Visualizing Graphs and Clusters as Maps - CiteSeerX

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

A BSTRACT 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 algorithmic framework for visualizing relational data with geographiclike maps. We illustrate the effectiveness of this approach with examples from several domains.

to understand the visualization of a biological experiment that was created by a statistician. When large data sets are drawn as point clouds or node-link graphs, it is sometimes possible to observe a visual similarity to geographic maps. For example, several small connected components next to a much larger component suggest several small islands next to a big continent. We took the next step in visualizing data directly as a geographic map. A map representation is familiar and intuitive; most people are very familiar with maps and nicely drawn maps often provide hours of enjoyable exploration. Many people take advantage of this familiarity with maps and manually create map-like representations that portray relations among abstract concepts. We were interested in automating the process which begins with the data and ends with a drawing of a map. In this process there are two main competing goals: First, we would like to be faithful to the data, by maintaining the inherent structure and relationships, without adding or implying non-existent structure. Second, we would like the final result to look like a map, using standard cartographic conventions. Our attempt to address these two goals led to a framework for a map-based data representation that we call GMap.

Keywords: Information Visualization; Clustering; Graph Drawing; Graph Coloring; Maps; Set Visualization. I NTRODUCTION With the growth of the Internet and scientific and technological advances, the world has seen an explosion in the generation and collection of data. This data is often relational, high-dimensional, or both. With such a wealth of data comes the need to understand it, analyze it, and use it. Visualization can play a key role in all of these steps, but especially so in the exploratory phase. Many useful techniques for visualizing abstract data sets have been considered in the past. Graphs made of nodes and links (or edges) are often used to capture the relationships between objects, and graph drawing allows us to visualize such relationships. Typically nodes are represented by points in two or three dimensional space, and edges are represented by lines between the corresponding vertices. For an example of a relational data set, consider the Amazon.com graph, where books are nodes and there is an edge between two books if people who have bought one of the books also buy the other. High-dimensional data sets, on the other hand, are often visualized as point clouds in two or three dimensional space. An example 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 the same as the number of musicians available at the website, and the value of each element is proportional to the number of times a user listens to the corresponding musician. In a point cloud visualization, each point is a user and two points are close to each other if the two users have similar music taste. Unfortunately, these standard approaches of node-link diagrams and point cloud representations often require considerable effort to comprehend. If we desire to make the data accessible to people outside the areas of computer science and statistics, providing more compelling drawings is an important task. This is certainly true for the ordinary user who might be curious about the recommendations made by Amazon.com, but is also true for the biologist who wishes

GM AP The GMap framework allows us to generate map-like representations from an abstract data set. Specifically, given a highdimensional data set or a graph with edge weights (e.g., the similarity between books as determined by purchase behavior at Amazon.com), it produces a drawing with a map-like look, with countries that enclose similar objects, outer boundaries that follow the outline of the vertex set, and inner boundaries that have the twists and turns found in real maps. A typical example is in Figure 1 and shows just under 1000 books.1 Our maps also can have lakes, islands, and peninsulas, similar to those found in real geographic maps. GMap is a framework in the true sense of the word, rather than a specific algorithm. It consists of four main steps, the first two steps can be achieved by a variety existing algorithms. For the last two steps we propose new algorithms. In the first step we take as input a graph or high-dimensional data set, and embed it into the plane. The statistics and scientific modeling communities have extensively explored this problem and provide many ways of doing this. Possible embedding algorithms include principal component analysis, multidimensional scaling (MDS), force-directed algorithms, or non-linear dimensionality reductions such as Locally Linear Embedding and Isomap. The second step takes this collection of points in the plane and aggregates them into clusters. Here, it is important to match the clustering algorithm to the embedding algorithm. For example, a geometric clustering algorithm such as k-means may be suitable for an embedding derived from MDS, as the latter tends to place similar points in the same geometric region with good separation between clusters. On the other hand, with an embedding derived from a

∗ e-mail:

[email protected] [email protected] ‡ e-mail: [email protected]. Work done while this author was at AT&T Labs. † e-mail:

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

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The Girl with the Dragon Tattoo

Oprahland I Know This Much Is True: A Novel 

The Elegance of the Hedgehog

The Secret Scripture

A Fraction of the Whole

Interpreter of Maladies

Siddhartha

The Glass Bead Game: 

Beneath the Wheel

Mythology

Incidents in the Life of a Slave Girl 

King Henry V 

D'Aulaires' Book of Greek Myths

Jane Eyre

Island 

Tree of Smoke: A Novel

Then We Came to the End: A Novel

The Savage Detectives: A Novel

Drown

A Clockwork Orange

CliffsNotes Jane Eyre

Hamlet 

King Lear

The Help

The Northern Clemency

Unaccustomed Earth: Stories 

Handle with Care: A Novel

The Guernsey Literary and Potato Peel Pie Society 

Olive Kitteridge: Fiction

Man Gone Down: A Novel

Nineteen Eighty-Four

Steppenwolf: A Novel

To Kill a Mockingbird

Great Expectations

The Dictionary of Classical Mythology

God's Bits of Wood 

The Associate

Letter to My Daughter

A Fine Balance 

2666: A Novel

The Ground Beneath Her Feet: A Novel

Fahrenheit 451

Demian

Narrative of the Life of Frederick Douglass 

The Taming of the Shrew 

King Henry IV, Part 2 

Half of a Yellow Sun

Stern Men

Still Life with Chickens: Starting Over in a House by the Sea

Out Stealing Horses: A Novel

The Moor's Last Sigh

The Last American Man

Stern Men: A Novel

Eat, Pray, Love: One Woman's Search for Everything Across Italy, India and Indonesia

Middlesex: A Novel 

Shalimar the Clown: A Novel

The Awakening

Waiting for Godot: A Tragicomedy in Two Acts

A Tree Grows in Brooklyn 

Golding's the Lord of the Flies 

A Tale of Two Cities 

Julius Caesar

The Tempest

The Library of Greek Mythology 

The Merry Wives of Windsor 

Heroes, Gods and Monsters of the Greek Myths

Twelfth Night

The Merchant of Venice 

Henry IV, Part 1 

Idylls of the King 

Copenhagen

Michael Frayn's Copenhagen in Debate: Historical Essays and Documents on the 1941 Meeting Between Niels Bohr and Werner Heisenberg

Night 

Animal Farm

The Picture of Dorian Gray - Oscar Wilde

The Invisible Man 

Othello 

The Winter's Tale 

Le Morte D'Arthur: The Winchester Manuscript 

All's Well That Ends Well 

The Once and Future King

The Satanic Verses: A Novel

Shame: A Novel

Midnight's Children: A Novel

War And Peace 

The Boy In the Striped Pajamas 

Infidel

Run: A Novel

Bridge of Sighs: A Novel 

Haroun and the Sea of Stories

Anthills of the Savannah

A Man of the People

Wide Sargasso Sea: A Novel

Twelfth Night: or, What You Will 

One Thousand and One Arabian Nights 

Shakespearea

As You Like It 

Rule of Saint Benedict in English

Eichmann in Jerusalem: A Report on the Banality of Evil 

Dr. Jekyll & Mr. Hyde 

A Midsummer Night's Dream 

King Lear

Hesiod's Theogony

Ecclesiastical History of the English People 

Brave New World and Brave New World Revisited

No Longer at Ease

Loving Frank: A Novel

The Maytrees: A Novel

A New Earth: Awakening to Your Life's Purpose 

Selfhelpistania

Three Cups of Tea: One Man's Mission to Promote Peace . . . One School at a Time

I Am the Messenger

Divisadero

The Enchantress of Florence: A Novel

Understanding Things Fall Apart: Selected Essays and Criticisms

Brave New World

The Good Earth 

Medea and Other Plays 

Saint George and the Dragon

Shakespeare Stories

The Aeneid

Four Plays by Aristophanes: The Birds; The Clouds; The Frogs; Lysistrata 

Chinua Achebe's Things Fall Apart: A Casebook 

Macbeth 

The Adventures of Robin Hood 

Girls at War

Achebe's Things Fall Apart: A Reader's Guide 

Madame Bovary

Chinua Achebe's Things Fall Apart 

Wiesel's Night

On My Own: The Art of Being a Woman Alone

Choose To Be Happy: A Guide to Total Happiness

A Writer's Workbook: Daily Exercises for the Writing Life

Happy for No Reason: 7 Steps to Being Happy from the Inside Out

The Book Thief

The Gathering

Home and Exile

Arrow of God

Things Fall Apart: A Novel

Things Fall Apart 

Heart of Darkness

Frankenstein 

Huxley's Brave New World 

Homeric Hymns

The Dore Gallery: His 120 Greatest Illustrations 

Fyodor Dostoevsky's Crime and Punishment 

Grendel

Beowulf 

Paradise Lost and Paradise Regained 

Divine Comedy: Inferno 

Classical Mythology

Rosencrantz and Guildenstern Are Dead

Beowulf: A New Verse Translation 

The Canterbury Tales 

The Oresteia: Agamemnon; The Libation Bearers; The Eumenides 

Greek Tragedies, Volume 1

Electra and Other Plays 

The Glass Castle: A Memoir

The History of Love: A Novel

The Namesake: A Novel

Never Let Me Go

On Beauty

Playing for Pizza

While Europe Slept: How Radical Islam is Destroying the West from Within

Wesley the Owl: The Remarkable Love Story of an Owl and His Girl

Collected Stories

Of Love and Other Demons 

Chronicle of a Death Foretold

A Passage to India

The Self-esteem Companion: Simple Exercises to Help You Challenge Your Inner Critic & Celebrate Your Personal Strengths

The Man From St. Petersburg

The Caged Virgin: An Emancipation Proclamation for Women and Islam

Alex & Me: How a Scientist and a Parrot Uncovered a Hidden World of Animal Intelligence--and Formed a Deep Bond in the Process

The English Patient

On Chesil Beach

One Hundred Years of Solitude 

Animal Farm and 1984

All Quiet on the Western Front

Chinua Achebe's Things Fall Apart 

The Innocent: A Novel

The Autumn of the Patriarch 

We

Stone Cold

A Dangerous Fortune

Night Over Water

The Key to Rebecca

Saturday

The Art of Racing in the Rain

Water for Elephants: A Novel

Memories of My Melancholy Whores

The Unbearable Lightness of Being: A Novel

Notes from Underground

The Stranger

Spark Notes Crime and Punishment

Mrs. Dalloway

Utopia 

A Modern Reader's Guide to Dante's the Divine Comedy

Dante's Divine Comedy: Hell, Purgatory, Paradise

Demons

No Exit and Three Other Plays

Orlando 

A Portrait of the Artist as a Young Man 

Dubliners 

Metamorphoses 

The Dore Bible Illustrations

War and Peace 

Stories of Anton Chekhov

Jacob's Room

A Reader's Guide to Finnegans Wake 

The Three Theban Plays 

Lysistrata and Other Plays 

Euripides I: Alcestis, The Medea, The Heracleidae, Hippolytus 

Dore's Dragons, Demons and Monsters 

The Eternal Husband and Other Stories

The Decameron

The Aeneid

The Divine Comedy: Inferno; Purgatorio; Paradiso 

Ten Plays by Euripides

The Essential Aeneid

Dore's Angels

The Inferno

The Consolation of Philosophy: Revised Edition 

Gilgamesh: A New Rendering in English Verse

Sophocles II: Ajax, The Women of Trachis, Electra & Philoctetes 

Dore's Illustrations for Paradise Lost 

The Epic of Gilgamesh: An English Verison with an Introduction 

Paradiso 

Vita Nuova

Aeschylus I: Oresteia: Agamemnon, The Libation Bearers, The Eumenides 

A Heartbreaking Work of Staggering Genius

Howards End

KFC

Eye of the Needle

Merle's Door: Lessons from a Freethinking Dog

Dewey: The Small-Town Library Cat Who Touched the World

Snow Flower and the Secret Fan: A Novel

Katherine

The Other Boleyn Girl 

Enduring Love: A Novel

Amsterdam: A Novel

The Memory Keeper's Daughter

Suite Francaise

The Kite Runner

The Adolescent

The Fall

The Constant Princess 

The Six Wives of Henry VIII

Amazing Gracie: A Dog's Tale

In the Skin of a Lion

The Gulag Archipelago, 1918-1956: An Experiment in Literary Investigation, Parts V-VII

The Gulag Archipelago 1918-1956 I-II

The Unbearable Lightness of Being 

The Double and The Gambler

The Aeneid of Virgil 

The Cambridge Companion to Dante 

Purgatory 

Euripides V: Electra, The Phoenician Women, The Bacchae 

Between the Acts 

A Thousand Splendid Suns

Dead Souls: A Novel

The Plague

The Years

The Virgin's Lover 

The Queen's Fool: A Novel 

Grace: A Novel

The Gulag Archipelago 1918-1956, Parts I - II

The Gulag Archipelago Volume 1: An Experiment in Literary Investigation 

The Gulag Archipelago: 1918-1956, An Experiment in Literary Investigation III - IV

