing. Our presentation is nar- might prefer some areas to be larger than others (e.g., due to the rative and informal. We refer the interested reader to the article [5] importance of the entities they represent). As an illustration, in Fig- for technical details and more references. ure 2, we assume that “node 1” is more important than the other

2 at the Symposium on Graph Drawing. The upper drawing exhibits the connected components and closely related nodes are indicated by proximity, but cluster structure is only hinted at. In the GMap version, the cluster structure is obvious. Coloring the nodes in the node-link drawing would still only imply the clusters. The GMap figure makes the clusters explicit as well as indicating strong cluster relations where two clusters share a border. When projecting high dimensional data into low dimensional (a) (b) space, distance distortion is inevitable, and the resulting figure will often have some anomalies and distortions. Thus, some strongly re- lated objects may be separated by seemingly unrelated objects. For example, in Figure 3, we see a cluster of North American authors split into three components in the southwest part of the map (the three beige components). The authors in the central component have had much more collaboration with European authors; those in the bottom-left component much less so. There is a singleton component sitting in the middle, reflecting the fact that this author, “North”, collaborated with both the European authors, and with the group of authors that form the bottom-left component. Such frag- (c) (d) mentations are inherent in the embedding and clustering algorithms used in the first two steps. However we have proposed ways [5] to Figure 2: (a) Voronoi diagram of vertices and corners of bounding use the clustering information to adjust the layout, so that the re- box; (b) better construction of outer boundaries through placement gions of countries are more contiguous, at the expense of some loss of random points; (c) Voronoi diagram of vertices and points inserted of relational information captured in the original embedding. around the bounding boxes of the labels; (d) the final map. We believe that the map-like visualization better captures some 2 of the cluster structure while at the same time providing an illus- two nodes, and use a larger label for that area. To make areas fol- tration that is more attractive to the typical user than the traditional low the shape of the labels, we first generate artificial points along scatterplots and node-link diagrams. Although we have not yet run the bounding boxes of the labels as shown in Figure 2(c). To make a formal user study, anecdotal evidence from our customers and the inner boundaries less uniform and more map-like, we perturb colleagues corroborates this claim. these points randomly instead of running strictly along the boxes. Here Voronoi cells that belong to the same vertex are colored in the Coloring the map same color, and cells that correspond to the random points on the outskirt are not shown. Cells of the same color are then merged to The final step, annotating the map with graphical attributes, in- give the final map in Figure 2(d). Note that instead of the bounding volves assigning good colors to the countries in our maps. The boxes of labels, we could use any 2D shapes, e.g., the outlines of Four Color Theorem states that only four colors are needed to color real countries, in order to obtain a desired look and proportion of any map so that no neighboring countries share the same color. It area, as long as these shapes do not overlap. is implicitly assumed that each country forms a connected region. We note that not all real maps have complicated boundaries. For This result, however, is of limited use to us because countries in our example, boundaries of the western states in the United States often maps are not always connected. Therefore, we will have to use one have long straight sections. We believe that irregular boundaries unique color for each cluster to avoid ambiguity. Estimation of the are more typical of historical and geographic boundaries, and lead number of colors an “average human” can discriminate, when color to more map-like results. But this is a matter of personal taste and pairs are presented side by side, ranges from tens of thousands to a our technique can generate maps of both styles. million. On the other hand, it takes much more effort when com- When mapping vertices that contain cluster information, in addi- paring colors that are similar. A further limiting factor is that 5% tion to merging cells that belong to the same vertex, we also merge of males are color blind, which rules out certain coloring schemes. cells that belong to the same cluster, thus forming regions of com- Finally, the limited palette of map-like coloring schemes reduces plicated shapes, with multiple vertices and labels in each region. At the choice of colors even more. this point we can add more geographic components to strengthen In GMap, we start with a coloring scheme from ColorBrewer the map metaphor. For instance, in places where there is significant (www.colorbrewer.org), and generate as many colors as the space between vertices in neighboring clusters, we can add lakes, number of countries by blending the base colors. As a result, our rivers, or mountain ranges to the map to indicate the distance. color space is linear and discrete. Because of the blending, any With the regions determined, we have a representation of the two consecutive colors in the linear array of colors are similar to data in which closely related objects, as determined by the graph each other. When applying these colors to the map, we want to topology and possibly edge weights, are drawn closely together. avoid coloring neighboring countries with such pairs of colors.3 This geometric information is then used to discover clusters among With this in mind, we need to solve a discrete optimization problem the objects. To emphasize the clusters, each is represented as a where we find the best color permutation such that the color differ- collection of geometric regions. ence between neighbors is maximized overall. This is achieved by Figure 3 shows the difference between a typical node-link graph a combination of two procedures. They both operate on the country layout and the result of applying GMap to the same data. (Indeed, graph. The country graph is created from the original graph after it the graph layout is first step of the GMap layout.) The data rep- has been embedded and clustered. Specifically, the country graph resents the graph of author collaborations between 1994 and 2004 contains a node for each country, with each edge representing two

2A weighted Voronoi diagrams can be used to make the area of each 3Although two non-neighboring countries with similar colors can lead Voronoi cell proportional to its weight. We do not use this approach, how- the viewer to believe that they are disjoint regions of the same country, this ever, because we want the Voronoi cell to also contain a specific shape, e.g., problem diminishes when the two countries are sufficiently far apart, as it is the bounding box of a label. unlikely that distant regions belong to the same cluster.

