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Data and Image Models

Maneesh Agrawala

CS 294-10: VisualizationFall 2007

AnnouncementsAuditors, please enroll in the class (1 unit, P/NP)

Requirements: Come to class and participate (online as well)Requirements: Assignment 1a and 1b

Enrollees, class participation requirementsComplete readings before classIn-class discussionPost at least 1 discussion substantive comment/question on wikiwithin a week of each lecture

All, add yourself to participants page on the wiki

Class wikihttp://vis.berkeley.edu/courses/cs294-10-fa07/wiki/

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Assignment 1a: Good and Bad Vis.

Find two visualizations one good and one bad

Use original sourcesJournalsScience magazinesNewspapersTextbooks

Make wiki page Clearly mark as good or badProvide short explanation Be prepared to succinctly describe in class on Wed Sep. 5

Due before class on Sep 5, 2007

Data and Image Models

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The big picture

task

dataphysical type

int, float, etc.abstract type

nominal, ordinal, etc.

domainmetadatasemantics conceptual model

processingalgorithms

mappingvisual encodingvisual metaphor

imagevisual channelretinal variables

[based on slide from Munzner]

Topics

Properties of data or informationProperties of the imageMapping data to images

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Data

Data models vs. Conceptual modelsData models are low level descriptions of the data

Math: Sets with operations on themExample: integers with + and × operators

Conceptual models are mental constructionsInclude semantics and support reasoning

Examples (data vs. conceptual)(1D floats) vs. Temperature(3D vector of floats) vs. Space

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Relational data modelRecords are fixed-length tuplesEach column (attribute) of tuple has a domain (type)Relation is schema and a table of tuplesDatabase is a collection of relations

Example: Digital cameras

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Relational algebra [Codd]

Data transformations (SQL)Selection (SELECT)Projection (WHERE)Sorting (ORDER BY)Aggregation (GROUP BY, SUM, MIN, …)Set operations (UNION, …)Join (INNNER JOIN)

Statistical data modelVariables or measurementsCategories or factors or dimensionsObservations or cases

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Statistical data modelVariables or measurementsCategories or factors or dimensionsObservations or cases

150157158163August

148160158166July

160158161162June

153161158164May

163161159162April

168166163165March

450 mg300 mgPlaceboControlMonth

Blood Pressure Study (4 treatments, 6 months)

Dimensions and measuresIndependent vs. dependent variables

Example: y = f(x,a)Dimensions: Domain(x) × Domain(a)Measures: Range(y)

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Sepal and petal lengths and widths for three species of iris [Fisher 1936].

Format of the data in Appendix 14, pp. 365-366

Chambers, Cleveland, Kleiner, Tukey, Graphical Methods for Data Analysis

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Data cube

Species

Organ

Measure

Petal

Sepal

Length

Width

I. setosa

I. verginica

I. versicolor

Projections summarize data

Multiscale visualization using data cubes [Stolte et al. 02]

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Taxonomy1D (sets and sequences)Temporal2D (maps)3D (shapes)nD (relational)Trees (hierarchies)Networks (graphs)

Are there others?

The eyes have it: A task by data type taxonomy for information visualization [Schneiderman 96]

Types of variables

Physical typesCharacterized by storage formatCharacterized by machine operations

Example: bool, short, int32, float, double, string, …

Abstract typesProvide descriptions of the dataMay be characterized by methods/attributesMay be organized into a hierarchy

Example: plants, animals, metazoans, …

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Nominal, ordinal and quantitativeN - Nominal (labels)

Fruits: Apples, oranges, …

O - OrderedQuality of meat: Grade A, AA, AAA

Q - Interval (Location of zero arbitrary)Dates: Jan, 19, 2006; Location: (LAT 33.98, LONG -118.45)Like a geometric point. Cannot compare directlyOnly differences (i.e. intervals) may be compared

Q - Ratio (zero fixed)Physical measurement: Length, Mass, Temp, …Counts and amountsLike a geometric vector, origin is meaningful

S. S. Stevens, On the theory of scales of measurements, 1946

From data model to data typeData model

32.5, 54.0, -17.3, …floats

Conceptual modelTemperature

Data typeBurned vs. Not burned (N)Hot, warm, cold (O)Continuous range of values (Q)

[based on slide from Munzner]

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Sepal and petal lengths and widths for three species of iris [Fisher 1936].

Q

O

N

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Image

Visual language is a sign system

Images perceived as a set of signs

Sender encodes information in signs

Receiver decodes information from signs

Semiology of Graphics, 1983

Jacques Bertin

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[Bertin, Semiology of Graphics, 1983]

Information in position

1. A, B, C are distinguishable 2. B is between A and C. 3. BC is twice as long as AB.

∴ Encode quantitative variables (Q)A

B

C

"Resemblance, order and proportional are the three signfields in graphics.” - Bertin

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Information in color and valueValue is perceived as ordered

∴ Encode ordinal variables (O)

∴ Encode continuous variables (Q) [not as well]

Hue is normally perceived as unordered∴ Encode nominal variables (N) using color

PositionSizeValueTextureColorOrientationShape

Note: Bertin does not consider 3D or timeNote: Card and Mackinlay extend the number of vars.

Visual variables

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Bertins’ “Levels of Organization”

N Nominal O OrderedQ Quantitative

N O Q

N O Q

N O Q

N O

N

N

N

Position

Size

Value

Texture

Color

Orientation

Shape

Note: Bertin actually breaks visual variables down into differentiating (≠) and associating (≡)

Note: Q < O < N

Encoding rules

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Univariate data1

CBA

factors

variable

A B C D

Univariate data

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5

3

1

0 20

Mean

low highMiddle 50%

Tukey box plot

1CBA

factors

variable

A B C D

A B C D E

[based on slide from Stasko]

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Bivariate data

Scatter plot is common

1CBA

2

A

B

C

D

E

F

[based on slide from Stasko]

Trivariate data

3D scatter plot is possible

1CBA

32

A

B

C

D

E

F

A

B

C

D

E

F

G

[based on slide from Stasko]

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Three variablesTwo variables [x,y] can map to points

Scatterplots, maps, …

Third variable [z] must use …Color, size, shape, …

Large design space (visual metaphors)

[Bertin, Graphics and Graphic Info. Processing, 1981]

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Multidimensional data

76543

1CBA

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2

How many variables can be depicted in an image?

Multidimensional data

“With up to three rows, a data table can be constructed directly as a single image …However, an image has only three dimensions. And this barrier is impassible.”

Bertin

76543

1CBA

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2

How many variables can be depicted in an image?

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Deconstructions

Stock chart from the late 90s

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Stock chart from the late 90s

x-axis: time (Q)y-axis: price (Q)

Playfair 1786

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Playfair 1786

x-axis: year (Q)y-axis: currency (Q)color: imports/exports (N, O)

Wattenberg 1998

http://www.smartmoney.com/marketmap/