One Day in the Life of Ivan Denisovich 

A Hero of Our Time 

Resistance, Rebellion, and Death: Essays

The New Bloomsday Book: A Guide Through Ulysses

Don Quixote

The Gulag Archipelago 1918-1956 Abridged: An Experiment in Literary Investigation 

In the First Circle: A Novel 

The Collected Tales of Nikolai Gogol

The First Man

To the Lighthouse 

Plutarch's Lives Volume 1 

Paradise 

Euripides IV: Rhesus, The Suppliant Women, Orestes, Iphigenia in Aulis 

The Rebel: An Essay on Man in Revolt

The Hours

Heart of a Dog

The Master and Margarita

Oblomov

Anthology Of Classical Myth: Primary Sources in Translation : with Additional Translations by Other Scholars and an Appendix on Linear B sources by Thomas G. Palaima

The Last Days of Socrates 

Pseudo Dionysius: The Complete Works 

Russiana

Nausea

Suttree

Ilf and Petrov's American Road Trip: The 1935 Travelogue of Two Soviet Writers

Execution by Hunger: The Hidden Holocaust

Kolyma Tales

The Solzhenitsyn Reader: New and Essential Writings, 1947-2005

August 1914

The Landmark Thucydides

Plutarch's Lives, Volume 2 

The History of the Peloponnesian War: Revised Edition 

The Annals of Imperial Rome 

Within the Whirlwind

The Harvest of Sorrow: Soviet Collectivization and the Terror-Famine

Man Is Wolf to Man: Surviving the Gulag

Red Cavalry

Eugene Onegin: A Novel in Verse 

Existentialism And Human Emotions 

Confessions 

Livy: The Early History of Rome, Books I-V 

Maximus Confessor: Selected Writings 

Gregory of Nyssa: The Life of Moses 

The Rise of the Roman Empire 

The Twelve Chairs 

Introduction to Metaphysics 

The Ethics Of Ambiguity

Moments of Being

Travels with Herodotus 

Plutarch: Lives of Noble Grecians and Romans 

Oresteia

Journey into the Whirlwind 

The Border Trilogy: All the Pretty Horses, the Crossing, Cities of the Plain 

Twelve Chairs

Survival In Auschwitz

The Soul and Barbed Wire: An Introduction to Solzhenitsyn

We Never Make Mistakes: Two Short Novels

Being and Time

All the Pretty Horses

Envy 

The Soviet Experiment: Russia, The USSR, and the Successor States

Solzhenitsyn: A Soul in Exile

White Guard

The Bhagavad Gita 

The Epic of Gilgamesh 

American Prometheus: The Triumph and Tragedy of J. Robert Oppenheimer

Oil!

The Life and Extraordinary Adventures of Private Ivan Chonkin 

The Christmas Sweater

Men in Black: How the Supreme Court Is Destroying America

A Dead Man's Memoir: A Theatrical Novel 

Basic Writings

Heidegger's Being And Time: A Reader's Guide 

A Room of One's Own

Gulliver's Travels

The Civil War 

Bernard of Clairvaux: Selected Works 

The Daodejing of Laozi

The Yoga Sutras of Patanjali: Commentary on the Raja Yoga Sutras by Sri Swami Satchidananda

A History of Histories: Epics, Chronicles, and Inquiries from Herodotus and Thucydides to the Twentieth Century 

Theban Plays

Politics 

Nicomachean Ethics

The Prince

The Jugurthine War / The Conspiracy of Catiline 

Rome and the Mediterranean: Books XXXI-XLV of the History of Rome from its Foundation 

Tao Te Ching 

The Trial and Death of Socrates

The Landmark Thucydides: A Comprehensive Guide to the Peloponnesian War

Ironies of Faith: The Laughter at the Heart of Christian Literature

Origen: An Exortation to Martyrdom, Prayer, and Selected Works

Leviathan 

The Republic Of Plato: Second Edition

One Hell of a Gamble: Khrushchev, Castro, and Kennedy, 1958-1964: The Secret History of the Cuban Missile Crisis

Khrushchev: The Man and His Era

The Fountainhead

The Forgotten Man: A New History of the Great Depression

Atlas Shrugged

The Fatal Eggs 

Augustine of Hippo: A Biography 

The Roman History: The Reign of Augustus 

The 5000 Year Leap: A Miracle That Changed the World

Capitalism and Freedom: Fortieth Anniversary Edition

The Bhagavad-Gita : Krishna's Counsel in Time of War 

Introductory Lectures on Psychoanalysis

Khrushchev's Cold War: The Inside Story of an American Adversary

Anthem

The Virtue of Selfishness 

My Grandfather's Son: A Memoir

An Inconvenient Book: Real Solutions to the World's Biggest Problems

The Communist Manifesto 

Second Treatise of Government

Capitalism: The Unknown Ideal

Do the Right Thing: Inside the Movement That's Bringing Common Sense Back to America

Surrender Is Not an Option: Defending America at the United Nations

Free to Choose: A Personal Statement

The Art Of War

Truman

Sashenka: A Novel

We the Living

The Real Benjamin Franklin 

The Real Thomas Jefferson 

Discourse on Method and Meditations on First Philosophy, 4th Ed.

Dialogues Concerning Natural Religion: The Posthumous Essays of the Immortality of the Soul and of Suicide

If Democrats Had Any Brains, They'd Be Republicans

The Real George Washington 

The Road to Serfdom: Text and Documents--The Definitive Edition 

The Second Sex

Grounding for the Metaphysics of Morals: With on a Supposed Right to Lie Because of Philanthropic Concerns

An Enquiry Concerning Human Understanding

A Bold Fresh Piece of Humanity

The Constitution of the United States of America, with the Bill of Rights and all of the Amendments; The Declaration of Independence; and the Articles of Confederation

The Feminine Mystique

The General Theory of Employment, Interest and Money

The World's Religions: Our Great Wisdom Traditions

The Whisperers: Private Life in Stalin's Russia

Culture Warrior

A Slobbering Love Affair: The True 

Liberal Fascism: The Secret History of the American Left, From Mussolini to the Politics of Meaning

The History of Sexuality, Vol. 1: An Introduction

An Introduction to Hinduism 

The Art of War

Four Texts on Socrates: Plato's Euthyphro, Apology, and Crito and Aristophanes' Clouds

Economics in One Lesson: The Shortest and Surest Way to Understand Basic Economics

What the Buddha Taught: Revised and Expanded Edition with Texts from Suttas and Dhammapada

On the Genealogy of Morals and Ecce Homo

Fringistan

The Federalist Papers 

Capitalism, Socialism, and Democracy

Black Skin, White Masks

Sun Tzu: The Art of War for Managers; 50 Strategic Rules

American Progressivism: A Reader

Lenin, Stalin, and Hitler: The Age of Social Catastrophe 

Gender Trouble: Feminism and the Subversion of Identity 

Civilization and Its Discontents

The Art of Seduction

On Liberty

Godless: The Church of Liberalism

The Return of Depression Economics and the Crisis of 2008

Sumerian Mythology: A Study of Spiritual and Literary Achievement in the Third Millennium B.C. 

On War

Real Change: From the World That Fails to the World That Works

The Anti-Federalist Papers and the Constitutional Convention Debates 

Backlash: The Undeclared War Against American Women

New Introductory Lectures on Psycho-Analysis: 

Gods, Demons and Symbols of Ancient Mesopotamia: An Illustrated Dictionary

Stalin and His Hangmen: The Tyrant and Those Who Killed for Him

The Case Against Barack Obama: The Unlikely Rise and Unexamined Agenda of the Media's Favorite Candidate

Ever Wonder Why? And Other Controversial Essays

Full Frontal Feminism: A Young Woman's Guide to Why Feminism Matters

The Beauty Myth: How Images of Beauty Are Used Against Women

The Future of an Illusion

Beyond the Pleasure Principle 

Fleeced: How Barack Obama, Media Mockery of Terrorist Threats, Liberals Who Want to Kill Talk Radio, the Do-Nothing Congress, Companies That Help Iran, and Washington Lobbyists for Foreign Governments Are Scamming Us ... and What to Do About It

Climate Confusion: How Global Warming Hysteria Leads to Bad Science, Pandering Politicians and Misguided Policies that Hurt the Poor

Power/Knowledge: Selected Interviews and Other Writings, 1972-1977

The Order of Things: An Archaeology of the Human Sciences

Fantasies of Flight

Faces in a Cloud: Intersubjectivity in Personality Theory

Self-Reliance and Other Essays 

Civil Disobedience and Other Essays 

Walden; Or, Life in the Woods 

The Valkyries

Rabbit Hole

The Seafarer Rock 'n' Roll: A New Play

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

Making the map

force-directed layout, a modularity based clustering [9] could be a better fit. The two algorithms are strongly related, and therefore we can expect vertices that are in the same cluster to also be physically close to each other in the embedding.

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 separating points not in the same cluster and outer boundaries preferably following the general outline of the point set. A naive approach for creating the map is to form the Voronoi diagram of the vertices based on the embedding information, together with four points on the corners of the bounding box. This is illustrated in Figure 2(a). Such maps often have sharp corners, and angular outer boundaries. We can generate more natural outer 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 than some preset threshold. Note that this step can be implemented efficiently using a suitable space decomposing data structure, such as a quadtree. This leads to boundaries that follow the shape of the point set. In addition, the randomness of the points on the outskirts gives rise to some randomness of the outer boundaries, thus making them more map-like, as seen in Figure 2(b). Furthermore, depending on the value of the threshold, this step can also result in the creation of lakes and fjords in areas where vertices are far apart from each other. Nevertheless, some inner boundaries remain artificially straight. At this point, we still note the undesirable feature that the “countries” all have roughly the same area (Figure 2(b)), whereas we might prefer some areas to be larger than others (e.g., due to the importance of the entities they represent). As an illustration, in Figure 2, we assume that “node 1” is more important than the other

In the third step, we use the two-dimensional embedding together with the clustering to create the actual map by delineating country boundaries, carving continental outlines, and separating islands from continents. This can be accomplished with the help of plane partitioning techniques such as Voronoi diagrams, but with new algorithmic techniques to ensure realistic looking outer and inner boundaries. In the fourth and final step, we add additional graphical attributes to the drawing in order to enhance its clarity, to serve as keys to the abstract data, or to simply make it more aesthetically appealing. This would involve assigning an appropriate set of colors to the various regions. We propose a spectral algorithm that maximize color difference between neighboring countries. In addition, we could add mountains to the map or overlay it with a heat map to indicate scalar values associated with geographic positions. While the first two steps have been the subject of hundreds of papers, the last two steps in this process are new. With this in mind, in the next sections we describe how we put together the embedding 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.

2

(a)

(b)

(c)

(d)

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 space, distance distortion is inevitable, and the resulting figure will often have some anomalies and distortions. Thus, some strongly related 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 fragmentations are inherent in the embedding and clustering algorithms used in the first two steps. However we have proposed ways [5] to use the clustering information to adjust the layout, so that the regions of countries are more contiguous, at the expense of some loss of relational information captured in the original embedding. We believe that the map-like visualization better captures some of the cluster structure while at the same time providing an illustration that is more attractive to the typical user than the traditional scatterplots and node-link diagrams. Although we have not yet run a formal user study, anecdotal evidence from our customers and colleagues corroborates this claim.