3 Figure 3: Node-link drawing compared to the GMap representation 4 countries that share a border. The first procedure turns the map col- Based on this style of use, GMap figures are most effective when oring problem into that of a continuous optimization problem on displayed as a large image, often a meter or more in width, or via an the country graph, interactive viewer. In the former case, the user can physically move to change the scale. In the latter case, the viewer provides the scale 2 max ∑ wi, j(ci − c j) , subject to ∑ ck = 1, (1) change and, at the same time, can provide some version of semantic {i, j}∈Ec k∈Vc zoom, so that more detail is added the more the user zooms in. In addition, an interactive viewer can provide such additional features where Ec is the set of edges in the country graph, scalar value ci as textual search or links connecting a feature on the map to some is the color (index) assigned to country i, and weighting factor wi, j external information. For example, clicking on a book shown in the measures how important it is to promote color difference between BookLand layout might take the user to its entry at Amazon.com. i j country and country . The solution is the largest eigenvector of Given the page size limitations of a traditional journal, the fig- the weighted Laplacian of the country graph. We then use the or- ures included here are scaled to illustrate some features of the dering induced by the values of the eigenvector as the color permu- GMap layout (Figures 4 and 8) or to give a high-level view of such tation. This is then followed by a greedy color swapping procedure maps. The reader is encouraged to explore some GMap layouts at to see if the color difference can be further improved. This heuristic the site indicated in Footnote 1. algorithm improves the color difference between neighbors signifi- We now consider how GMap works in practice with various dif- cantly compared with a random color assignment. ferent data sets. In the first, we visualize the “landscape” of music Figure 4 illustrates the difference between a simple, random col- artists. In the second, we visualize the “landscape” of books as oring and a coloring obtained using our approach. Note, for ex- implied by user purchase behavior at Amazon.com. In the third, ample, that in the random coloring, the countries in the middle are we visualize international trade data. Finally, we look at TV pro- assigned colors in a green-gray palette, making it difficult to distin- grams based on users’ viewing habits. In our implementation we guish them. In the lower, optimized coloring, the separate regions use a scalable force-directed layout algorithm for step one and a in the central part are much more evident. modularity-based clustering algorithm for step two. USING GMAPTO VISUALIZE SET RELATIONS It is important to note that in all cases the countries and their geography in the resulting maps are not part of the input data, but GMap is designed for visualizing cluster relations as maps, where emerge from the graph layout and clustering algorithms. This gives each item is assumed to belong to one cluster and hence one coun- the user a potential tool to discover structure based solely on local try. However, the same algorithm can be easily adapted to vi- data. sualize multiple relations among a set of objects. Byelas and Telea [3] proposed visualizing set relations using deformed convex MusicLand hulls. Collins et al. [4] proposed “bubblesets,” based on isocon- To create a land of music, we collected data from a web crawl tours. GMap provides a different approach. of the last.fm website. As an Internet radio and music To apply GMap for visualizing sets, we work on one set at a time. community website, it has over 30 million users, and recom- Items not in the active set are considered obstacles, and treated the mends music based on user profiles. Over several years, the same as random points inserted in the GMap algorithm. Applying recommender system has collected information about how one GMap then gives us a map of one country. By repeating this process band/musician/composer/artist is related to another in terms of how for multiple sets, and using transparency to allow overlapping parts many listeners of one also enjoy the other. For each composer, of the regions to be seen, we achieve a visualization of multiple the last.fm website lists the top 250 related composers. For exam- sets. ple, Beethoven is considered to have “super similarity” to Mozart, To avoid a country being disconnected, we add edges to link Bach, and Brahms, “very high similarity” to Mendelssohn, Schu- items in the same set. The edge addition process is similar to that mann, and Vivaldi 4 The website also provides the number of lis- of Collins et al. [4]. Edges are then routed as splines to avoid hit- teners of each musician. In April 2009, we crawled the website ting items not in the active set, when possible. Artificial points are by starting with Beethoven, and the top 20 musicians most sim- inserted along the spline edges. When GMap is applied, distant ilar to Beethoven, provided that each has at least 100,000 listen- items are connected by “bridges” along the edges. Figure 5 shows ers5. We then found the top 20 most similar musicians to each of a group of 55 photos from the Yale Face Database [7], represent- those with at least 100,000 listeners and proceed recursively. Our ing portraits using different expressions and lightings. The photos crawl yielded a graph with 2782 musicians, with edge weights cor- are embedded in 2D using MDS. The distance between two photos responding to the similarity between musicians. We further pruned is calculated using principal component analysis of a matrix of 55 this graph by only taking edges that have “super similarity”. Fi- rows, with each row a vector of the pixel values of a photo. Even nally, ignoring singletons, we end up with 2588 vertices. We then with careful pre-processing, the embedding does not always put the laid out the graph, clustered the vertices, and generated the Musi- same persons in the same neighborhood. Without set visualization, cLand map as shown in Figure 6. We next examine some of the it is difficult to identify all photos of the same person. Figure 5 countries in MusicLand in more detail. shows three sets of photos, each set belonging to a single person. The Mainland: The vast majority of musicians/bands is located As can be seen, each country is connected, and each avoids pho- in a single continent. While it is not as easy to spot major trends tos not in the set. This example shows that GMap provides a good along the main axes, many of the clusters are well-defined and alternative for set visualization. neighboring clusters make sense from a musical point of view. A GMAP CASE STUDIES cluster of classic rock on the east shore begins with Eric Clapton and Janis Joplin in the south, goes through the Who in the middle The GMap layout is meant to accentuate clusters in fairly large graphs. Gleaning information from the maps typically involves an 4Note that we do not know last.fm’s formal definition of “super similar- interactive, multi-scale process, similar to that used for exploring ity”, “very high similarity”, or “high similarity”. geographic maps. One views the map at small scale to sense the 5The reason we added a cut off of 100,000 listeners is that the number overall layout, the major regions, and how they relate to each other. of listeners of musicians seem to follow a power law distribution. Without One then zooms in to see local detail, and to traverse the map along the cut off, our crawl did not finish after over a week of crawling, during small features. At some point, one may zoom out again to put the which time we observed well over 1/2 million musicians, many with only a local details into a global context. few hundred listeners.

5 Figure 4: A random color assignment (top) vs. an optimized color assignment (bottom) that maximizes color differences between neighbors

6 Figure 5: Using GMap to visualize multiple sets. Photos in the same set belongs to the same person. before reaching the heavy rock cluster of AC/DC and Iron Maiden axes. Along the first axis, the west contains modern composers in the north. Farther to the north is the grunge cluster anchored by such as Ravel, Satie, and Part¨ , while the east contains 17th century Nirvana and Alice in Chains. composers such as Bach, Handel, and Albinoni. Along the second On the west coast of the main continent, we find a cluster of elec- axis, the north has a high concentration of opera composers such as tronic music, featuring Fatboy Slim, Daft Punk, and DJ Shadow. To Verdi, Rossini, and Puccini, whereas the south has more orchestral the north are avant-garde electronic bands like Aphex Twin, while and instrumental composers such as Holst, Elgar, and Stravinsky. in the extreme west are electronic classics such as Vangelis. To the Not surprisingly, Mozart and Beethoven are the most popular com- south is a compact and well-defined cluster of dance music repre- posers in the classical music cluster. The islands of Erik Satie and sented by Paul Oakenfold and ATB. Arvo Part¨ connect the big island in the east with the westernmost island of contemporary classical music represented by minimalists In the center of the map, there is a well-defined concentration of Philip Glass and Michael Nyman. female singer-songwriters such as Alanis Morissette, Norah Jones, and Amy Winehouse. Pop music is to the southeast of here with ABBA and Eurythmics, while hip-hop and rap music is southwest BookLand with Beyonce and Alicia Keys. Many e-commerce websites provide recommendations to allow for The Islands: There are two notable island regions in Musi- exploration of related items. Traditionally this is done in the form cLand: in the northeast is Reggae island, while the chain of islands of a flat list. For example, Amazon typically lists around 5-6 books off Rocky Coast in the southeast make up the Classical Archipelago. under “Customers Who Bought This Item Also Bought”, with a By zooming in (Figure 7), it is easy to find some general patterns in clickable arrow to allow a customer to see further related items. the layout of the archipelago along the East-West and North-South Instead of a flat list, which provides a very limited view of the

7 Madness

The Specials

The Skatalites

Desmond Dekker UB40

Toots and Bob Marley &The Maytals

Shaggy Inner Circle Jimmy Cliff

Beenie Man Peter Tosh Bob Marley Die Fantastischen Buju Banton Anthony BThe Wailers Clueso Peter Fox Sean Paul Vier Fettes Brot Culcha Candela Max Romeo Jan Delay Seeed Deichkind Eek-A-Mouse Patrice Ziggy Marley Gentleman Capleton Barrington Levy Burning Spear Dennis Brown

Black Uhuru Gregory Isaacs Sizzla Dane Cook Damian Marley Horace Andy The Upsetters Israel Vibration Culture Steel Pulse

Adam Sandler Lee "Scratch" Perry The Aquabats Augustus Pablo Monty Python Richard Cheese Alpha Blondy

