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Foundations of Visual Analytics Pat Hanrahan Director, RVAC Stanford University

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Analytical Reasoning Facilitated by Interactive Visualization

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Why is a Picture (Sometimes) Worth 10,000 Words

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Let’s Solve a Problem: Number Scrabble Herb Simon

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Number Scrabble Goal: Pick three numbers that sum to 15

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Number Scrabble Goal: Pick three numbers that sum to 15 A: B:

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Number Scrabble Goal: Pick three numbers that sum to 15 A: B:

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Number Scrabble Goal: Pick three numbers that sum to 15 A: B:

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Number Scrabble Goal: Pick three numbers that sum to 15 A: B:

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Number Scrabble Goal: Pick three numbers that sum to 15 A: B:

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Number Scrabble Goal: Pick three numbers that sum to 15 A: B: ?

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Tic-Tac-Toe

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X

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X O

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X O X

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X O XO

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X O XO X

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X O XO X O

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Problem Isomorph 348 591 726 Magic Square: All rows, columns, diagonals sum to 15

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Switching to a Visual Representation 8 591 726 34

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8 591 726 34

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348 591 726

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348 591 726

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348 591 726 ?

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348 591 726

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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

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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

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Number Representations Norman and Zhang

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Number Representations Counting – Tallying Adding – Roman numerals Multiplication – Arabic number systems XXIII + XII = XXXIIIII = XXXV

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Zhang and Norman, The Representations of Numbers, Cognition, 57, 271-295, 1996

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Distributed Cognition 1. Separate power & baseIE 2. Get base valueEI 3. Multiply base valuesII 4. Get power valuesIE 5. Add power valuesIE 6. Combine base & powerIE 7. Add resultsIE RomanArabic Arabic more efficient than Roman External (E) vs. Internal (I) process

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Long-Hand Multiplication 34 x 72 68 238 2448 From “Introduction to Information Visualization,” Card, Schneiderman, Mackinlay

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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

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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

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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

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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, …

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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?

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Computation Steering vs. Interactive Simulation

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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, …

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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?

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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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