Figure 2: (a) Voronoi diagram of vertices and corners of bounding box; (b) better construction of outer boundaries through placement of random points; (c) Voronoi diagram of vertices and points inserted around the bounding boxes of the labels; (d) the final map.

two nodes, and use a larger label for that area. 2 To make areas follow the shape of the labels, we first generate artificial points along the bounding boxes of the labels as shown in Figure 2(c). To make the inner boundaries less uniform and more map-like, we perturb these points randomly instead of running strictly along the boxes. Here Voronoi cells that belong to the same vertex are colored in the 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 give the final map in Figure 2(d). Note that instead of the bounding boxes of labels, we could use any 2D shapes, e.g., the outlines of real countries, in order to obtain a desired look and proportion of area, as long as these shapes do not overlap. We note that not all real maps have complicated boundaries. For example, boundaries of the western states in the United States often have long straight sections. We believe that irregular boundaries are more typical of historical and geographic boundaries, and lead to more map-like results. But this is a matter of personal taste and our technique can generate maps of both styles. When mapping vertices that contain cluster information, in addition to merging cells that belong to the same vertex, we also merge cells that belong to the same cluster, thus forming regions of complicated shapes, with multiple vertices and labels in each region. At this point we can add more geographic components to strengthen the map metaphor. For instance, in places where there is significant space between vertices in neighboring clusters, we can add lakes, rivers, or mountain ranges to the map to indicate the distance. With the regions determined, we have a representation of the data in which closely related objects, as determined by the graph topology and possibly edge weights, are drawn closely together. This geometric information is then used to discover clusters among the objects. To emphasize the clusters, each is represented as a collection of geometric regions. Figure 3 shows the difference between a typical node-link graph layout and the result of applying GMap to the same data. (Indeed, the graph layout is first step of the GMap layout.) The data represents the graph of author collaborations between 1994 and 2004

The final step, annotating the map with graphical attributes, involves assigning good colors to the countries in our maps. The Four Color Theorem states that only four colors are needed to color any map so that no neighboring countries share the same color. It is implicitly assumed that each country forms a connected region. This result, however, is of limited use to us because countries in our maps are not always connected. Therefore, we will have to use one unique color for each cluster to avoid ambiguity. Estimation of the number of colors an “average human” can discriminate, when color pairs are presented side by side, ranges from tens of thousands to a million. On the other hand, it takes much more effort when comparing colors that are similar. A further limiting factor is that 5% of males are color blind, which rules out certain coloring schemes. Finally, the limited palette of map-like coloring schemes reduces the choice of colors even more. In GMap, we start with a coloring scheme from ColorBrewer (www.colorbrewer.org), 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. Because of the blending, any two consecutive colors in the linear array of colors are similar to each other. When applying these colors to the map, we want to avoid coloring neighboring countries with such pairs of colors.3 With this in mind, we need to solve a discrete optimization problem where we find the best color permutation such that the color difference between neighbors is maximized overall. This is achieved by a combination of two procedures. They both operate on the country graph. The country graph is created from the original graph after it has been embedded and clustered. Specifically, the country graph contains a node for each country, with each edge representing two

2 A weighted Voronoi diagrams can be used to make the area of each Voronoi cell proportional to its weight. We do not use this approach, however, because we want the Voronoi cell to also contain a specific shape, e.g., the bounding box of a label.

3 Although two non-neighboring countries with similar colors can lead the viewer to believe that they are disjoint regions of the same country, this problem diminishes when the two countries are sufficiently far apart, as it is unlikely that distant regions belong to the same cluster.

Coloring the map

3

Figure 3: Node-link drawing compared to the GMap representation

4

Based on this style of use, GMap figures are most effective when displayed as a large image, often a meter or more in width, or via an interactive viewer. In the former case, the user can physically move to change the scale. In the latter case, the viewer provides the scale change and, at the same time, can provide some version of semantic zoom, so that more detail is added the more the user zooms in. In addition, an interactive viewer can provide such additional features as textual search or links connecting a feature on the map to some external information. For example, clicking on a book shown in the BookLand layout might take the user to its entry at Amazon.com. Given the page size limitations of a traditional journal, the figures included here are scaled to illustrate some features of the GMap layout (Figures 4 and 8) or to give a high-level view of such maps. The reader is encouraged to explore some GMap layouts at the site indicated in Footnote 1. We now consider how GMap works in practice with various different data sets. In the first, we visualize the “landscape” of music artists. In the second, we visualize the “landscape” of books as implied by user purchase behavior at Amazon.com. In the third, we visualize international trade data. Finally, we look at TV programs based on users’ viewing habits. In our implementation we use a scalable force-directed layout algorithm for step one and a modularity-based clustering algorithm for step two. 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 emerge from the graph layout and clustering algorithms. This gives the user a potential tool to discover structure based solely on local data.

countries that share a border. The first procedure turns the map coloring problem into that of a continuous optimization problem on the country graph, max

∑

{i, j}∈Ec

wi, j (ci − c j )2 , subject to

∑ ck

= 1,

(1)

k∈Vc

where Ec is the set of edges in the country graph, scalar value ci is the color (index) assigned to country i, and weighting factor wi, j measures how important it is to promote color difference between country i and country j. The solution is the largest eigenvector of the weighted Laplacian of the country graph. We then use the ordering induced by the values of the eigenvector as the color permutation. This is then followed by a greedy color swapping procedure to see if the color difference can be further improved. This heuristic algorithm improves the color difference between neighbors significantly compared with a random color assignment. Figure 4 illustrates the difference between a simple, random coloring and a coloring obtained using our approach. Note, for example, that in the random coloring, the countries in the middle are assigned colors in a green-gray palette, making it difficult to distinguish them. In the lower, optimized coloring, the separate regions in the central part are much more evident. U SING GM AP TO V ISUALIZE S ET R ELATIONS GMap is designed for visualizing cluster relations as maps, where each item is assumed to belong to one cluster and hence one country. However, the same algorithm can be easily adapted to visualize multiple relations among a set of objects. Byelas and Telea [3] proposed visualizing set relations using deformed convex hulls. Collins et al. [4] proposed “bubblesets,” based on isocontours. GMap provides a different approach. To apply GMap for visualizing sets, we work on one set at a time. Items not in the active set are considered obstacles, and treated the same as random points inserted in the GMap algorithm. Applying GMap then gives us a map of one country. By repeating this process for multiple sets, and using transparency to allow overlapping parts of the regions to be seen, we achieve a visualization of multiple sets. To avoid a country being disconnected, we add edges to link items in the same set. The edge addition process is similar to that of Collins et al. [4]. Edges are then routed as splines to avoid hitting items not in the active set, when possible. Artificial points are inserted along the spline edges. When GMap is applied, distant items are connected by “bridges” along the edges. Figure 5 shows a group of 55 photos from the Yale Face Database [7], representing portraits using different expressions and lightings. The photos are embedded in 2D using MDS. The distance between two photos is calculated using principal component analysis of a matrix of 55 rows, with each row a vector of the pixel values of a photo. Even with careful pre-processing, the embedding does not always put the same persons in the same neighborhood. Without set visualization, it is difficult to identify all photos of the same person. Figure 5 shows three sets of photos, each set belonging to a single person. As can be seen, each country is connected, and each avoids photos not in the set. This example shows that GMap provides a good alternative for set visualization.

MusicLand To create a land of music, we collected data from a web crawl of the last.fm website. As an Internet radio and music community website, it has over 30 million users, and recommends music based on user profiles. Over several years, the recommender system has collected information about how one band/musician/composer/artist is related to another in terms of how many listeners of one also enjoy the other. For each composer, the last.fm website lists the top 250 related composers. For example, Beethoven is considered to have “super similarity” to Mozart, Bach, and Brahms, “very high similarity” to Mendelssohn, Schumann, and Vivaldi 4 The website also provides the number of listeners of each musician. In April 2009, we crawled the website by starting with Beethoven, and the top 20 musicians most similar to Beethoven, provided that each has at least 100,000 listeners5 . We then found the top 20 most similar musicians to each of those with at least 100,000 listeners and proceed recursively. Our crawl yielded a graph with 2782 musicians, with edge weights corresponding to the similarity between musicians. We further pruned this graph by only taking edges that have “super similarity”. Finally, ignoring singletons, we end up with 2588 vertices. We then laid out the graph, clustered the vertices, and generated the MusicLand map as shown in Figure 6. We next examine some of the countries in MusicLand in more detail. The Mainland: The vast majority of musicians/bands is located in a single continent. While it is not as easy to spot major trends along the main axes, many of the clusters are well-defined and neighboring clusters make sense from a musical point of view. A 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

GM AP C ASE S TUDIES The GMap layout is meant to accentuate clusters in fairly large graphs. Gleaning information from the maps typically involves an interactive, multi-scale process, similar to that used for exploring geographic maps. One views the map at small scale to sense the overall layout, the major regions, and how they relate to each other. One then zooms in to see local detail, and to traverse the map along small features. At some point, one may zoom out again to put the local details into a global context.

4 Note

that we do not know last.fm’s formal definition of “super similarity”, “very high similarity”, or “high similarity”. 5 The reason we added a cut off of 100,000 listeners is that the number of listeners of musicians seem to follow a power law distribution. Without the cut off, our crawl did not finish after over a week of crawling, during which time we observed well over 1/2 million musicians, many with only a 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 in the north. Farther to the north is the grunge cluster anchored by Nirvana and Alice in Chains. On the west coast of the main continent, we find a cluster of electronic music, featuring Fatboy Slim, Daft Punk, and DJ Shadow. To the north are avant-garde electronic bands like Aphex Twin, while in the extreme west are electronic classics such as Vangelis. To the south is a compact and well-defined cluster of dance music represented by Paul Oakenfold and ATB. In the center of the map, there is a well-defined concentration of 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 with Beyonce and Alicia Keys. The Islands: There are two notable island regions in MusicLand: in the northeast is Reggae island, while the chain of islands off Rocky Coast in the southeast make up the Classical Archipelago. By zooming in (Figure 7), it is easy to find some general patterns in the layout of the archipelago along the East-West and North-South

axes. Along the first axis, the west contains modern composers such as Ravel, Satie, and P¨art, while the east contains 17th century composers such as Bach, Handel, and Albinoni. Along the second axis, the north has a high concentration of opera composers such as Verdi, Rossini, and Puccini, whereas the south has more orchestral and instrumental composers such as Holst, Elgar, and Stravinsky. Not surprisingly, Mozart and Beethoven are the most popular composers in the classical music cluster. The islands of Erik Satie and Arvo P¨art connect the big island in the east with the westernmost island of contemporary classical music represented by minimalists Philip Glass and Michael Nyman. BookLand Many e-commerce websites provide recommendations to allow for exploration of related items. Traditionally this is done in the form of a flat list. For example, Amazon typically lists around 5-6 books under “Customers Who Bought This Item Also Bought”, with a clickable arrow to allow a customer to see further related items. Instead of a flat list, which provides a very limited view of the

7

Madness The Specials

The Skatalites

Bob Marley & Sean Paul The Wailers

Desmond Dekker

UB40

Toots and The Maytals

Shaggy

Clueso

Die Fantastischen Vier

Jimmy Cliff

Inner Circle

Beenie Man

Peter Tosh

Bob Marley

Buju Banton

Peter Fox

Fettes Brot

Anthony B

Max Romeo

Culcha Candela

Jan Delay

Seeed Eek-A-Mouse

Deichkind

Patrice

Ziggy Marley Capleton

Gentleman

Burning Spear

Barrington Levy

Damian Marley

Big D and the Kids Table

Lee "Scratch" Perry

Red Sparowes

65daysofstatic

Low

Mono

Do Make Say Think

Pretty Girls Make Graves

Beach House Alan Silvestri

The Dismemberment Plan

Liars

Hans Zimmer

The Fiery Furnaces

Yo La Tengo

Howard Shore

Craig Armstrong

Squarepusher

Boards of Canada

Secret Machines

Albert Hammond, Jr.

Amon Tobin 9 Lazy 9

Mr. Scruff

Xploding Plastix

Jazzanova

Nuspirit Helsinki

Trüby Trio

Ian Pooley

Mike Oldfield

Tangerine Dream

De-Phazz

Gabin

Blue Six

Minus 8

Gregorian

Stéphane Pompougnac

Enya

Kitaro

Thunderball

St. Germain

dZihan & Kamien

Amethystium

Secret Garden

Bliss

David Arkenstone

FC/Kahuna

Mr. Oizo

Yves Larock

Supermode

Daft Punk

Zero 7

Télépopmusik

Modjo

The Prodigy

Alpha

Armand van Helden

Timo Maas

Planet Funk

Placebo

Klaxons

Paul Oakenfold

Olive

Smoke City

Kyau vs. Albert

ATB

Cosmic Gate

Butterfly Boucher

Aqua

Milk Inc.

Serge Gainsbourg

Jacques Brel

Charles Aznavour

Girls Aloud

Charlotte Gainsbourg

Carla Bruni

Siobhan Donaghy

Lady GaGa

New York Dolls

The Velvet Underground

Jewel

Meredith Brooks

Suzanne Vega

The Veronicas

Billy Idol

Duran Duran

Bob Dylan

Squeeze

Testament Kid Rock

After Forever

Tristania

Kreator

Danko Jones

The Darkness

Black Label Society

Annihilator

Sirenia

Lacuna Coil

Megadeth Xandria

Sonata Arctica

HammerFall

Judas Priest Blind Guardian Edguy

Manowar

Cinderella Quiet Riot

Twisted Sister

DragonForce

Dio Accept

Mötley Crüe

Within Temptation Kamelot

Apocalyptica

Stratovarius

Gamma Ray

Running Wild

Hanoi Rocks

KISS

Epica

Avantasia

Helloween

Saxon

White Lion

Black Sabbath

Iced Earth

Nightwish

Evergrey

Dream Theater

Nevermore

Rage

Scorpions

Sex Pistols

Bon JoviDeep Purple

The Undertones

The Damned

Symphony X

Pain of Salvation

Ayreon

Riverside Liquid Tension Experiment

Ramones

Buzzcocks

Roxy Music

Velvet Revolver

Rainbow

Van Halen

Stiff Little Fingers

The Stranglers

Tarja Turunen

Demons & Wizards

Guns N' Roses Whitesnake

Haggard

Angra

Primal Fear

Europe Alice Cooper

Aerosmith

The Jam

Therion

Bruce Dickinson

AC/DC

David Lee Roth

Def Leppard

The Clash

Edenbridge

Evanescence

Leaves' Eyes

Ozzy Osbourne

W.A.S.P.