Transplants

Hot Water King Tubby Music Big D and theThe Mighty South Park Mighty Bosstones

Operation Ivy Reel Big Mad Caddies Kids TableFish Slint Catch 22 "Weird Al" mewithoutYou The Vandals Red Sparowes The Suicide The Blood Less Than Machines Brothers Jake The Bouncing God Is The Good YankovicDescendents Souls Every Time Life Propagandhi Q and Pelican 65daysofstatic Not U Isis Comeback Kid Me First and the Good Riddance Silversun Pickups Rancid Gimme Gimmes Blindside Oceansizean Astronaut Meshuggah Converge I Die A Silver Fear Before the March dredg Low Neurosis The Bled Mt. Zion At the Psapp of Flames John Barry Between the Buried NOFX Norma Jean The Horrors and Me Anti-Flag Strike Anywhere The Sea Broadcast Godspeed You! Sparta Goldfinger The Fall Mono Black Emperor and Cake Tunng ...And You Will Know Us The Dillinger of Troy Bernard Herrmann Escape Plan Lagwagon You Say Party! We Stereolab Drive-In Biffy Clyro Jonny Greenwood Say Die! Thom Yorke This Will Destroy You Cursive Dead Poetic The DonnasMastodon Strung Out Guided by Tortoise Millencolin Smog Calexico Voices Ben Gibbard Casiotone for the by the Trail of... Ennio Morricone Les Savy Painfully Alone Xiu Xiu Explosions in Fav Youth Group Glassjaw Circa Survive the Sky Rise Against The Faint Lali Puna Bad Religion Klaus Badelt The Thermals The Bird and Pennywise Poison the Destroyer Well the Bee Silver Jews Sahara Hotnights Clutch Thrice Pavement Alexisonfire Ted Leo and The Dismemberment The Black She Wants Red House The Sounds No Use for Underoath Jerry Goldsmith Do Make The Pharmacists Bring Me Pretty Girls Plan Keys Revenge Pinback Painters a Name Thursday the Horizon Say Think Make Graves Mogwai Built to Evergreen Terrace British Sea AFI Secret Machines Albert Hammond, Saves the Drop Dead, Power Kyuss The Almost Chiodos The Stills Jr. Day Alkaline Trio Gorgeous Kent The Fiery Beach HouseJames Horner Radiohead Furnaces A Static boysetsfire Alan Silvestri The Black Fu Manchu Emery Yo La The Appleseed Lullaby A Day Eighteen Visions Tocotronic Saosin Caesars Heart Procession Spill The Kills Boys Night Enter Shikari Liars The Dears Tengo Stephen Malkmus Cast The Cooper The Juliana Out Temple Clause Slut Monster Magnet Theory Head Automatica Finch Harry Gregson-Williams John Williams Clinic Sparklehorse The Get Scary Kids Thomas Newman Up Kids Scaring Kids Elefant Hans Zimmer The American The Devil Deerhoof John Vanderslice The Wrens Sugarplum Fairy to Remember Analog Set The Polyphonic Wears Prada The NotwistBen Folds MxPx Fightstar Enon Alesana Venetian Snares Mercury Rev Nine Black Spree Daphne Loves Bayside From First Alps Derby µ-Ziq Straylight Run Spitalfield Shiny Toy to Last Howard Shore The Hold Senses Fail Test Icicles Tiger Lou Johnossi Interpol Grandaddy Guns August Burns Steady Sebadoh Silverstein Red James Newton Menomena Glasvegas The Hives From Autumn Danny Elfman Be Your Ambulance LTD to Ashes Mouse on Howard Own Pet Further Seems The Early Hidden in The OffspringHalifax WIZO Squarepusher The Ataris Mars Mando Diao Forever Plain View The Subways The Last November Aphex Twin Her Space Lambchop Rufio Hawthorne Heights Apostle of Ugly Casanova Shadow Puppets The Brian Escape The Holiday Tapes 'n AFX Hustle Sunset Rubdown Jonestown Massacre Funeral for Haste the Efterklang Fate Tapes The Honorary a Friend Matchbook Romance Day ImmortalBurzum Craig Armstrong Plaid Moneybrother My American Unwritten Law Ricardo Villalobos Autechre Arctic Monkeys Title Queens of the Say Anything The Dead Wagon Christ The Beta Stone Age Sherwood Heart Avenged Sevenfold Bright EyesModest Mouse Babyshambles Aiden 60s Band Spoon Therapy? Tool Boards of MUM Deerhunter The Walkmen The Postal Tomte It Dies Armor for Bleeding Through Cradle of Canada Neutral Milk Service Idlewild Brand New Billy Talent Today Satyricon Arovane Håkan Hellström Sleep Filth The Clientele The Ordinary Anberlin Luke Vibert LFO TV on Louis XIV The Perishers Mae Acceptance Dr. Dog Boys The Paddingtons Rocky Votolato Ben Folds Autopilot Off Sondre Lerche Kettcar Stars of The Album Five Story of The Rascals The Von Leaf Wolf Parade Relient K Puscifer the Lid The Most Yeah Yeah Black Rebel The Starting the Year J.B.O. Emperor Gui Boratto Spank Rock Bondies Taking Back Green DayAllister Dimmu Borgir Serene Republic Yeahs Death Cab Motorcycle Club Line Team Sleep Roots Manuva Dashboard Confessional Sunday Cold War for Cutie The Matches The Used Amiina Jarvis Cocker A.C. Newman Midlake Kids The Vines Brendan Benson Daedelus Oh No! Tokyo Police Dntel Seabear Hotel Jimmy Eat Serj Tankian DJ Vadim Oh My! 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Beth Gibbons & Laura Veirs Lucinda Williams Toploader Edwin McCain Junior Senior Fun Lovin' Howie Day Sonata Arctica Rustin Man Lamb Stereo MC's Dave Matthews & Linkin Park Therion Santogold Criminals Amos Lee Matchbox Twenty Warrant Roger Sanchez BlondesTim Reynolds Rosenstolz Tesla Way Out Chromeo Hooverphonic Pete Murray Matt Nathanson Bruce Dickinson Evanescence Angus & Jack Johnson West Anna Ternheim The John HammerFall BT The Presets Scissor SistersJulia Stone Xavier Rudd Rob Thomas Counting Crows Kosheen Butler Trio Crash Test Ratt Booty Luv Mika Gillian Welch Veruca Salt Duncan Sheik The Replacements Falco Paolo Nutini Jim Sturgess Epica Jay-Jay Johanson Justin Nozuka Dummies Poison Skid Row Sasha Hüsker Dü W.A.S.P. Edguy Olive Deee-Lite Avantasia Gus Gus Paramore L7 Cinderella Manowar Maria Taylor Tristan Prettyman Matt Wertz Within Temptation Supreme Beings The Ting Mandalay Stina Nordenstam Ingrid Michaelson The Cult Tings James Blunt of Leisure Patty Griffin Josh Kelley Lenny Kravitz Barenaked Ladies Quiet Riot Judas Priest Kamelot Daniel Powter Helloween Flunk Fiona Apple Martha Wainwright U2 Mission of Saxon Hybrid Blind Guardian Paul OakenfoldEverything but Bono White Lion Moloko Burma Herbert GrönemeyerMorrissey DragonForce Benny Benassi Chicane Ane Brun Rosie Thomas R.E.M. Twisted Sister Dio the Girl Kate Nash Missy Higgins Jon McLaughlin Gabriel & Poe M.I.A. Rachael Yamagata Townes Van Flyleaf The Smiths Accept Schiller Dresden Alphabeat Liz Phair Hercules and Zandt Maroon 5 Skunk Anansie Gang of Mötley Crüe Gamma Ray Stratovarius Nightwish Goldfrapp Haggard Bang Gang Butterfly Boucher Jason Mraz Echo & David Byrne David Lee Running Wild Love Affair Four Wire Nena Black Sabbath Basement Jaxx Esthero Anja Garbarek Dragonette 10,000 Maniacs Talking Heads The Cure Wax Poetic The Bunnymen Flipsyde Brandi Carlile Vienna Teng Fort Minor Roth A Fine Gym Class Gavin DeGraw Pati Yang The Sisters Blank & Tiësto Martina Topley-Bird Shivaree PJ Harvey Heroes Apocalyptica Sia Nick Cave and the of Mercy Jones Frou Frou Beth Orton INXS KISS Angra Bad Seeds Markus Schulz Cowboy Junkies Iced Earth Primal Fear Tarja Turunen Smoke City Ryan Cabrera Demons & Solar Stone The Sugarcubes Azure Ray Television Bauhaus Def Leppard Blue Foundation Bitter:Sweet Kate Havnevik The