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

X O

Tic-Tac-Toe

X

O

X O

X

Tic-Tac-Toe

X

O

X O

X

O

Problem Isomorph

34 8

59 1

72 6

Magic Square: All rows, columns, diagonals sum to 15

Switching to a Visual Representation

8

59 1

72 6

34

Switching to a Visual Representation

8

59 1

72 6

34

Switching to a Visual Representation

34 8

59 1

72 6

Switching to a Visual Representation

34 8

59 1

72 6

Switching to a Visual Representation

34 8

59 1

72 6

?

Switching to a Visual Representation

34 8

59 1

72 6

Why is a Picture Worth 10,000 Words?Reduce search time

Pre-attentive (constant-time) search process

Spatially-indexed patterns store the “facts”

Reduce memory load

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

Adding – Roman numerals

Multiplication – Arabic number systems

XXIII + XII = XXXIIIII = XXXV

Zhang and Norman, The Representations of Numbers,

Cognition, 57, 271-295, 1996

Distributed Cognition

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. Add power values I E

6. Combine base & power I E

7. Add results I E

Roman Arabic

Arabic more efficient than Roman

External (E) vs. Internal (I) process

Long-Hand Multiplication

34x 72

68238

2448

From “Introduction to Information Visualization,”

Card, Schneiderman, Mackinlay

Power of Representations

The representational effect

Different representations have different cost-structures / ”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 is domain knowledge added?

When are computers good pattern finders? When are people good pattern finders?

Computation Steeringvs.

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