The Cult

The Sisters of Mercy

Bow Wow Wow

XTC

The Gathering

Anthrax

Siouxsie and the Banshees

Paradise Lost

Theatre of Tragedy

Extreme

Ratt

Skid Row

The Smiths The Cure

Bauhaus

The Boomtown Rats

Public Image Ltd.

My Dying Bride

Anathema

Slayer

Exodus

Metallica

Venom

Ministry

Killing Joke

Adam and the Ants

MC5

Tiamat

Moonspell

Pantera

Turbonegro

Ugly Kid Joe

Warrant

Poison

Herbert Grönemeyer

Nena

The Fall

The 69 Eyes

Type O Negative

Backyard Babies

Sunrise Avenue

2raumwohnung

Mr. Big

Tesla

Morrissey

Bono

Nick Cave

Danzig

HIM

Soulfly

Motörhead

Wire

Flipsyde

Devo

Poets of the Fall

The Hellacopters

mia

Wir sind Helden

Andrew W.K. Iron Maiden

Annett Louisan

Rosenstolz

Paul Weller

Orchestral Manoeuvres in the Dark

Prince & The Revolution

Prince

John Cale

Mission of Burma

David Byrne

The Church

Oingo Boingo

Machine Head

Sepultura

The Rasmus

CKY

Juli

Linkin Park

Jim Sturgess

Joy Division

New Order

Joan Baez

Blondie Simple Minds

Patti Smith

Nico

Gang of Four

INXS

The Psychedelic Furs

Tom Waits

Sparks

Electronic

Heaven 17

Ani DiFranco

Tracy Chapman

U2

Skunk Anansie

Nick Cave and the Bad Seeds

The The

The Stooges

Sheryl Crow

Lene Marlin

Amy Macdonald

Barenaked Ladies

Fort Minor

Talking Heads

Television

Leonard Cohen

John Mayer Trio

Thomas Dolby

Tori Amos

Sam Sparro

Robyn

Édith Piaf

DJ BoBo

Maria Mena

Katy Perry

Michelle Branch

Keren Ann

Echo & The Bunnymen

Ryan Cabrera

The Beautiful South

The Be Good Tanyas

Saliva

Silbermond

Falco

L7

Lenny Kravitz

Daniel Powter

10,000 Maniacs

Gavin DeGraw

Teddy Geiger

John Mayer

Shawn Colvin

Puddle of Mudd

Creed

Reamonn

Jay-Z and Linkin Park

Dave Matthews & Tim Reynolds

Hüsker Dü

Flyleaf

Gym Class Heroes

Cowboy Junkies

Steve Earle

Paula Cole

Fuel

Bush

Dave Matthews

Dave Matthews Band

The Replacements

Jon McLaughlin

Townes Van Zandt

Jason Mraz

James Morrison

Lisa Loeb

Dar Williams

Ratatat

Josh Kelley

Martha Wainwright

Liz Phair

Beth Orton

Aimee Mann

Natalie Merchant

Heather Nova

Chantal Kreviazuk

Fugazi

Minutemen

Spin Doctors

Crash Test Dummies

Paramore

Matt Wertz

James Blunt

Patty Griffin

Poe

PJ Harvey

Sarah Slean

Charlotte Martin

Sara Bareilles

Vanessa Carlton

Nerina Pallot

Blues Traveler

Deep Blue Something

Toad the Wet Sprocket

Matchbox Twenty

Rob Thomas

Duncan Sheik

Fear Factory

Mushroomhead

SOiL

Skillet

12 Stones

Seether Theory of a Deadman

Alter Bridge

Goo Goo Dolls

Hootie & the Blowfish

Hole

Eagle-Eye Cherry

Five for Fighting

Edwin McCain

Howie Day

Veruca Salt

Justin Nozuka

Vienna Teng

Brandi Carlile

Shivaree

Anna Nalick

KT Tunstall

The Cardigans

Sophie Zelmani

Róisín Murphy

Sandi Thom

DJ Danger Mouse

Lasgo DJ Sammy Ian Van Dahl

Paolo Nutini

Rosie Thomas

Missy Higgins

Rachael Yamagata

Hercules and Love Affair

Azure Ray

Yael Naim

Jem

Emilie Simon

Sophie Ellis-Bextor

Sash! Armin van Buuren

Toploader

Matt Nathanson

Gillian Welch

Tristan Prettyman

Kate Nash

Alphabeat

Kate Havnevik

Imogen Heap

Emiliana Torrini

Françoise Hardy

Live

The Last Goodnight

Vertical Horizon

Sister Hazel

OneRepublic

James

Auf der Maur

Mat Kearney

Newton Faulkner

Amos Lee

Sia

France Gall

The Verve Pipe

The Smashing Pumpkins

The Script

Nick Drake

Joshua Radin

Donavon Frankenreiter

Lucinda Williams

Mika

Ingrid Michaelson

Ane Brun

Dragonette

Anja Garbarek

Bitter:Sweet

Brazilian Girls

April March

The Lightning Seeds

Busted

Tonic

Train John Martyn

Tim Buckley

Matt Costa

Rufus Wainwright

Joan as Police Woman

Pete Murray

Maria Taylor

The Ting Tings

Stina Nordenstam

M.I.A.

Bang Gang

The Sugarcubes

Blue Foundation

Joe Dassin

The Weepies

Garbage

Laura Veirs

Xavier Rudd

Katatonia

Strapping Young Lad

Coal Chamber American Head Charge

Static-X

Nonpoint

Thousand Foot Krutch Cold

Finger Eleven

Crossfade

Shinedown

Nickelback

John Frusciante

Lamb of God

Powerman 5000

Spineshank

Mudvayne

Drowning Pool

Sevendust

Trapt

Staind

Default

Daughtry

Collective Soul Fastball

Citizen Cope

David Gray

G. Love

G. Love & Special Sauce

The Calling

McFly

Gin Blossoms

Smile Empty Soul

3 Doors Down

Our Lady Peace

Red Hot Chili Peppers

Soul Asylum Nine Days

Smash Mouth

New Radicals

Goldfrapp Frou Frou A Fine Frenzy Avril Lavigne The B-52's Björk Annie Iggy Pop Lily Allen Alanis Morissette

Esthero

Pati Yang

Martina Topley-Bird

Vengaboys

Ferry Corsten

The Click Five

Colin Hay

Brett Dennen

Ron Sexsmith

Third Eye Blind

Dispatch

4 Non Jeff Buckley Blondes Jack Johnson Counting Crows Fiona Apple Maroon 5R.E.M. Vashti Bunyan

The Beautiful Girls

My Brightest Diamond

The John Butler Trio

Flunk

Moloko

Wax Poetic

Fragma

Above & Beyond

Angus & Julia Stone

Ocean Colour Scene

Josh Ritter

Mason Jennings

Laura Marling

Regina Spektor

Bonnie Somerville

Fun Lovin' Criminals

Anna Ternheim

Deee-Lite

Gus Gus Supreme Beings of Leisure

Mandalay

Everything but the Girl

Gabriel & Dresden

Tiësto

Markus Schulz

Robert Miles

System F

CocoRosie

Bat for Lashes

The Dresden Dolls

Santogold

The Presets

Basement Jaxx

Chicane

Paul van Dyk Sylver

Blank & Jones Solar Stone

Neko Case

Devendra Banhart

Lykke Li

Kashmir

Ladyhawke

Mew

Junior Senior

Chromeo

Sugar Ray

Semisonic

O.A.R.

Gary Jules

Joe Purdy

Antony and the Johnsons

Mirah

Empire of the Sun

Cansei de Ser Sexy

Lo-Fi-Fnk

New Young Pony Club

Yelle

Calvin Harris

Jay-Jay Johanson

Sasha

Hybrid

Schiller

Cut Copy

Datarock

Hot Chip Scissor Sisters

Kavinsky

DJ Mehdi

Stereo MC's

Pete Yorn

Damien Rice The Wallflowers

Cary Brothers

Josh Rouse

Ray LaMontagne

Dope

Slipknot

Ko:042fn Flaw

Adema

Papa Roach

Earshot

Evans Blue

Opeth Sentenced

Amorphis

Hinder

The Exies

Dishwalla

Better Than Ezra

Ryan Adams

Tom McRae

Ed Harcourt

Alexi Murdoch

Stone Sour

Element Eighty Taproot TRUSTcompany

Limp Bizkit 10 Years

Liquido

Chris Daughtry

Korpiklaani Ensiferum

Kalmah

Norther

Clawfinger

P.O.D. Chevelle

Breaking Benjamin Three Days Grace

Blind Melon

Marcy Playground

Finntroll

Dark Tranquillity

Sportfreunde Stiller

Alien Ant Farm

Candlebox

Sublime

Bedouin Soundclash

Violent Femmes

The Jesus and Mary Chain

Billy Bragg & Wilco

Uncle Tupelo

Simple Plan

Eve 6

Fool's Garden

Slightly Stoopid

Hoobastank

Days of the New

Mother Love Bone

311

Blue October

Cobra Starship

Everclear

Panic at the Disco

Death

Kittie

Otep

Dry Kill Logic

Godsmack

Morbid Angel

Children of Bodom Chimaira

Pain

Mad Season

Screaming Trees

The Presidents of the United States of...

The Fray

The Bluetones

Carcass

Rob ZombieDevilDriver

Crazy Town

Beatsteaks

Ill Niño

Wheatus

Meat Puppets

Soul Coughing

They Might Be Giants Remy Zero

Sleeper

Fionn Regan

Hello Saferide

Van She

Simian Mobile Disco

Justice

SebastiAn

Stereo Total

Archive

Hooverphonic Kosheen

Guster

Mudhoney

Butthole Surfers

Fall Out Boy Lifehouse

Electric Six

Eisley

The La's

White Zombie

Trivium

(hed) Planet Earth

Killswitch Engage Die Ärzte

Incubus

Guano ApesDisturbed

Mark Lanegan

Boys Like Girls

Frank Black

The Breeders

Aqualung

The Charlatans

Caliban

Madsen

Tenacious D

Pearl Jam

Temple of the Dog

Jerry Cantrell

Cannibal Corpse

Turisas

Arch Enemy

Deathstars

Die Toten Hosen

Eddie Vedder

Stone Temple Pilots

Bloodhound Gang

The Academy Is...

Richard Ashcroft

Ben Kweller

Pedro the Lion

In Flames

Unearth

Lostprophets

Angels & Airwaves

Soundgarden

Alice in Chains Nirvana Lit

At the Gates

Amon Amarth Bloodbath

Soilwork

Shadows Fall

Donots

Napalm Death

The Haunted

Hypocrisy

Skindred

Oomph!

Rage Against the Machine

Chris Cornell

Foo Fighters

Good Charlotte

We The Kings

Plain White T's

Rammstein

Bullet For My Valentine

All That Remains

30 Seconds to Mars

Yellowcard

My Chemical Romance

Switchfoot

The All-American Rejects

Helmet

Emperor

Nile

Deftones

American Hi-Fi

Cute Is What We Aim For

The Hush Sound

Augustana

Harvey Danger

Travis

Thirteen Senses

Gomez

Delays

Elliott Smith

Joseph Arthur

M. Ward

José González

St. Vincent

The Pipettes

Midnight Juggernauts Röyksopp

Tricky

Lamb

Portishead

Beth Gibbons & Rustin Man

BT

The Verve Ian Brown

Scouting for Girls

Tegan and Sara

Willy Mason

Vetiver

Kings of Convenience

Junior Boys

Forever the Sickest Kids

Metro Station

Gorillaz

Cake

Satyricon

Dimmu Borgir

Behemoth

Vader

Deicide

36 Crazyfists

System of a Down

+44

blink-182

Bowling for Soup

Quietdrive

Cradle of Filth

J.B.O.