Beautiful Paul Weller Paul van Sarah Slean Leonard Cohen Hanoi Rocks Wizards Brazilian Girls Aimee Mann Teddy Geiger South AC/DC Anna Nalick James Morrison The The Siouxsie and KT Tunstall The Psychedelic Fragma Frenzy Charlotte Martin the Banshees Europe Joy Division Evergrey Tom Waits Furs Guns N' Robert Miles Imogen Heap The Cardigans Sara Bareilles The Fall Ministry Joe Dassin Emiliana Torrini Steve Earle John Mayer Devo Nick Cave Killing Joke Alice Cooper Roses Nevermore Yael Naim The Stooges New Order Sophie Zelmani The Be The Clash Above & April March Avril LavigneJohn Mayer Trio The B-52's Beyond Nerina Pallot Vanessa Carlton Heather Nova Natalie Merchant Lisa Loeb Good Tanyas Rage Dyk Vengaboys Björk Jem Chantal Kreviazuk Whitesnake Scorpions Sparks Sylver France Gall Thomas Dolby Ferry Corsten Dar Williams Public Image The Boomtown Françoise Hardy Emilie Simon Paula Cole Shawn Colvin Joan Baez The Church Sex Pistols System F Róisín Murphy New York Electronic Oingo Boingo Rats Dream Theater Ltd. Aerosmith Dolls AnnieSophie Ellis-Bextor The Velvet Pain of Velvet Revolver Kyau vs. Katy Perry Maria Mena Patti Smith The Jam The Undertones Symphony X Ayreon Salvation Sash! Sandi Thom Tori Amos Underground Van Halen Rainbow Albert DJ Danger Stiff Little Armin van Heaven 17 MC5 Adam and Lasgo Michelle Branch Iggy Pop Fingers Riverside Mouse Serge Gainsbourg Ratatat Billy Idol Bow Wow Buuren Lily Allen Sheryl Crow Orchestral Manoeuvres in XTC DJ Sammy Jacques Brel Keren Ann Sam Sparro Wow Charles Aznavour Alanis Morissette Ani DiFranco Prince Prince & the Dark Girls Aloud Siobhan Donaghy Nico Ian Van Robyn Tracy Chapman The Revolution The Stranglers Liquid Tension Amy Macdonald Lene Marlin John Cale Ramones Dahl Lady GaGa Jewel Meredith Brooks The Damned Deep Purple Experiment Blondie Buzzcocks The Exploited Cosmic Gate Duran Duran Milk Inc. Charlotte Gainsbourg Bob Dylan DJ BoBo Carla Bruni The Veronicas Squeeze the AntsRoxy Music Dead Kennedys Aqua K's Choice Lou Reed Ultravox Bon Jovi Everlast The Human Simple Minds Blue Öyster Kylie Minogue Joni Mitchell Joan Osborne League Bryan Ferry Cult ATB Darude Novaspace Édith Piaf Sugababes Natalie Imbruglia Flobots The Buggles Thompson Twins Suzanne Vega Visage Berlin Minor Threat Motorcycle Andain Bob Dylan and Rank 1 La Bouche Gabriella Cilmi Sarah McLachlan Joe Jackson The Cars Ted Nugent Vanessa Paradis Rachel Stevens Take That Colbie Caillat The Band Jon Bon Nouvelle Vague Kim Wilde The Small Immortal Technique A Flock Jovi Bad Brains Safri Duo Groove Coverage Culture Beat Emmylou Harris Faces Kate Ryan All Saints Indigo Girls dead prez Uriah Heep Dido Men Without of Seagulls Camille ABC Japan iiO 4 Strings Will Young Hats The Pretenders Elvis Costello & The Band Special D. Lucie Silvas Texas The Police The Corrs Kelly Clarkson The Attractions Ashlee Simpson Yazoo Pink Martini Melissa Etheridge k.d. lang Paul Simon Men at Cheap Trick Scooter Dannii Minogue Geri Halliwell Soft Cell Tears for Sweet Annie Lennox Nazareth Marco V Haddaway Work Sting Black Flag Girl Talk Kelly Osbourne Frankie Goes Spandau Ballet 2 Unlimited Meat Loaf Bryan Adams Mauro Picotto Snap! Delta Goodrem Dolly Parton to Hollywood Midnight Oil Pulsedriver Pink Hilary Duff Dead or Talk Talk Basshunter Adele Sinéad O'Connor Kate Bush Jedi Mind Alive Foreigner Styx Boston Atomic Kitten Emma Bunton Erasure Foghat UFO DJ Shog Infernal September Tricks Dr. Alban Jesse McCartney Melanie C The Cranberries Alphaville Howard Jones The Knack P!nk The Go-Go's Elvis CostelloSimon & Pet Shop Gary Numan CascadaAlcazar The Wreckers Lindsay Lohan Garfunkel Technotronic S Club Lighthouse Family Boys Fears Chris Isaak Humble Pie Alice Deejay Eurythmics 7 Spice Girls Mutya Buena Cat Stevens Joe Walsh Brooklyn Bounce Britney Spears Terence Trent Fine Young Bomfunk MC's Eiffel 65 Nik Kershaw Crosby, Stills, Nash D'Arby Carole King Cannibals James Taylor Thin Lizzy Boyzone Duffy & Young House of Natasha Bedingfield Aly & Donovan A*Teens Ace of Mandy Moore Van Morrison Crowded House Pain Paris Hilton AJ Marianne Faithfull Paris Combo Base Blue The Sonics Neil Young & Handsome Boy Daniel Bedingfield Bachman-Turner Overdrive MF DOOM Crazy Horse Bonnie Raitt Gigi D'Agostino Modeling School Jonas Brothers Alison Moyet Culture Club Gal Costa N*E*R*D Stacie Orrico Madvillain Gwen Stefani Shayne Ward Bananarama Robert Palmer Robbie Williams Miley Cyrus Grace Jones The Who Cypress Hill Heart DANGERDOOM Savage Garden Jessica Simpson Huey Lewis & Grand Funk Darren Hayes Westlife Ronan Keating a-ha Don McLean Neil Young Steve Miller Slade Deltron 3030Blackalicious The Bangles The News Journey Railroad No Doubt Yello Pat Benatar Band Madonna Cyndi LauperBette Midler Status Quo Dr. Octagon Bruce Springsteen Caetano Veloso Leona Lewis John Hiatt The J. The Pussycat Jamelia Ashley Tisdale Vanessa Hudgens Taylor Swift Alison Krauss Seal Rick Astley Laura Branigan Bebel Gilberto Gnarls Barkley Jordin Sparks REO Speedwagon Geils Band Katharine McPhee O-Zone Quasimoto Solange Nicole Scherzinger Rihanna Dolls Cutting Crew Jackson Browne Gary Moore Black Star Steppenwolf Hieroglyphics The Pointer Kim Carnes Camouflage Del tha Jurassic 5 Donna Summer Belinda Carlisle Gilberto Gil Beastie Boys Backstreet Boys Sisters John Mellencamp Funkee Homosapien Crosby, Stills Buffalo Springfield Katie Melua Simply Red Sandra Carly Simon Level 42 Stevie Nicks ZZ Top Talib Kweli Common Nelly Furtado Christina Aguilera Eddie Money & Nash Danity Kane Kat DeLuna Cibelle Elis Regina De La Anastacia Peter Frampton Chico Buarque OutKast Lupe Fiasco Steve Winwood Free Soul JoJo Gabrielle Paul Young Golden Earring Wham! Little Brother Bonnie Tyler Warren Zevon Madlib Atmosphere Don Henley The Guess CunninLynguists Cher Mr. Mister Bob Seger Three Dog The Yardbirds Jorge Ben Who Arrested Development The Roots Jennifer Lopez Lipps, Inc. Night Bad Company Michelle Williams Cassie El-P Carrie Underwood Jim Croce Lynyrd Skynyrd Chic Led Zeppelin Lisa Ekdahl Billy Ocean Starship John Denver Woody Guthrie *NSYNCFergie Eva Cassidy Irene Cara The Doobie Amy WinehousePaula Abdul Sage Francis Mos Def Survivor Rod Stewart Brothers Dilated Peoples Beyoncé Corinne Bailey Wet Wet Eagles João Gilberto Village People Sister Sledge Olivia Newton-John Neil Diamond Creedence Clearwater Rae Wet A Tribe Cherish George Michael Smokie Asia The Byrds Revival Djavan Clipse Jennifer Hudson Aesop Rock Kanye West Destiny's Child Big Star Mariah Carey Kelly Rowland Sarah Connor Boney M. Kenny Loggins Modern Talking Art of Billy Joel The Kinks Stan Getz The Pharcyde Whitney Houston Fleetwood Mac Marisa Monte Murs Jay-Z KC and the Noise Hall & Q-Tip Céline Dion Carpenters Gordon Lightfoot Chicago Sunshine Band Chris de Oates Ry Cooder The Rolling Roger Waters Page & Gang Starr Ciara Dixie Chicks Tina Turner Ashanti Roxette Burgh Electric Light Stones Plant Bee Gees Mike & The Spencer Christina Milian Janet Jackson