```Foundations of
Visual Analytics
Pat Hanrahan
Director, RVAC
Stanford University
Analytical Reasoning
Facilitated by
Interactive Visualization
Why is a Picture
(Sometimes) Worth
10,000 Words
Let’s Solve a Problem:
Number Scrabble
Herb Simon
Number Scrabble
Goal: Pick three numbers that sum to 15
Number Scrabble
Goal: Pick three numbers that sum to 15
A:
B:
Number Scrabble
Goal: Pick three numbers that sum to 15
A:
B:
Number Scrabble
Goal: Pick three numbers that sum to 15
A:
B:
Number Scrabble
Goal: Pick three numbers that sum to 15
A:
B:
Number Scrabble
Goal: Pick three numbers that sum to 15
A:
B:
Number Scrabble
Goal: Pick three numbers that sum to 15
A:
B:
?
Tic-Tac-Toe
Tic-Tac-Toe
X
Tic-Tac-Toe
X
O
Tic-Tac-Toe
X
O
X
Tic-Tac-Toe
X
O
O
X
Tic-Tac-Toe
X
O
X
O
X
Tic-Tac-Toe
X
O
X
X
O
O
Problem Isomorph
4
3
8
9
5
1
2
7
6
Magic Square: All rows, columns, diagonals sum to 15
Switching to a Visual Representation
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9
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6
Switching to a Visual Representation
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6
Switching to a Visual Representation
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3
8
9
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6
Switching to a Visual Representation
4
3
8
9
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6
Switching to a Visual Representation
4
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8
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?
Switching to a Visual Representation
4
3
8
9
5
1
2
7
6
Why is a Picture Worth 10,000 Words?
Reduce search time

Pre-attentive (constant-time) search process

Spatially-indexed patterns store the “facts”

Working memory is limited

Store information in the diagram
Allow perceptual inference

Map inference to pattern finding
Larkin and Simon, Why is a diagram (sometimes) worth 10,000
words, Cognitive Science, 1987
The Value of Visualization
It is possible to improve human performance by 100:1

Faster solution

Fewer errors

Better comprehension
The best representation depends on the problem
Number Representations
Norman and Zhang
Number Representations
Counting – Tallying
XXIII + XII = XXXIIIII = XXXV
Multiplication – Arabic number systems
Zhang and Norman, The Representations of Numbers,
Cognition, 57, 271-295, 1996
Distributed Cognition
External (E) vs. Internal (I) process
Roman
Arabic
1.
Separate power & base
I
E
2.
Get base value
E
I
3.
Multiply base values
I
I
4.
Get power values
I
E
5.
I
E
6.
Combine base & power
I
E
7.
I
E
Arabic more efficient than Roman
Long-Hand Multiplication
34
x 72
68
238
2448
From “Introduction to Information Visualization,”
Card, Schneiderman, Mackinlay
Power of Representations

The representational effect
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
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Different representations have different coststructures / ”running” times
Distributed cognition

Internal representations (mental models)

External representations (cognitive artifacts)
Representations 101

Representations are not the real thing

Manipulate symbols to perform useful work
Modeling and Simulation
Simulation for computer graphics is sophisticated

Diversity of phenomenon

Complexity of the environment

Robustness

Range of models: fast to accurate
Lots of breakthroughs: one small example is GPUs
which may become the major platform for scientific
computation
Mathematics of Visual Analysis
MSRI, Berkeley, CA, Oct 16-17, 2006
Organizers: P. Hanrahan, W. Cleveland, S. Harabagliu,
P. Jones, L. Wilkinson
Participants: J. Arvo, A. Braverman, J. Byrnes, E.
Candes, D. Carr, S. Chan, N. Chinchor, N. Coehlo, V.
de Silva, L. Edlefsen, R. Gentleman, G. Lebanon, J.
Lewis, J. Mackinlay, M. Mahoney, R. May, N.
Meinshausen, F. Meyer, M. Muthukrishnan, D.
Nolan, J-M. Pomarede, C. Posse, E. Purdom, D.
Purdy, L. Rosenblum, N. Saito, M. Sips, D. W.
Temple Lang, J. Thomas, D. Vainsencher, A.
Vasilescu, S. Venkatasubramanian, Y. Wang, C.
Wickham, R. Wong Kew
Supporting Interaction
Panelists: William Cleveland, Robert Gentleman, Muthu
Muthukrishnan, Suresh Venkatasubramanian,
Emmanuel Candez

Fast algorithms: streaming and approximate
algorithms, compressed sensing, randomized
numerical linear algebra, …

Fast systems: map-reduce, column stores,
beyond R, …
Finding Patterns
Panelists: Peter Jones, Vin de Silva, Francois Meyer,
Naoki Saito, Michael Mahoney

How to represent patterns?

Data/dimensional reduction vs. transformation to
meaningful form?

Are humans required to build good models? How

When are computers good pattern finders? When
are people good pattern finders?
Computation Steering
vs.
Interactive Simulation
Integrating Heterogenous Data
Panelists: Sanda Harabagliu, John Byrnes, Jean-Michel
Pomeranz, Christian Posse, Guy Lebanon

Many important datatypes: text and language,
audio, video, image, sensors, logs, transactions,
nD relations, …

How to fuse into common semantic
representation?

Beyond the desktop to new representations of
information spaces: vispedia, jigsaw, …
Smart Visual Analysis
Panelists: Leland Wilkinson, Jock Mackinlay, Jim Arvo,
Amy Braverman, Dan Carr

Automatic graphical presentation and
summarization; guided analysis

How do people reason about uncertainty?
Summary
Visual analytics merges

Cognitive psychology

Mathematics and computation (algm, stat, nlp)

Interactive visualization techniques
Need to rethink how these capabilities are combined
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