Heaven Shall Burn

Sugarcult

Audioslave

Hellogoodbye

Jack's Mannequin The Good, The Bad & The Queen

Elastica Mansun

Phantom Planet

Happy Mondays

Damien Jurado

All Time Low

Ween

Pixies

Bleeding Through

Atreyu

As I Lay Dying

Scars On Broadway

SR-71

Midtown

Motion City Soundtrack

Graham Coxon

Blur

Eels

Supergrass

The Stone Embrace Zwan Roses

Orson

Bonnie 'Prince' Billy

Bon Iver

Suede The Divine Comedy

Feeder

Stereophonics

Starsailor

Snow Patrol

It Dies Today

Puscifer

Team Sleep

The Red Jumpsuit Apparatus

Mayday Parade

Immortal

Tool

Kettcar

Amber Pacific Box Car Racer

Cartel

The Rocket Summer

Dinosaur Jr.

The White Stripes

Keane

Oasis The Music Athlete

Therapy?

A Perfect Circle

Story of the Year

Madina Lake

Zebrahead

Sum 41

Eagles of Death Metal

Pulp

Haste the Day

The Used

Mest

Secondhand Serenade

Burzum

WIZO

Avenged Sevenfold

Funeral for a Friend

Tomte

Billy Talent

Allister

New Found Glory

Hit the Lights

Kill Hannah

Manic Street Preachers

Escape The Fate

Green Day

Taking Back Sunday

August Burns Red

Serj Tankian

Jimmy Eat World

Weezer

The Hoosiers

Tindersticks

Rilo Kiley

Songs: Ohia

Jenny Lewis with The Watson Twins

Joanna Newsom

El Perro del Mar

The Teenagers

The Black Ghosts

Uffie

I Monster

Dirty Vegas

Deep Dish Way Out West

Wilco

Great Lake Swimmers

Andrew Bird

The Starting Line

The Matches

The Spill Canvas

Ash

Nada Surf

Matt Pond PA

The Coral

Badly Drawn Boy

Hawthorne Heights

Aiden

Armor for Sleep

Anberlin

Acceptance

The Devil Wears Prada

From Autumn to Ashes

Matchbook Romance

Unwritten Law

Eighteen Visions

Enter Shikari

Alesana From First to Last Silverstein

Halifax

Rufio

Copeland

Kula Shaker

Turin Brakes

Coldplay

The Bees

The Raveonettes

Coconut Records

The Feeling

Noah and the Whale

The Whip

Erlend Øye

Mylo

Morcheeba

Moby Prodigy

Roger Sanchez

Booty Luv

Conor Oberst

Primal Scream

The Blow

Emily Haines & the Soft Skeleton

Patrick Wolf

Teitur

Sneaker Pimps

Faithless

Jakatta

StoneBridge Shapeshifters Martin Solveig

Benassi Bros.

Benny Benassi

Zoot Woman

Digitalism

Sébastien Tellier

Metric

Fleet Foxes

Mystery Jets

Beirut

Sufjan StevensIron & MGMT Wine Cat Power Feist

Jet

OK Go

I Am Kloot

Hard-Fi

Air Traffic

Sun Kil Moon

Mates of State

Final Fantasy I'm From Barcelona

Black Kids

Surkin

Groove Armada

Fatboy Slim

Junior Jack

Pendulum

Axwell

Michael Gray

Global Deejays

Stardust

The Chemical Brothers

The Crystal Method

Eric Prydz

Fedde le Grand

Does It Offend You, Yeah?

Just Jack

Goose

Justice vs Simian

Massive Attack

Terranova

Late of the Pier

Shitdisco

Boys Noize

Uniting Nations

David Guetta

Tiga

Audio Bullys

Leftfield

Cassius

Kinobe

Apollo 440

Ride

Foals

Friendly Fires

!!!

IAMX

Soulwax

The Zutons

One Night Only

Tilly and the Wall

Rooney

Elbow

Kasabian

The Libertines

Guillemots

The Magic Numbers

The Shins

Jens Lekman

The Whitest Boy Alive

Hadouken!

Fujiya & Miyagi

MSTRKRFT

Vitalic

Mint Royale

Propellerheads

Junkie XL

Laurent Wolf

Stars

Peter Bjorn and John The Concretes

The Go! Team

The Tough Alliance

Fischerspooner

Vive la Fête

UNKLE

The Wombats

The Decemberists

Au Revoir Simone

The Raconteurs

Razorlight

The Enemy

Editors

Larrikin Love

Vampire Weekend

Tom Vek

The Rapture

Chicks on Speed

The Avalanches

Death in Vegas Crystal Castles

The Knife

Air

José Padilla

Alex Gaudino Bob Sinclar Pakito Vinylshakerz

Fluke

Lunatic Calm

Clannad

Celtic Woman

Phoenix

Robots in Disguise

ADULT.

Zombie Nation Swayzak

Yonderboi Underworld

Doves

The Killers

The Rakes

Galaxie 500

The Long Blondes

Shearwater

Architecture in Helsinki

Los Campesinos! Akron/Family

The Ataris

Something Corporate

Super Furry Animals

Fightstar

Evergreen Terrace

boysetsfire

Drop Dead, Gorgeous

Chiodos

A Static Lullaby

Scary Kids Scaring Kids

Wolfmother

Ben Lee

The Courteeners

We Are Scientists

The Cribs

The Thrills

The Boy Least Likely To

My Bloody Valentine

LCD Soundsystem

Felix da Housecat

Alter Ego Fila Brazillia

Thievery Corporation

Karunesh

Loreena McKennitt

Conjure One

Miss Kittin & The Hacker

Ladytron

Freestylers Waldeck

Tosca

Mediæval Bæbes Guru Josh Project

Miss Kittin

Laurent Garnier

Blue States

Bent

Sofa Surfers

Lemongrass

Era

Afterlife Overseer

The Maccabees

White Lies

Broken Social Scene

The Dandy Warhols

Kaiser Chiefs

The Automatic

My Morning Jacket

GoodBooks

Band of Horses

Camera Obscura

Love Is All

Kaki King

Suburban Kids With Biblical Names

The Flaming Lips

The Fratellis

Maxïmo Park

Belle and Sebastian Bloc Party Muse

Ra Ra Riot

The Dodos

The Apples in Stereo

Jamie T

Paco de Lucía

The Streets

Client

Boozoo Bajou

Alex Gopher

Enigma Gotan Project

Yanni

Moya Brennan

Blackmore's Night

Lemon Jelly

Kruder & Dorfmeister

Dimitri From Paris

Federico Aubele

Deep Forest

Jean-Michel Jarre

Panda Bear

DeVotchKa Gogol Bordello

Freezepop

The Pigeon Milburn Detectives

Someone Still Loves You Boris Yeltsin

Mae

Dashboard Confessional

Jarvis Cocker

Brendan Benson

Bring Me the Horizon

A Day to Remember

Saosin

Finch

Head Automatica

The Offspring

MxPx

Hidden in Plain View

My American Heart

The Format

Dirty Pretty Things

Boy Kill Boy

The View

Kings of Leon

The Sunshine Underground

Okkervil River Shout Out Louds

Gipsy Kings

Slowdive The Books

The Radio Dept.

M83

Peaches

The Dust Brothers

Cut Chemist

Art Brut

The Futureheads The Holloways

Clap Your Hands Say Yeah

of Montreal

Asobi Seksu

Cocteau Twins

Dizzee Rascal

Modeselektor

Rob Dougan

Bonobo

Grizzly Bear The Unicorns

Kid Loco

Peace Orchestra

Spiritualized

Emery

The Almost

Alkaline Trio

Relient K

The Vines

Hot Hot Heat

Poison the Well Alexisonfire

Underoath

Boys Night Out

Say Anything

Circa Survive

Thursday

Brand NewAutopilot Off

Black Rebel Motorcycle Club

Sonic Youth

The Bravery

Little Man Tate

AFI

Spitalfield

The Early November

Sherwood

Ben Folds Five

Rocky Votolato

Sondre Lerche

Queens of the Stone Age

The Strokes

The Rifles

Blood Red Shoes

Good Shoes Bishop Allen

Death From Above 1979

Sleater-Kinney

The New Pornographers

Lady Sovereign

Diplo

Ulrich Schnauss

Telefon Tel Aviv

DJ Shadow

Orbital

Llorca

Vangelis

Talvin Singh

Eluvium

Caribou

Tiefschwarz

Aim

Jon Kennedy

Red Snapper Parov Stelar

Hird

Beanfield

Nicola Conte

Kaskade

Wax Tailor

DJ Cam

Nightmares on Wax

William Orbit

Mo' Horizons

The Funky Lowlives

Nitin Sawhney

Blonde Redhead The National

The Honorary Title

Idlewild

The Von Bondies

The Kooks

Voxtrot

The Brian Jonestown Massacre

Glassjaw

Senses Fail

Franz Ferdinand IMA Robot Beck

The Cinematics Rogue Wave

Straylight Run

Further Seems Forever

The Perishers

Death Cab for Cutie

Cold War Kids

The Young Knives

The Spinto Band

Arcade Fire

Louis XIV

The Paddingtons

The Rascals

Yeah Yeah Yeahs Midlake

Tokyo Police Club

Animal Collective

Rodrigo y Gabriela

RJD2

Micatone

LTJ Bukem

Delerium

Fink

Quantic

The Orb

The Future Sound of London

Koop

Kyoto Jazz Massive

Funki Porcini

The Cinematic Kid Koala Orchestra

The KLF

Banco de Gaia Jaga Jazzist

Bugge Wesseltoft

Beady Belle Jazzamor

Yeasayer

Bikini Kill

Sigur Rós

Ellen Allien Clint Mansell

DJ Krush

4hero

Wolf Parade

Oh No! Oh My!

Islands

Frightened Rabbit

Manitoba

808 State Skalpel

The Ordinary Boys

Dr. Dog

A.C. Newman

Beulah

The Magnetic Fields

múm

David Holmes

The Clientele

Spoon

The Postal Service

The Walkmen

Håkan Hellström

The Most Serene Republic

Dntel

The Microphones

Dead Poetic

Thrice

Rise Against

Bayside

The Get Up Kids

Daphne Loves Derby

Shiny Toy Guns

The Last Shadow Puppets

The Beta Band

Babyshambles

Saves the Day

The Juliana Theory

Monster Magnet

The Notwist

Sebadoh

The Hives

The Subways

The Dead 60s

Modest Mouse

The Gossip

Four Tet

Apparat

The Herbaliser

Blockhead

The Quantic Soul Orchestra

The Album Leaf

Amiina

Prefuse 73

Arctic Monkeys

Mando Diao

Lambchop

Tocotronic

Kyuss

Ben Folds

Slut

The Polyphonic Spree

Grandaddy

Ambulance LTD

Tapes 'n Tapes

TV on the Radio

Deerhunter

Seabear

Le Tigre Ellen Allien & Apparat

Booka Shade

The Fall of Troy

No Use for a Name

Fu Manchu The Cooper Temple Clause

Nine Black Alps

Mercury Rev

Bright Eyes

The Bled

Strike Anywhere

Bad Religion

Pennywise

The Sounds

The Appleseed Cast

The Kills

Stephen Malkmus

Interpol

Johnossi Glasvegas

Moneybrother

Nathan Fake

DJ Food

Tiger Lou Be Your Own Pet

Ugly Casanova

Sunset Rubdown

Stars of the Lid

Spank Rock

Gui Boratto

DJ Vadim

Coldcut

Alice Russell

Neutral Milk Hotel

MUM

LFO

Daedelus

Her Space Holiday

Apostle of Hustle

Efterklang

Autechre

Arovane Luke Vibert

Roots Manuva

Up, Bustle and Out

Menomena

Danny Elfman

AFX Plaid

Ricardo Villalobos

Wagon Christ

The Hold Steady

Test Icicles

James Newton Howard

Comeback Kid

Fear Before the March of Flames

Norma Jean Anti-Flag

Strung Out

Elefant

Sugarplum Fairy

µ-Ziq

Mouse on Mars

Propagandhi

Good Riddance

Millencolin

Radiohead Red House Painters

Sparklehorse

The American Analog Set

The Wrens

Sahara Hotnights Pavement

British Sea Power

The Stills

Enon

John Vanderslice

Venetian Snares

Built to Spill

Pinback

Every Time Blindside I Die

Descendents

Lagwagon

Clutch

Lali Puna

The Faint

Silver Jews

She Wants Revenge

Clinic

The Black Heart Procession

Caesars

The Dears

Deerhoof

Ted Leo and The Pharmacists

The Black Keys

Kent

James Horner

John Williams

Harry Gregson-Williams Thomas Newman

Aphex Twin

Ben Gibbard

Youth Group

Mogwai

The Bouncing Souls

Me First and the Gimme Gimmes

Mastodon

Guided by Voices

Calexico

The Bird and the Bee

The Dillinger Escape Plan

Jonny Greenwood

Biffy Clyro

Smog

The Thermals

The Blood Brothers

NOFX

Between the Buried and Me

Tunng

Cursive

Tortoise

Les Savy Fav

Destroyer

Rancid

Goldfinger

Neurosis

Psapp

The Horrors

Sparta

Stereolab

This Will Destroy You

Explosions in the Sky

Xiu Xiu

Klaus Badelt

Jerry Goldsmith

Isis

Silversun Pickups

dredg

The Sea and Cake

Godspeed You! Black Emperor

You Say Party! We Say Die!