Hot Chocolate Taj Mahal Toto Lisa Stansfield Orchestra Jimi Hendrix Rick James The Mechanics Masta Ace The Brand Pharoahe MonchCalled Quest Tom PettyDavis Group Love Richard Marx New Heavies Nas Pharrell America Los Hermanos Public Enemy Joss Stone Cliff Richard Kenny Rogers Us3 Incognito Justin Timberlake LeAnn Rimes Diana Ross The Black Antônio Carlos Estelle Brandy Martina McBride The Jimi Robert Plant Des'ree Barbra Streisand 13th Floor Crowes Air Supply Michael Bolton Elton John Tom Petty and Kansas Eric B. Amerie Wild Cherry The Zombies Elevators Hendrix Experience KRS-One Black Eyed the Heartbreakers The Allman Ohio Players The Troggs Astrud Gilberto & Rakim Brothers Band Dave Brubeck Phil Collins Kelis Parliament Chris Rea Eve Alicia Keys Gloria Gaynor Barry Manilow The Animals Dexter Gordon Run-D.M.C. Keri Hilson ABBA Mya Cream Monica Martha Reeves & Vanessa da Notorious B.I.G. Toni Braxton Shania TwainNorah Jones Kool & Cameo Joe Cocker David Gilmour Funkadelic Jobim Lionel Richie Dusty Springfield The Vandellas Traffic Mata Redman Big L Enrique Iglesias The Gang Petula Clark Mobb Deep Sade Nancy Sinatra Gloria Estefan Leadbelly will.i.am LL Cool Genesis Lil' Kim Missy Elliott The Doors Naughty by J Keyshia Cole Tamia India.Arie Earth, Wind Sly & The B.B. King The Lovin' Blind Faith Nature Peas Tweet Fountains of Jefferson Airplane The Dave N.W.A Salt-N-Pepa Dionne Warwick Diana Ross and Ike & Ten Years Pink Floyd Cannonball Adderley & Fire Family Stone Spoonful Thalía Barry White The Supremes Tina Turner Gladys Knight & After Wayne Syd Barrett Brubeck QuartetJamiroquai Macy Gray Muddy Waters Mary J. The Turtles Timbaland Erykah Badu Anita Baker The Pips Dire Straits Ludacris Blige Chaka Khan Madcon Jadakiss Faith Evans Maxwell Faith Hill John Lee Robert Johnson The Hollies Mark Knopfler The Beach Guru TLC Commodores The Moody Derek and Sonny Rollins M.O.P. The Supremes War Hooker Boys P. Diddy Stacey Kent James Brown Blues The Dominos Brian Wilson Busta Rhymes Aaliyah Jill Scott The Four Supertramp The Temptations Smokey Robinson and The Ronettes Teenage Fanclub Puff Daddy The Isley Tops The Meters Madeleine Peyroux the Miracles Gentle Giant Sean Kingston Brothers Ice Cube Chris Brown Robin Thicke En Vogue Lauryn HillAngie Stone Method Man John Legend Wu-Tang Clan Sir Mix-A-Lot Shirley Bassey The O'Jays The Mamas & Steely Dan Rory Gallagher Iron Butterfly & Redman Fat Joe Will Smith Luther Vandross The Posies Anthony Hamilton Randy Crawford Dr. John Manfred Mann Herman's Hermits The Papas Dr. Dre T-Pain Ne-Yo Akon Marvin Gaye The Marvelettes Big Brother & The Celia Cruz Van der Fabolous Paulina Rubio D'Angelo Marc Anthony Diana Krall J.J. Cale Holding Company Wyclef Jean Graaf Generator Janis Joplin The Lemonheads Art Blakey & The Usher Jamie Foxx Howlin' Wolf Raekwon Method Man Lil' Wayne The Spinners Andy Williams Jazz Messengers MC Hammer John Mayall Eazy-E Jamie Cullum Focus Stevie Ray Vaughan and The Game Nelly Musiq Giuseppe Verdi Lee Morgan Flo Rida Tim McGraw Double Trouble Baby Bash Jethro Tull Grateful Dead Giacomo Puccini Aretha Franklin King Crimson Ja Rule Fugees Ricky Martin Luis Miguel Bobby Valentino Eric Clapton Horace Silver Minnie Riperton Bill Withers Roy Orbison Lizz Wright Stevie Wonder Rush John Coltrane Donny Hathaway Camel Johnny Winter DMX The Monkees Bow Wow Rascal Flatts Curtis Mayfield Edwin Starr Stevie Ray 50 Cent Roy Ayers Buddy Guy John Mayall & Twista Chayanne Freddie Hubbard T.I. Mario GinuwineShakiraBrian McKnight Vaughan The Bluesbreakers GZA/Genius 2Pac Omarion Bobby Womack Al Green RZA Reik Phish Jane Monheit Natalie Cole Gioacchino Rossini Wayne Shorter Babyface Garth Brooks Ray Charles Charlie Parker Mims Procol Harum Coolio Marques Houston Sam Cooke George Harrison Canned Heat Paul McCartney Young Jeezy Juanes Peter Cincotti Ol' Dirty Rick Ross Chamillionaire Ray J Brad Paisley Cassandra Wilson Roberta Flack Isaac Hayes McCoy Tyner Joe Georges Bizet Bastard Dizzy Gillespie Billie Holiday R. Kelly Bo Diddley Xzibit The Beatles Chingy K-Ci & Wilson Pickett Lloyd Banks G-Unit Ricardo Arjona Lonestar Buddy Holly Craig David Chuck Berry Ghostface JoJo Shirley Horn Albert King Keith Urban Eartha Kitt Lloyd Michael Bublé Peggy Lee Etta James The Shirelles Al Jarreau B.B. King & Snoop Dogg Julieta Venegas Sin Bandera Alan Jackson John Lennon Charles Mingus Vanilla Ice The Righteous Eric Clapton Jim Jones Boyz II La Oreja de Jackie Wilson Brothers Yes Donald Byrd Obie Trice Men Van Gogh The Alan Jagged Edge Kenny Chesney Nancy Wilson Sarah Vaughan Soulja Boy Harry Connick, Dinah Washington Parsons Project Toby Keith Jr. Elvis Presley Ringo Starr Warren G Sam & Jerry Lee Young Buck Nina Simone Carl Perkins Peter Gabriel Paul McCartney Belanova Alejandro Sanz Dave Lewis Miles Davis Thelonious Monk Bubba Sparxxx Maná & Wings Johann Strauss Cam'ron Carmen McRae Otis Redding Solomon Burke II 112 Del Shannon Keith Jarrett Trick Daddy Aterciopelados Bill Haley and Emerson, Lake Richard Wagner Bill Evans Juelz Santana Jarabe de Lou Rawls the Comets Blackstreet Ella Fitzgerald Palo The Everly Richard Strauss Anita O'Day Blossom Dearie Amaral Brothers Ricky Nelson D12 Petey Pablo Bone Thugs-N-Harmony Fats DominoLittle Richard El Canto Wings Café Tacuba Perry Como & Palmer Chet Baker del Loco Nat King Eddie Cochran Robert Schumann Herbie Hancock Cole Lena Horne Booker T. & Frédéric Chopin Mel Tormé The MG's Hector Berlioz Ying Yang Pitbull George Benson Tony Bennett Twins Bebe The Blues Pyotr Ilyich Gene Vincent Gil Scott-Heron Franz Liszt Tchaikovsky Jaco Pastorius Chick Corea Enanitos Verdes Julie London Brothers Franz Schubert Rosemary Clooney Percy Sledge Louis Armstrong Michael Nyman Lil Jon Claude Debussy Zbigniew Preisner Melendi Los Fabulosos Chubby Checker Johannes Brahms Frank Sinatra Sergei Rachmaninoff Ella Fitzgerald & Jimmy Buffett Edvard Grieg Sammy Davis, Bing Crosby Louis Armstrong Weather ReportEminem Andrés Calamaro Jr. EstopaLouis Prima Al Di Doris Day Wolfgang Amadeus Lil Jon & The Ludwig van Charlie Feathers Arvo Pärt Mozart Meola East Side Boyz Erik Satie The Drifters Gabriel Fauré Los Rodríguez Joaquín Sabina Gustav Mahler The Platters Jean Sibelius Cadillacs Johann Sebastian Dean Martin Felix Mendelssohn Ben E. Bach Maurice Ravel Mahavishnu Orchestra Three 6 Soda Stereo Philip GlassKronos Quartet Mafia Brenda Lee Henry Purcell Wes Montgomery Chambao Josh Groban Modest Petrovich Franz Joseph Daddy Yankee Mussorgsky Haydn Georg Friedrich Duke Ellington Bobby Darin Vince Guaraldi Antonín Dvo:0159ák Trio Beethoven Händel Don Omar King Judy Garland The Coasters Sergei Prokofiev Johann Pachelbel Amparanoia Paul Anka Camille Saint-Saëns Antonio Vivaldi Django Reinhardt Georg Philipp Ojos de Sir Edward Dmitri Shostakovich Brujo Elgar Igor Stravinsky Cab Calloway Andrea Bocelli Tomaso Giovanni Benny Goodman Luciano Pavarotti Penguin Cafe Albinoni Count Basie Macaco Samuel Barber Telemann