Casiotone for the Painfully Alone

Meshuggah

At the Drive-In ...And You Will Know UsThom Yorke The Donnas by the Trail of... Oceansize

Bernard Herrmann

mewithoutYou

The Vandals

The Suicide Machines

Less Than Jake

The Good Life

Q and Not U

A Silver Mt. Zion

Broadcast

John Barry

Ennio Morricone

Operation Ivy

Catch 22

God Is Pelican an Astronaut

Steel Pulse

Augustus Pablo

"Weird Al" Yankovic Converge

Mad Caddies

Reel Big Fish

Slint

Hot Water Music

South Park

The Upsetters Culture

Alpha Blondy King Tubby

Monty Python

Transplants

The Mighty Mighty Bosstones

Dennis Brown

Horace Andy

Adam Sandler

Israel Vibration

The Aquabats Richard Cheese

Gregory Isaacs

Black Uhuru

Sizzla

Dane Cook

The Exploited

Dead Kennedys

Dido Tears for Sting Bryan Adams Black Flag The Cranberries Fears Elvis Costello Eurythmics Britney Spears Gwen Stefani The Who Slade a-ha Bruce Springsteen Deltron 3030 Madonna Cyndi Lauper Bebel Gilberto Beastie Boys Level 42 Golden Earring Mr. Mister Jim Croce Billy Ocean Fergie Beyoncé Amy Winehouse Chic A Tribe Djavan Aesop Rock Billy Joel The Kinks Jimi Hendrix Called Quest Tom Petty Antônio Carlos Air Supply Black Eyed Kelis Alicia Keys Norah Jones ABBA Cream Jobim Genesis The Doors Peas Jamiroquai Dire Straits James Brown Aaliyah Busta Rhymes Lauryn Hill Akon Ne-Yo Celia Cruz Diana Krall Janis Joplin Aretha Franklin Jethro Tull Stevie Wonder Roy Orbison Eric Clapton ShakiraBabyface T.I. Freddie Hubbard 2Pac Rank 1

Darude

Novaspace

Andain

Motorcycle

La Bouche

Groove Coverage

Safri Duo

Marco V Pulsedriver iiO

4 Strings

Special D.

Scooter

Gal Costa

A*Teens

Blue

Cypress Hill

DANGERDOOM

Savage Garden

Darren Hayes

Westlife

The Brand New Heavies

Nas

Public Enemy

Us3

Eve

LL Cool J

Lil' Kim

Missy Elliott

Keyshia Cole

Tweet

Salt-N-Pepa

Jadakiss

Art Blakey & The Jazz Messengers

TLC

Chris Brown

John Legend

Nelly

D'Angelo

Lloyd Banks

Chingy

G-Unit

K-Ci & JoJo

Craig David

Miles Davis

Obie Trice

Bubba Sparxxx

Keith Jarrett Bill Evans

112

Cam'ron

D12

Herbie Hancock

Trick Daddy

Juelz Santana

Kenny Chesney Toby Keith

Amaral

Aterciopelados Blackstreet

Harry Connick, Jr.

Nancy Wilson

Sarah Vaughan

Dinah Washington

Ella Fitzgerald Lou Rawls Carmen McRae

Jarabe de Palo

Anita O'Day

Otis Redding

Nat King Cole

John Lennon Elvis Presley

Solomon Burke

Yes

Carl Perkins

Enanitos Verdes

Rosemary Clooney

Jimmy Buffett

Sammy Davis, Jr.

Bing Crosby

Bill Haley and the Comets

Little Richard

Duke Ellington

King

Soda Stereo Wes Montgomery

Daddy Yankee

Chambao

Amparanoia

Don Omar

Django Reinhardt

Count Basie Benny Goodman

Ojos de Brujo

Cab Calloway

Josh Groban Bobby Darin

Vince Guaraldi Trio Judy Garland

The Alan Parsons Project

Emerson, Lake & Palmer Paul McCartney & Wings

Johann Strauss II Richard Wagner Richard Strauss

Wings

Eddie Cochran

The Blues Brothers

Percy Sledge

Frédéric Chopin

Pyotr Ilyich Tchaikovsky

Franz Liszt

Michael Nyman

The Drifters

Hector Berlioz Claude Debussy Robert Schumann

Gene Vincent

Charlie Feathers

Chubby Checker

Ella Fitzgerald & Louis Armstrong

Joaquín Sabina

The Platters

Dean Martin

Three 6 Mafia

Mahavishnu Orchestra

Peter Gabriel

Del Shannon

Booker T. & The MG's

Gil Scott-Heron

Julie London

Melendi

Louis Prima

Jerry Lee Lewis

Ricky Nelson

Perry Como Lena Horne

Bebe

Los Rodríguez

Gioacchino Rossini

The Beatles

Albert King

Fats Domino

The Everly Brothers

Blossom Dearie

Mel Tormé

Tony Bennett

George Benson

Andrés Calamaro

Giacomo Puccini

Georges Bizet

Canned Heat

B.B. King & Eric Clapton

Louis Armstrong Frank Sinatra Los Fabulosos Estopa Doris Day Cadillacs Ben E.

Pitbull

Lil Jon

Lil Jon & The East Side Boyz

Giuseppe Verdi

John Mayall & The Bluesbreakers

Phish

Ringo Starr

Sam & Dave

The Lemonheads

Grateful Dead

Rush

The Monkees

Procol Harum

George Harrison

Buddy Holly

Chuck Berry

Jackie Wilson

Iron Butterfly

Stevie Ray Vaughan and Double Trouble

Johnny Winter

Stevie Ray Vaughan

Bo Diddley

The Shirelles The Righteous Brothers

El Canto del Loco

Café Tacuba

Ying Yang Twins Chick Corea

Al Di Meola

Maná

Rory Gallagher

The Posies

Big Brother & The Holding Company

John Mayall

Focus

Etta James

Brian Wilson

Teenage Fanclub

Steely Dan

The Mamas & The Papas

Herman's Hermits

J.J. Cale

Buddy Guy

Ray Charles

Paul McCartney

Peggy Lee

Robert Plant

Pink Floyd

Syd Barrett

Derek and The Dominos

Supertramp

Manfred Mann

Van der Graaf Generator

Camel

Nina Simone

Alejandro Sanz

The Beach Boys

Jefferson Airplane

Fountains of Wayne

Ten Years After

Gentle Giant

Dr. John

Howlin' Wolf

Andy Williams

Petey Pablo

Bone Thugs-N-Harmony Chet Baker

Weather ReportEminem Jaco Pastorius

La Oreja de Van Gogh

Belanova

Eartha Kitt

Blind Faith

Mark Knopfler

The Moody Blues

The Ronettes

The Meters

Edwin Starr

Sam Cooke

Wilson Pickett Shirley Horn Michael Bublé

Al Jarreau

Sin Bandera

Boyz II Men

Jagged Edge

Young Buck

Thelonious Monk

Smokey Robinson and the Miracles

The Marvelettes

Isaac Hayes

Lonestar

Keith Urban

Julieta Venegas

Vanilla Ice

Soulja Boy

Warren G

The Lovin' Spoonful

The Hollies

King Crimson

Alan Jackson

Ricardo Arjona

Lloyd Snoop Dogg

Jim Jones

The Four Tops

Al Green

Bobby Womack

Roberta Flack

The Black Crowes

The Jimi Hendrix Experience

David Gilmour

Bill Withers

Curtis Mayfield

Cassandra Wilson

Joe Cocker

The Turtles

John Lee Hooker

The Temptations

The Spinners

Donny Hathaway

Roy Ayers

Natalie Cole

Peter Cincotti

Page & Plant

Roger Waters

13th Floor Elevators

The Animals

B.B. King

Robert Johnson

The O'Jays

Minnie Riperton

Billie Holiday

Jane Monheit

Garth Brooks

Brad Paisley

Led Zeppelin

Big Star

The Allman Brothers Band

Chris Rea

Muddy Waters

War

The Supremes

The Troggs

Traffic

Sly & The Family Stone

Gladys Knight & The Pips

The Isley Brothers

Shirley Bassey

Jamie Cullum

Rascal Flatts

Reik

Juanes Joe

Bad Company

Creedence Clearwater Revival

Love

Kansas

The Zombies

Leadbelly

Tim McGraw

Lizz Wright

Charles Mingus

Ike & Tina Turner

Tom Petty and the Heartbreakers

Funkadelic

Luis Miguel

Chayanne

Brian McKnight

Marques Houston

Ghostface

Donald Byrd

Commodores

Stacey Kent

Luther Vandross

America

The Rolling Stones

Electric Light Orchestra

The Spencer Davis Group

Toto

Elton John

Marc Anthony

Ricky Martin

Ginuwine

Mario

R. Kelly Ray J

Chamillionaire

Dizzy Gillespie

Taj Mahal

Phil Collins

Martha Reeves & The Vandellas

Marvin Gaye

Paulina Rubio

Fugees

Bobby Valentino

Omarion

Mims

Rick Ross

Diana Ross and The Supremes

Free

The Guess Who

The Yardbirds

The Byrds

Fleetwood Mac

Kenny Rogers

Parliament

Nancy Sinatra

Chaka Khan

Madeleine Peyroux

Randy Crawford

Anthony Hamilton

Baby Bash

Bow Wow

Twista

Coolio

Young Jeezy Xzibit

Anita Baker

Angie Stone

En Vogue

Musiq

Flo Rida

Earth, Wind & Fire

Barry White

Faith Hill

Petula Clark

ZZ Top

Peter Frampton

The Doobie Brothers

Eagles

Chicago

Ry Cooder

Michael Bolton

Cameo

Dusty Springfield

Buffalo Springfield

Three Dog Night

Lynyrd Skynyrd

Gordon Lightfoot

Ohio Players

Dionne Warwick

Macy Gray

Erykah Badu

Maxwell

Wyclef Jean

Jamie Foxx

Usher

MC Hammer

Ja Rule

50 Cent

McCoy Tyner

Robin Thicke

Will Smith

T-Pain

Lil' Wayne

The Game

DMX

Charlie Parker

Crosby, Stills & Nash

Bob Seger

Rod Stewart

Asia

Richard Marx

Barbra Streisand

Barry Manilow

India.Arie

Mary J. Blige

Faith Evans

Jill Scott

Sean Kingston

Sir Mix-A-Lot

Fat Joe

Eazy-E

John Coltrane

Wayne Shorter

Ol' Dirty Bastard

Bee Gees

Rick James

Kool & The Gang

Lionel Richie

Sade

Gloria Estefan

Tamia

Don Henley

Status Quo

Gary Moore

Steppenwolf

Warren Zevon

Survivor

Hall & Oates

Mike & The Mechanics

Cliff Richard

Shania Twain

Toni Braxton

P. Diddy

Puff Daddy

Ice Cube

Method Man & Redman

Fabolous

Method Man

RZA

Hot Chocolate

Wild Cherry

Thalía

Madcon

Dr. Dre

Raekwon

Monica

Timbaland

M.O.P.

Sonny Rollins

Mya

The J. Geils Band

John Mellencamp

Eddie Money

Steve Winwood

Neil Diamond

Kenny Loggins

Chris de Burgh

Diana Ross

Des'ree

Grand Funk Railroad

Steve Miller Band

Neil Young

Journey

REO Speedwagon

Jackson Browne

Stevie Nicks

Woody Guthrie

John Denver

Smokie

Art of Noise

Carpenters

Lisa Stansfield

Joss Stone

LeAnn Rimes

Martina McBride

Enrique Iglesias

Naughty by Nature

Lee Morgan

Horace Silver

Janet Jackson

Brandy

Don McLean

John Hiatt

Cutting Crew

Starship

Modern Talking

Gloria Gaynor

Keri Hilson

will.i.am

Ludacris

Wu-Tang Clan

Estelle

Bachman-Turner Overdrive

Camouflage

Paul Young

Bonnie Tyler

Wet Wet Wet

Olivia Newton-John

Boney M.

KC and the Sunshine Band

Tina Turner

Bad Brains

Nazareth

UFO

Thin Lizzy

Neil Young & Crazy Horse

Heart

Huey Lewis & The News

Pat Benatar

Kim Carnes

Carly Simon

Irene Cara

Sister Sledge

Village People

George Michael

Céline Dion

Amerie

Run-D.M.C.

N.W.A

Yello

Laura Branigan

Sandra

Wham!