Glenn Miller Luigi Boccherini Sarah Brightman Orchestra Gustav Holst

Figure 6: The landscape of music

The Lemonheads Giuseppe Verdi ful Dead Giacomo Puccini

Gioacchino Rossini Georges Bizet

Johann Strauss II Richard Wagner Richard Strauss

Hector Berlioz Robert Schumann Frédéric Chopin

Pyotr Ilyich Franz Liszt Claude Debussy Tchaikovsky Franz Schubert Michael Nyman Zbigniew Preisner Sergei Rachmaninoff Johannes Brahms Edvard Grieg Arvo Pärt Erik Satie Wolfgang Amadeus Ludwig van Gabriel FauréGustav Mahler Mozart Jean Sibelius Johann Sebastian Felix MendelssohnBeethoven Kronos Quartet Maurice Ravel Bach Philip Glass Modest Petrovich Franz Joseph Henry Purcell Georg Friedrich Mussorgsky Antonín Dvorák Haydn Händel

Sergei Prokofiev Camille Saint-Saëns Johann Pachelbel Antonio Vivaldi

Sir Edward Georg Philipp Dmitri Shostakovich Elgar Telemann Igor Stravinsky Tomaso Giovanni Penguin Cafe Albinoni Orchestra Samuel Barber

Gustav Holst Luigi Boccherini

Figure 7: Part of the classical archipelago

8 Frankenstein Chinua Achebe's Things Fall Understanding Things Fall Apart: No Longer Apart: A Casebook Selected Essays and Criticisms at Ease A Man of Midnight's Children: The Moor's Huxley's Brave New Chinua Achebe's Things Fall Last Sigh Wiesel's Night the People A Novel World Apart Brave New World and cbeth War And Brave New World Revisited Peace Half of a The Ground Beneath Her The Good Brave New Yellow Sun Dr. Jekyll & Mr. God's Bits of Feet: A Novel Earth 1984 World Interpre t Hyde Wide Sargasso Sea: Wood A Novel The God of Small Malad Things: A Novel Lord of the Animal Farm Night Nineteen Eighty-Four The Picture of Dorian Flies Gray - Oscar Wilde Catch-22 The Rest Is Noise: Listening The Bri Waiting for Godot: A The Awakening to the Twentieth Century of Fahrenheit 451 A Tree Grows in Tragicomedy in Two Acts Invisible Golding's the Lord of A Clockwork Brooklyn Man the Flies Orange The Sun Demian Also Rises Steppenwolf: A Narrative of the Life Island The Catcher in The Great of Frederick Douglass Novel The Bluest the Rye East of Gatsby Slaughterhouse-Five: A Eye A Tale of Two To Kill Eden Novel Native Son Cities a Mockingbird Beloved Siddhartha Of Mice and Their Eyes Were Watching Black Boy Men God CD Jane Eyre The Scarlet The Glass Bead The Great The Old Man and Passing: Beneath the Letter Game: Gatsby CD The Sea The Short Stories of F. Scott The Things Wheel A Farewell Invisible Man Fitzgerald: A New Collection They Carried Mythology Gertrude: A To Arms In Our Narcissus and Goldmund: Jane Novel The Adventures of One Flew Over the Time A Novel Huckleberry Finn Cuckoo's Nest: Fitzgerald's The Great Narcissus and AmericanaFor Whom the Quicksand and Zo Incidents in the Life of Gatsby Passing Goldmund Bell Tolls The Invisible a Slave Girl f Two Islands in the Stream Their Eyes Were Man The Crucible : A Novel nniversary Spark Notes The Watching God The Autobiography of Benjamin Spark Notes The Adventures Scarlet Letter Plum Bun: A Novel Franklin of Huckleberry Finn Without a Moral To Have and The Perennial Have Not Philosophy The Grapes of A Moveable Hawthorne's The Scarlet Spark Notes The Their Eyes Were Watching Of Mice Zora Neale Hurston's Their Eyes Were Wrath Feast Letter Great Gatsby God Literature Guide & Men Watching God: A Casebook sion The Journey to the East Travels with Charley in The Complete Short Stories of Ernest Steinbeck's the Grapes of Spark Notes Huxley and A Raisin in Search of America: Cannery Row: The Portable Harlem Rena Hemingway: The Finca Vigia Edition Wrath Invisible Man God: Essays the Sun Reader a The Glass Spark Notes The Grapes Cat's Cradle: In Search of History - Tortilla Flat Mother Night: The Blacker the Moksha: Aldous Huxley's Classic Writings on Menagerie of Wrath A Novel Home To Salem Witch Trials A Novel Berry g Heights Psychedelics and the Visionary Experience Harlem The Winter of Our Breakfast of Champions: Death of a Twilight: The Complete Illustrated Discontent A Novel Welcome to the Monkey New Essays on Their Eyes Long Day's Journey Salesman