Paula Abdul

Sarah Connor

Dixie Chicks

Mobb Deep

Cannonball Adderley

Guru

Christina Milian

Donovan

Crowded House

Lipps, Inc.

Eva Cassidy

Corinne Bailey Rae

Mariah Carey

Roxette

Pharrell

Notorious B.I.G.

Big L

Rick Astley

The Pointer Sisters

Belinda Carlisle

Simply Red

Gabrielle

Carrie Underwood

Lisa Ekdahl

Justin Timberlake

Dexter Gordon

Redman

The Bangles

Seal

Alison Krauss

Taylor Swift

Katie Melua

Anastacia

JoJo

Eric B. & Rakim

Dave Brubeck

GZA/Genius

Vanessa Hudgens

Katharine McPhee

Destiny's Child

Ashanti

Foghat

Joe Walsh

Crosby, Stills, Nash & Young

Bonnie Raitt

Robert Palmer

Cher

Pharoahe Monch

The Dave Brubeck Quartet

Ashley Tisdale

Jordin Sparks

Christina Aguilera

Jennifer Lopez

Cherish

Kelly Rowland

Whitney Houston

KRS-One

Vanessa da Mata

Van Morrison

Donna Summer

Nelly Furtado

Cassie

Jennifer Hudson

Sweet

Boston

Humble Pie

Cat Stevens

James Taylor

Culture Club

Uriah Heep

Cheap Trick

Styx

Foreigner

The Knack

Simon & Garfunkel

Gary Numan

Bananarama

Minor Threat

Ted Nugent

Jon Bon Jovi

The Small Faces

The Band

Meat Loaf

Midnight Oil

Howard Jones

Nik Kershaw

The Sonics

Alison Moyet

Bette Midler

Leona Lewis

Jamelia

Kat DeLuna

Michelle Williams

*NSYNC

Kanye West

Ciara

Incognito

Astrud Gilberto

Jessica Simpson

The Pussycat Dolls

Rihanna

Danity Kane

Lupe Fiasco

OutKast

Bob Dylan and The Band

The Cars

The Police

Men at Work

Talk Talk

Alphaville

Chris Isaak

Carole King

Blue Öyster Cult

Bryan Ferry

Joe Jackson

Elvis Costello & The Attractions

The Pretenders

Spandau Ballet

The Go-Go's

Fine Young Cannibals

Marianne Faithfull

Grace Jones

Miley Cyrus

Robbie Williams

Jay-Z

Q-Tip

Berlin

A Flock of Seagulls

Japan

Paul Simon

Frankie Goes to Hollywood

Dead or Alive

Erasure

Pet Shop Boys

Duffy

Aly & AJ

Mandy Moore

Shayne Ward

Ronan Keating

Nicole Scherzinger

Solange

Common

The Roots

Mos Def

Clipse

Masta Ace

Paris Hilton

Men Without Hats

ABC

Yazoo

Soft Cell

Annie Lennox

Jedi Mind Tricks

Terence Trent D'Arby

The Pharcyde

Murs

Gang Starr

Los Hermanos

Natasha Bedingfield

Stacie Orrico

Thompson Twins

The Buggles

Visage

dead prez

k.d. lang

Kate Bush

Lighthouse Family

Backstreet Boys

Talib Kweli

De La Soul

Arrested Development

Dilated Peoples

Stan Getz

Sinéad O'Connor

Lindsay Lohan

No Doubt

Gnarls Barkley

Black Star

Little Brother

Atmosphere

CunninLynguists

Sage Francis

The Wreckers

Daniel Bedingfield

N*E*R*D

Jurassic 5

Chico Buarque

El-P

Hilary Duff

Jesse McCartney

P!nk

Mutya Buena

Boyzone

House of Pain

Ace of Base

Ultravox

The Human League

Kim Wilde

Immortal Technique

Indigo Girls

Melissa Etheridge

Dolly Parton

Pink

Adele

Melanie C

Blackalicious

Hieroglyphics

Del tha Funkee Homosapien

Elis Regina

Marisa Monte

Ashlee Simpson

Delta Goodrem

Emma Bunton

Spice Girls

Joni Mitchell

Flobots

Emmylou Harris

Texas

Kelly Clarkson

Kelly Osbourne

S Club 7

Dr. Octagon

Caetano Veloso

Gilberto Gil

Madlib

Jorge Ben

Sarah McLachlan

Colbie Caillat

Will Young

Lucie Silvas

Geri Halliwell

Atomic Kitten

September

Infernal

Jonas Brothers

Madvillain

Quasimoto

O-Zone

Cibelle

João Gilberto

Lou Reed

Joan Osborne

Take That

All Saints

The Corrs

Paris Combo

Handsome Boy Modeling School

MF DOOM

Gigi D'Agostino

K's Choice

Natalie Imbruglia

Gabriella Cilmi

Rachel Stevens

Dannii Minogue

Girl Talk

Alcazar

Alice Deejay

Brooklyn Bounce

Eiffel 65

Kylie Minogue

Pink Martini

Cascada

Dr. Alban

Everlast

Sugababes

Kate Ryan

Basshunter

DJ Shog

Technotronic

Camille

Vanessa Paradis

Nouvelle Vague

Culture Beat

2 Unlimited

Haddaway

Snap!

Mauro Picotto

Bomfunk MC's

Zbigniew Preisner

Arvo Pärt Kronos Quartet

Erik Satie

Franz Schubert

Edvard Grieg

Wolfgang Amadeus Mozart

Gustav Mahler

Jean Sibelius

Felix Mendelssohn

Maurice Ravel

Philip Glass

Brenda Lee

Ludwig van Beethoven Johannes Brahms

Sergei Rachmaninoff

Gabriel Fauré

Modest Petrovich Mussorgsky

Antonín Dvo:0159ák

Camille Saint-Saëns

The Coasters

Sergei Prokofiev

Paul Anka

Andrea Bocelli

Penguin Cafe Orchestra

Luciano Pavarotti

Macaco

Glenn Miller Sarah Brightman

Dmitri Shostakovich

Sir Edward Elgar

Igor Stravinsky

Franz Joseph Haydn

Johann Sebastian Bach Henry Purcell Georg Friedrich Händel

Georg Philipp Telemann Johann Pachelbel

Antonio Vivaldi

Tomaso Giovanni Albinoni

Samuel Barber

Gustav Holst

Luigi Boccherini

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

Michael Nyman

Zbigniew Preisner Erik Satie

Gabriel Fauré Gustav Mahler Kronos Quartet

Jean Sibelius

Maurice Ravel

Philip Glass

Modest Petrovich Mussorgsky Sergei Prokofiev

Igor Stravinsky Penguin Cafe Orchestra

Antonín Dvorák

Camille Saint-Saëns

Wolfgang Amadeus Ludwig van Mozart Johann Sebastian Beethoven

Felix Mendelssohn

Bach

Franz Joseph Haydn

Georg Friedrich Händel

Antonio Vivaldi Sir Edward Elgar

Dmitri Shostakovich

Franz Schubert

Johannes Brahms Edvard Grieg

Sergei Rachmaninoff Arvo Pärt

Frédéric Chopin

Pyotr Ilyich Tchaikovsky

Franz Liszt

Claude Debussy

Georg Philipp Telemann

Samuel Barber Gustav Holst

Figure 7: Part of the classical archipelago

8

Henry Purcell

Johann Pachelbel

Luigi Boccherini

Tomaso Giovanni Albinoni

Frankenstein 

cbeth 

The Good Earth 

Night 

A Tale of Two Cities 

Gertrude: A Novel

Steppenwolf: A Novel

Of Mice & Men

The Journey to the East

Twilight: The Complete Illustrated

Being And Nothingness

The Ethics Of Ambiguity

Being and Time Phenomenology of Perception 

 And Human ns 

The Myth of Sisyphus: And Other Essays

The Years

The Plague

The Adolescent Resistance, Rebellion, and Death: Essays

The Brothers Karamazov

b's Room

The Double and The Gambler

No Exit and Three Other Plays Spark Notes Crime and Punishment Chinua Achebe's Things Fall Apart 

Welcome to the Monkey

The Soul and Barbed Wire: An Introduction to Solzhenitsyn

Dead Souls: A Novel

The Idiot

Demons

The Stranger

The Soviet Experiment: Russia, The U and the Successor States

Journey into the Whirlwind 

The Twelve Chairs 

The Harvest of S Collectivization and

Man Is Wolf to Man: Surviving the Gulag

A Hero of Our Time 

The Unbearable Lightness of Being: A Novel We

A Passage to India

Chronicle of a Death Foretold

The Remains of the Day

Water for Elephants: A Novel

The Th A On Chesil Beach

Collected Stories

On Beauty

Home and

Dewey: The Small Who Touche Saturday

The English Patient

The Autumn of the Patriarch 

Of Love and Other Demons  Never Let Me Go

Atone

The Memory Keeper's Daughter

Snow Flower and the Secret Fan: A Novel

Memories of My Melancholy Whores

One Hundred Years of Solitude 

Notes from Underground

Suite Francaise

The Kite Runner

A Heartbreaking Work of Staggering Genius

Howards End

Stories of Anton Chekhov

The Book of Laughter and Forgetting

In the Skin of a Lion

The Gulag Archipelago, 1918-1956: An Experiment in Literary Investigation, Parts V-VII

The Gulag Archipelago 1918-1956 I-II

Gulag: A History

The Gulag Archipelago 1918-1 Parts I - II

The Gulag Archipelago Volume 1: An Experiment in Literary Investigation 

August 1914

The Unbearable Lightness of Being 

War and Peace 

The Gulag Archipelago 1918-1956 Abridged: An Experiment in Literary Investigation 

In the First Circle: A Novel 

A Thousand Splendid Suns

Animal Farm and 1984 All Quiet on the Western Front

Home To Harlem 

New Essays on Their Eyes

Rescuing Sprite: A Dog Lover's Story of Joy and Anguish

The Gulag Archipelago: 1918-1956, An Experiment in Literary Investigation III - IV

One Day in the Life of Ivan Denisovich 

The Eternal Husband and Other Stories

The Fall

Mrs. Dalloway

Cancer Ward

Heart of a Dog

The Collected Tales of Nikolai Gogol

The First Man

The Blacker the Berry 

Mother Night: A Novel

We Never Make Mistakes: Two Short Novels

The Solzhenitsyn Reader: New and Essential Writings, 1947-2005

Introduction to Metaphysics 

The Rebel: An Essay on Man in Revolt

The Portable Harlem Rena Reader 

Warning to the West

The Master and Margarita

Oblomov

Zo

Zora Neale Hurston's Their Eyes Were Watching God: A Casebook 

Red Cavalry

Russiana

Eugene Onegin: A Novel in Verse 

sea

Men in Black: How the Supreme Court Is Destroying America

White Guard

A Room of One's Own

The Fountainhead

Quicksand and Passing 

The Invisible Man 

Spark Notes Invisible Man

Cat's Cradle: A Novel

Breakfast of Champions: A Novel

Solzhenitsyn: A Soul in Exile

Basic Writings

Heidegger's Being And Time: A Reader's Guide 

Steinbeck's the Grapes of Wrath 

Tortilla Flat

Invisible Man In Our Time

Plum Bun: A Novel Without a Moral

Their Eyes Were Watching God Literature Guide 

Spark Notes The Grapes of Wrath

Atlas Shrugged

A Dead Man's Memoir: A Theatrical Novel 

Their Eyes Were Watching God

Spark Notes The Scarlet Letter

Spark Notes The Great Gatsby

The Complete Short Stories of Ernest Hemingway: The Finca Vigia Edition

The Forgotten Man: A New History of the Great Depression

The Fatal Eggs 

Fitzgerald's The Great Gatsby 

For Whom the Bell Tolls

Hawthorne's The Scarlet Letter 

Death of a Salesman 

Long Day's Journey

Capitalism and Freedom: Fortieth Anniversary Edition

Beloved

Passing:  The Things They Carried

The Short Stories of F. Scott Fitzgerald: A New Collection

A Farewell To Arms

The Winter of Our Discontent 

Personal Statement

The Daodejing of Laozi

A Moveable Feast

In Search of History Salem Witch Trials 

The Bri of

Black Boy

Spark Notes The Adventures of Huckleberry Finn

To Have and Have Not

Interpre Malad

The Bluest Eye

Native Son

Their Eyes Were Watching God CD

One Flew Over the Cuckoo's Nest: 

Cannery Row:

The Glass Menagerie

Moksha: Aldous Huxley's Classic Writings on Psychedelics and the Visionary Experience

The Great Gatsby

Slaughterhouse-Five: A Novel

Islands in the Stream : A Novel

The Grapes of Wrath 

Travels with Charley in Search of America: 