The Forgotten Man: A New History The Fountainhead Personal Statement Rescuing Sprite: A Dog Lover's Story of the Great Depression of Joy and Anguish The Soviet Experiment: Russia, The U Capitalism and Freedom: Fortieth Atlas Shrugged Solzhenitsyn: A Soul and the Successor States Anniversary Edition in Exile The Soul and Barbed Wire: Journey into the An Introduction to Solzhenitsyn The Twelve The Harvest of S Men in Black: How the Supreme Whirlwind The Fatal Chairs Collectivization and Eggs Court Is Destroying America A Dead Man's Memoir: We Never Make Mistakes: nomenology of A Theatrical Novel Two Short Novels Man Is Wolf to The Daodejing Spirit Red Cavalry Man: Surviving the Gulag of Laozi Heidegger's Being And Time: Basic Writings A Reader's Guide Warning to the West White Guard A Room of The Solzhenitsyn Reader: New The Gulag Archipelago 1918-1956 Abridged: An Being And Being and In the First Circle: Gulag: A One's Own and Essential Writings, 1947-2005 Experiment in Literary Investigation Nothingness Time A Novel History Introduction to Phenomenology of Metaphysics The Ethics Cancer Ward The Gulag Archipelago Volume 1: An The Gulag Archipelago 1918-1 Perception August 1914 Of Ambiguity Experiment in Literary Investigation Parts I - II

Eugene Onegin: A Novel Heart of in Verse The Gulag Archipelago, 1918-1956: An Experiment In the Skin of a Dog The Gulag Archipelago: 1918-1956, An Experiment sea The Master in Literary Investigation, Parts V-VII a Lion in Literary Investigation III - IV Oblomov and Margarita One Day in the Life A Thousand And Human of Ivan Denisovich Atone Splendid Suns The Gulag Archipelago The Memory ns The Myth of SisyphuRussianas: The Rebel: An Essay Suite Francaise The Collected Tales of 1918-1956 I-II Keeper's Daughter And Other Essays on Man in Revolt Nikolai Gogol Dewey: The Small A Hero of Our The Unbearable Lightness of The Book of Laughter The Kite Snow Flower and the Who Touche The First Time Dead Souls: Being and Forgetting Runner Secret Fan: A Novel Saturday Man A Novel The Plague The Years The Adolescent A Heartbreaking Work of Water for Elephants: Howards End Resistance, Rebellion, and Staggering Genius The Eternal Husband and A Novel The English Death: Essays War and Other Stories Patient The Fall Peace The Unbearable Lightness of Memories of My The Autumn of the The Th The Double and Being: A Novel Melancholy Whores Patriarch A The Gambler The Idiot On Chesil The Brothers Stories of We The Glass Castle: b's Room Beach Anton Chekhov One Hundred Years of A Memoir Karamazov Collected Stories Demons Solitude Lov No Exit and Three Notes from Love in the Time A Other Plays Underground of Cholera The Maytrees: Of Love and Other The History of Love: A Novel The Remains of A Novel The Stranger Demons Spark Notes Crime Animal Farm the Day Chronicle of a Mrs. Dalloway and Punishment and 1984 The Gathering Death Foretold On Beauty Never Let The Namesake: All Quiet on the Me Go A Novel Divisadero Chinua Achebe's Things Fall A Passage Western Front Apart to India Home and Bridg

Figure 8: Two of the central clusters in BookLand. neighborhood, there have been attempts to convey the underlining same book, but with different publishers or different bindings, by connectivity of the products through graph visualization. None of matching books with the same title. The underlying graph for this the existing approaches, however, gives a comprehensive view of map contains 913 vertices and 3410 edges. With an average degree the relationship and the clustering structures. of nearly eight, peripheral vertices in this map have only a handful of edges while central vertices have more than 20 immediate neigh- Using our GMap algorithm, we obtained the map in Fig- bors. We next examine several of the BookLand countries in more ure 1. The underlying data is obtained with a breadth-first traver- detail (cf. Figures 8 and 1). sal following Amazon’s “Customers Who Bought This Item Also Bought” links, starting from the root node, Orwell’s 1984. Links Americana: Somewhat surprisingly, Orwell’s 1984 along with are followed up to a distance of twelve from the root node. We Animal Farm ended up in the west corner of a region populated then trim the graph by keeping only vertices of distance nine or less mostly by American writers. Britain is also represented by Gold- from the root vertex. We further merge nodes that represent the ing’s The Lord of the Flies and Huxley’s Brave New World along

9 with Burgess’s Clockwork Orange, which connect the British cor- partners. ner of the region to the main part dominated by 20th century Amer- ican classics. Bradbury’s Fahrenheit 451 and Salinger’s Catcher TVLand in the Rye provide a transition to a variety of well-known novels: Steinbeck’s Grapes of Wrath and Of Mice and Men, Hemingway’s As a last example, we consider a map derived from TV viewer data. For Whom the Bell Tolls, Fitzgerald’s Great Gatsby, Heller’s Catch- The objects are TV shows, with an edge between two shows if sev- 22, and Kesey’s One Flew Over a Cuckoo’s Nest. eral viewers watched both. The edges are weighted by the number Russiana: To the north of Americana lies one of the largest of such viewers. We illustrate how GMap can be used in the con- countries in BookLand, dominated by Russian literature and his- text of recommendation systems with the aid of heat map overlays, tory. The core contains classic novels by Dostoyevsky (The Broth- tailored to an individual viewer. ers Karamazov), Tolstoy (War and Peace), and Solzhenitsyn (The Figure 10 shows such a map for a typical but fictitious viewer. Gulag Archipelago, Cancer Ward). In the west, there is, unex- Based on the observed viewing habits of a specific viewer, and on pectedly, a cluster of Camus books (The Stranger, The Plague, The those of other viewers, a recommendation system can suggest pos- Fall), all well connected with the Russian classics. sible new shows. In order for the labels to be readable in a journal From the map, we can also see some high-level connections. format, our map displays a small subset of the TV shows and con- There is the not too surprising proximity of self-help books with sists of six countries. The countries capture several types of shows books recommended by Oprah Winfrey. We also find the group of by genre. In the southwest are two countries corresponding to TV recent vampire novels adjacent to the cluster of Victorian novels. A shows for children, with the smaller targeting younger kids with closer investigation shows that vampire novels are only connected Dora the Explorer and Wow Wow Wubbzy. In the northwest is a to the rest of the graph through Jane Austen. cluster of shows about fashion and entertainment such as Say Yes to Dress and E! News. The large country in the north contains popu- TradeLand lar sitcoms such as Seinfeld, Cheers, and Frasier. In the northeast is a cluster of crime shows (NCIS and Law & Order). The cluster Figure 9 is a map visualizing the trade relations between all coun- in the southeast is not as thematically focused but contains popular tries. Bilateral trade data between each of the 209 countries shows of several types: The Oprah Winfrey Show, So You Think You and its top trading partners were acquired from Mathematica’s Can Dance, and Dateline NBC. In each country the TV shows are CountryData package. The font size of a label is proportional to colored based on the strength of the recommendation; that is, the the logarithm of the total trade volume of the country, and the color lighter the color, the stronger the recommendation, as in a typical of a label reflects whether a country has a trade surplus (black) or geographic map where shading of colors are used to represent hills deficit (red). and valleys. The label color gives an easy way to spot the oil-rich countries Maps like this provide a global view not available in the tradi- with large surpluses, which are distributed all over the world as tional list of recommendations and offer a more appealing presen- well as in our map: Middle East (Saudi Arabia, Kuwait), Europe tation than a scatterplot or a node-link diagram. The map provides (Russia), South America (Venezuela), Africa (Nigeria, Equatorial a context for recommendations, allowing a user to understand the Guinea). On the other hand, the countries with huge deficits are reasoning behind the recommendation: when considering highly- mostly in Africa (Sierra Leone, Senegal, Ethiopia) with the United recommended shows the user can check out nearby, related shows; States, the clear outlier. or explore a path of shows to a new area. Many countries in close geographic proximity end up close in our map, e.g, Central American countries like Honduras, El Sal- RELATED WORK vador, Nicaragua, Guatemala and Costa Rica are close to each other in the northeast. Similarly the three Baltic republics, Latvia, Lithua- There are many papers in geography about accurately and appeal- nia and Estonia, are close to each other in the northwest. This is ingly representing a given geographic region, or on re-drawing an easily explained by noting that geographically close countries tend existing map subject to additional constraints. Examples of the first to trade with each other. There are easy-to-spot exceptions: North kind of problem are found in traditional cartography, e.g., the 1569 Korea is not near South Korea, Israel is not particularly close to Mercator projection of the sphere onto 2D Euclidean space. Car- Jordan or Syria. tograms provide an example of the second kind of problem, where The G8 countries (Canada, France, Germany, Italy, Japan, Rus- the goal is to redraw a map so that the geographical areas are pro- sia, United Kingdom, and the United States) are all in close prox- portional to some metric, an idea which dates back to 1934 and is imity to each other in the center of the map. Two of the largest still popular today (e.g., the New York Times’ red-blue maps of the and closest countries in our map are China and the United States. US, showing the presidential election results in 2000 and 2004 with Clearly, the proximity is due to the very large trade volume rather states drawn proportional to population). than geographic closeness. All these countries are in the largest Work in information visualization has produced many ways of cluster which is dominated by European countries in the west, representing data, some even adopting the name “map.” Most of Asian countries in the east, and Middle Eastern countries in the these have little visual connection with geographic maps. The map south. of science [1] uses vertex coloring in a graph drawing to provide Interestingly, we see from the map that African countries are dis- an overview of the scientific landscape, based on citations of jour- tributed in several clusters in close proximity to China (a major trad- nal articles. Treemaps [11], squarified treemaps [2], and the more ing partner to many African countries), the United States (trading recent newsmaps represent hierarchical information by means of less with Africa these days), and around former colonizers (e.g., space-filling tilings, allocating area proportional to some metric. Togo, Cameroon and Senegal, which are all close to France). On Concept maps are diagrams showing relationships among con- the other hand, Caribbean and South and Central American coun- cepts [10]. Somewhat similar are cognitive maps and mind-maps tries form several clusters in the north of the map. In addition, these used to represent words or ideas linked to and arranged around a clusters are mostly contiguous, essentially forming a supercluster. central key word. This differentiation between Latin America and Africa is clearly In self-organizing maps (SOM) [8], an unsupervised learning al- brought out by the GMap figure. gorithm places objects on a two-dimensional grid such that similar Finally, we note that the periphery of the map contains small objects are close to each other. Unlike GMap, SOM creates a “map” countries from around the world, and countries with few trading by coloring cells of the grid based on a feature value; therefore it