A Raisin in the Sun

Huxley and God: Essays

East of Eden

The Old Man and The Sea

The Adventures of Huckleberry Finn

The Perennial Philosophy 

The Rest Is Noise: Listening to the Twentieth Century

Americana

The Scarlet Letter

The Autobiography of Benjamin Franklin 

nomenology of Spirit 

The God of Small Things: A Novel

Siddhartha

The Great Gatsby CD

The Crucible

g Heights

The Ground Beneath Her Feet: A Novel

The Sun Also Rises

The Catcher in the Rye

Island 

Narcissus and Goldmund: A Novel

Narcissus and Goldmund

Incidents in the Life of a Slave Girl 

a 

Half of a Yellow Sun

The Awakening

The Glass Bead Game: 

Beneath the Wheel

sion

God's Bits of Wood 

Wide Sargasso Sea: A Novel

A Clockwork Orange

Of Mice and Men 

Jane Eyre

f Two nniversary 

The Moor's Last Sigh

Midnight's Children: A Novel

Nineteen Eighty-Four

To Kill a Mockingbird

Mythology

A Man of the People

War And Peace 

Fahrenheit 451

Demian

Narrative of the Life of Frederick Douglass 

 Jane

No Longer at Ease

Catch-22 Waiting for Godot: A Tragicomedy in Two Acts

A Tree Grows in Brooklyn 

Golding's the Lord of the Flies 

Brave New World and Brave New World Revisited Brave New World

1984

Animal Farm

Lord of the Flies 

The Picture of Dorian Gray - Oscar Wilde  Invisible Man 

Chinua Achebe's Things Fall Apart 

Wiesel's Night

Dr. Jekyll & Mr. Hyde 

t 

Understanding Things Fall Apart: Selected Essays and Criticisms

Chinua Achebe's Things Fall Apart: A Casebook  Huxley's Brave New World 

Love in the Time of Cholera 

The Glass Castle: A Memoir

The History of Love: A Novel

The Namesake: A Novel

The Maytrees: A Novel

Lov A

The Gathering Divisadero Bridg

Figure 8: Two of the central clusters in BookLand.

neighborhood, there have been attempts to convey the underlining connectivity of the products through graph visualization. None of the existing approaches, however, gives a comprehensive view of the relationship and the clustering structures.

same book, but with different publishers or different bindings, by matching books with the same title. The underlying graph for this map contains 913 vertices and 3410 edges. With an average degree of nearly eight, peripheral vertices in this map have only a handful of edges while central vertices have more than 20 immediate neighbors. We next examine several of the BookLand countries in more detail (cf. Figures 8 and 1).

Using our GMap algorithm, we obtained the map in Figure 1. The underlying data is obtained with a breadth-first traversal following Amazon’s “Customers Who Bought This Item Also Bought” links, starting from the root node, Orwell’s 1984. Links are followed up to a distance of twelve from the root node. We then trim the graph by keeping only vertices of distance nine or less from the root vertex. We further merge nodes that represent the

Americana: Somewhat surprisingly, Orwell’s 1984 along with Animal Farm ended up in the west corner of a region populated mostly by American writers. Britain is also represented by Golding’s The Lord of the Flies and Huxley’s Brave New World along

9

partners.

with Burgess’s Clockwork Orange, which connect the British corner of the region to the main part dominated by 20th century American classics. Bradbury’s Fahrenheit 451 and Salinger’s Catcher 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 For Whom the Bell Tolls, Fitzgerald’s Great Gatsby, Heller’s Catch22, and Kesey’s One Flew Over a Cuckoo’s Nest. Russiana: To the north of Americana lies one of the largest countries in BookLand, dominated by Russian literature and history. The core contains classic novels by Dostoyevsky (The Brothers Karamazov), Tolstoy (War and Peace), and Solzhenitsyn (The Gulag Archipelago, Cancer Ward). In the west, there is, unexpectedly, a cluster of Camus books (The Stranger, The Plague, The Fall), all well connected with the Russian classics. From the map, we can also see some high-level connections. There is the not too surprising proximity of self-help books with books recommended by Oprah Winfrey. We also find the group of recent vampire novels adjacent to the cluster of Victorian novels. A closer investigation shows that vampire novels are only connected to the rest of the graph through Jane Austen.

TVLand As a last example, we consider a map derived from TV viewer data. The objects are TV shows, with an edge between two shows if several viewers watched both. The edges are weighted by the number of such viewers. We illustrate how GMap can be used in the context of recommendation systems with the aid of heat map overlays, tailored to an individual viewer. Figure 10 shows such a map for a typical but fictitious viewer. Based on the observed viewing habits of a specific viewer, and on those of other viewers, a recommendation system can suggest possible new shows. In order for the labels to be readable in a journal format, our map displays a small subset of the TV shows and consists of six countries. The countries capture several types of shows by genre. In the southwest are two countries corresponding to TV shows for children, with the smaller targeting younger kids with Dora the Explorer and Wow Wow Wubbzy. In the northwest is a cluster of shows about fashion and entertainment such as Say Yes to Dress and E! News. The large country in the north contains popular sitcoms such as Seinfeld, Cheers, and Frasier. In the northeast is a cluster of crime shows (NCIS and Law & Order). The cluster in the southeast is not as thematically focused but contains popular shows of several types: The Oprah Winfrey Show, So You Think You Can Dance, and Dateline NBC. In each country the TV shows are colored based on the strength of the recommendation; that is, the lighter the color, the stronger the recommendation, as in a typical geographic map where shading of colors are used to represent hills and valleys. Maps like this provide a global view not available in the traditional list of recommendations and offer a more appealing presentation than a scatterplot or a node-link diagram. The map provides a context for recommendations, allowing a user to understand the reasoning behind the recommendation: when considering highlyrecommended shows the user can check out nearby, related shows; or explore a path of shows to a new area.

TradeLand Figure 9 is a map visualizing the trade relations between all countries. Bilateral trade data between each of the 209 countries and its top trading partners were acquired from Mathematica’s CountryData package. The font size of a label is proportional to the logarithm of the total trade volume of the country, and the color of a label reflects whether a country has a trade surplus (black) or deficit (red). The label color gives an easy way to spot the oil-rich countries with large surpluses, which are distributed all over the world as well as in our map: Middle East (Saudi Arabia, Kuwait), Europe (Russia), South America (Venezuela), Africa (Nigeria, Equatorial Guinea). On the other hand, the countries with huge deficits are mostly in Africa (Sierra Leone, Senegal, Ethiopia) with the United States, the clear outlier. Many countries in close geographic proximity end up close in our map, e.g, Central American countries like Honduras, El Salvador, Nicaragua, Guatemala and Costa Rica are close to each other in the northeast. Similarly the three Baltic republics, Latvia, Lithuania and Estonia, are close to each other in the northwest. This is easily explained by noting that geographically close countries tend to trade with each other. There are easy-to-spot exceptions: North Korea is not near South Korea, Israel is not particularly close to Jordan or Syria. The G8 countries (Canada, France, Germany, Italy, Japan, Russia, United Kingdom, and the United States) are all in close proximity to each other in the center of the map. Two of the largest and closest countries in our map are China and the United States. Clearly, the proximity is due to the very large trade volume rather than geographic closeness. All these countries are in the largest cluster which is dominated by European countries in the west, Asian countries in the east, and Middle Eastern countries in the south. Interestingly, we see from the map that African countries are distributed in several clusters in close proximity to China (a major trading partner to many African countries), the United States (trading less with Africa these days), and around former colonizers (e.g., Togo, Cameroon and Senegal, which are all close to France). On the other hand, Caribbean and South and Central American countries form several clusters in the north of the map. In addition, these clusters are mostly contiguous, essentially forming a supercluster. This differentiation between Latin America and Africa is clearly brought out by the GMap figure. Finally, we note that the periphery of the map contains small countries from around the world, and countries with few trading

R ELATED W ORK There are many papers in geography about accurately and appealingly representing a given geographic region, or on re-drawing an existing map subject to additional constraints. Examples of the first kind of problem are found in traditional cartography, e.g., the 1569 Mercator projection of the sphere onto 2D Euclidean space. Cartograms provide an example of the second kind of problem, where the goal is to redraw a map so that the geographical areas are proportional to some metric, an idea which dates back to 1934 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). Work in information visualization has produced many ways of representing data, some even adopting the name “map.” Most of these have little visual connection with geographic maps. The map of science [1] uses vertex coloring in a graph drawing to provide an overview of the scientific landscape, based on citations of journal articles. Treemaps [11], squarified treemaps [2], and the more recent newsmaps represent hierarchical information by means of space-filling tilings, allocating area proportional to some metric. Concept maps are diagrams showing relationships among concepts [10]. Somewhat similar are cognitive maps and mind-maps used to represent words or ideas linked to and arranged around a central key word. In self-organizing maps (SOM) [8], an unsupervised learning algorithm places objects on a two-dimensional grid such that similar objects are close to each other. Unlike GMap, SOM creates a “map” by coloring cells of the grid based on a feature value; therefore it

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Figure 9: A map of trade relations between countries.

operates on a discrete grid space without a clear inner boundary between “countries”. Furthermore, the grid tends to fit a rectangular box, 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 [3] use deformed convex hulls to highlight areas of interest in UML diagrams. Collins et al. [4] use “bubblesets,” based on isocontours, to depict multiple relations among a set of objects. Simonetto et al. [12] 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 regions, these works differ from ours in that they create regions that overlap with each other, with the goal of faithfully representing set relationships, while we take the map metaphor seriously, assuming that regions do not overlap and aiming for a cartographic verisimilitude. However, as Figure 5 shows, our approach can also be used for visualizing sets. 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 and the B¨ucherlandes map by Woelfle from the same period. More recent drawings include maps of programming language concepts and online communities. While most such maps are generated in an ad hoc manner by hand and are not strictly based on underlying data, they are often visually appealing. Generating synthetic geography has a large literature, connected to its use in computer games and movies. Most of the work relies

on variations of a fractal model. These techniques could provide additional photo-realism, and may be used in future extension of our work. C ONCLUSION AND F UTURE W ORK We believe that the GMap algorithmic framework, by capitalizing on an ancient and familiar visual metaphor, introduces a significant new style of viewing abstract relational and cluster data that users will find aesthetically appealing and helpful in understanding the data. From informal observation, we have found that people, when faced with a traditional graph drawing and a map of the same data, spend significantly longer time studying the map, and they find non-trivial structural information without any prompting. For example, several viewers of BookLand 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 [6]. While the approach of visualizing relational information with the aid of geographical maps is general, here we showed one particular implementation, where embedding and clustering algorithms are coupled with novel mapping and coloring algorithms. There are specific idiosyncrasies we would like to address. For example, GMap can produce countries that are disconnected. We have proposed ways [5] to use the cluster information to adjust the layout so that the regions of countries are more contiguous, at the expense of some loss of graph information. We are planning further investigation into balancing country connectedness and the preservation of

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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. Finally, our algorithm is efficient and can handle large graphs. As a reference point, all maps in this paper were generated in a few seconds. Mapping a larger graph with 440, 000 vertices took 4 minutes on a typical processor. The resulting maps look best on large, wall-sized posters and display walls. To make such maps more useful for exploration of large data sets on commonly available media, we have developed an interactive interface that can search, zoom and pan easily on the maps (see footnote 1).

[6] E. R. Gansner, Y. F. Hu, S. G. Kobourov, and C. Volinsky. Putting recommendations on the map - visualizing clusters and relations. In Proceedings of the 3rd ACM Conference on Recommender Systems. ACM, 2009. [7] A. Georghiades, P. Belhumeur, and D. Kriegman. From few to many: Illumination cone models for face recognition under variable lighting and pose. IEEE Trans. Pattern Anal. Mach. Intelligence, 23(6):643– 660, 2001. [8] T. Kohonen. Self-Organizing Maps. Springer, 2000. [9] M. E. J. Newman. Modularity and community structure in networks. Proc. Natl. Acad. Sci. USA, 103:8577–8582, 2006. [10] J. D. Novak and A. J. Ca˜nas. The theory underlying concept maps and how to construct them. Technical report, Institute for Human and Machine Cognition, January 2006. [11] B. Shneiderman. Tree visualization with tree-maps: A 2-D spacefilling approach. ACM Transactions on Graphics, 11(1):92–99, 1992. [12] P. Simonetto, D. Auber, and D. Archambault. Fully automatic visualisation of overlapping sets. Computer Graphics Forum, 28:967–974, 2009.

Acknowledgments We would like to thank Stephen North for helpful discussions, and Carlos Scheidegger for help with the image process example. R EFERENCES [1] K. Boyack, R. Klavans, and K. Borner. Mapping the backbone of science. Scientometrics, 64(3):351–374, 2005. [2] M. Bruls, K. Huizing, and J. van Wijk. Squarified treemaps. In Joint 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 Transactions 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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