10 Figure 9: A map of trade relations between countries.

operates on a discrete grid space without a clear inner boundary be- on variations of a fractal model. These techniques could provide tween “countries”. Furthermore, the grid tends to fit a rectangular additional photo-realism, and may be used in future extension of box, so that the overall outline of the point set often follows that our work. shape. Also related is work on visualizing subsets of a set of items us- CONCLUSIONAND FUTURE WORK ing geometric regions to indicate the grouping. Byelas and Telea [3] We believe that the GMap algorithmic framework, by capitalizing use deformed convex hulls to highlight areas of interest in UML di- on an ancient and familiar visual metaphor, introduces a signifi- agrams. Collins et al. [4] use “bubblesets,” based on isocontours, cant new style of viewing abstract relational and cluster data that to depict multiple relations among a set of objects. Simonetto et users will find aesthetically appealing and helpful in understanding al. [12] automatically generate Euler diagrams which provide one the data. From informal observation, we have found that people, of the standard ways, along with Venn diagrams, for visualizing when faced with a traditional graph drawing and a map of the same subset relationships. Apart from differences in the algorithms used data, spend significantly longer time studying the map, and they to generate regions, these works differ from ours in that they cre- find non-trivial structural information without any prompting. For ate regions that overlap with each other, with the goal of faithfully example, several viewers of BookLand observed that the “gateway” representing set relationships, while we take the map metaphor se- to Fringistan is Rand’s Atlas Shrugged. We plan to perform formal riously, assuming that regions do not overlap and aiming for a car- user studies of the interaction with graphs and maps, in the context tographic verisimilitude. However, as Figure 5 shows, our approach of visualizing recommendations [6]. can also be used for visualizing sets. While the approach of visualizing relational information with the Representing imagined places on a map as if they were real coun- aid of geographical maps is general, here we showed one partic- tries also has a long history, e.g., the 1930’s Map of Middle Earth ular implementation, where embedding and clustering algorithms by Tolkien and the Bucherlandes¨ map by Woelfle from the same pe- are coupled with novel mapping and coloring algorithms. There riod. More recent drawings include maps of programming language are specific idiosyncrasies we would like to address. For example, concepts and online communities. While most such maps are gen- GMap can produce countries that are disconnected. We have pro- erated in an ad hoc manner by hand and are not strictly based on posed ways [5] to use the cluster information to adjust the layout so underlying data, they are often visually appealing. that the regions of countries are more contiguous, at the expense of Generating synthetic geography has a large literature, connected some loss of graph information. We are planning further investiga- to its use in computer games and movies. Most of the work relies tion into balancing country connectedness and the preservation of

11 Figure 10: Personalized recommendation heat map for a typical user. Regions where the highest recommended shows sit are lighter. Regions of low scores are darker.

graph information. [6] E. R. Gansner, Y. F. Hu, S. G. Kobourov, and C. Volinsky. Putting Finally, our algorithm is efficient and can handle large graphs. recommendations on the map - visualizing clusters and relations. In As a reference point, all maps in this paper were generated in a few Proceedings of the 3rd ACM Conference on Recommender Systems. seconds. Mapping a larger graph with 440,000 vertices took 4 min- ACM, 2009. utes on a typical processor. The resulting maps look best on large, [7] A. Georghiades, P. Belhumeur, and D. Kriegman. From few to many: wall-sized posters and display walls. To make such maps more use- Illumination cone models for face recognition under variable lighting ful for exploration of large data sets on commonly available media, and pose. IEEE Trans. Pattern Anal. Mach. Intelligence, 23(6):643– we have developed an interactive interface that can search, zoom 660, 2001. and pan easily on the maps (see footnote 1). [8] T. Kohonen. Self-Organizing Maps. Springer, 2000. [9] M. E. J. Newman. Modularity and community structure in networks. Acknowledgments Proc. Natl. Acad. Sci. USA, 103:8577–8582, 2006. [10] J. D. Novak and A. J. Canas.˜ The theory underlying concept maps We would like to thank Stephen North for helpful discussions, and and how to construct them. Technical report, Institute for Human and Carlos Scheidegger for help with the image process example. Machine Cognition, January 2006. [11] B. Shneiderman. Tree visualization with tree-maps: A 2-D space- REFERENCES filling approach. ACM Transactions on Graphics, 11(1):92–99, 1992. [1] K. Boyack, R. Klavans, and K. Borner. Mapping the backbone of [12] P. Simonetto, D. Auber, and D. Archambault. Fully automatic visual- science. Scientometrics, 64(3):351–374, 2005. isation of overlapping sets. Computer Graphics Forum, 28:967–974, [2] M. Bruls, K. Huizing, and J. van Wijk. Squarified treemaps. In Joint 2009. Eurographics and IEEE TCVG Symposium on Visualization, pages 33–42. Press, 1999. [3] H. Byelas and A. Telea. Visualization of areas of interest in software architecture diagrams. In SoftVis’06: Proceedings of the 2006 ACM Symposium on Software Visualization, pages 105–114, 2006. [4] C. Collins, G. Penn, and S. Carpendale. Bubble sets: Revealing set relations with isocontours over existing visualizations. IEEE Trans- actions on Visualization and Computer Graphics, 15(6):1009–1016, 2009. [5] E. R. Gansner, Y. F. Hu, and S. G. Kobourov. Gmap: Drawing graphs and clusters as map. In IEEE Pacific Visualization Symposium, pages 201 – 208, 2010.

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