Information visualization: representation

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Information visualization lecture 3

representation

Katrien Verbert Department of Computer Science

Faculty of Science Vrije Universiteit Brussel

[email protected]

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Anscombe's quartet

Property Value

Mean of x 9

Variance of x 11

Mean of y 7.50

Variance of y 4.122 or 4.127

Correla8on between x and y 0.816

Linear regression line for each data set

y = 3.00 + 0.500x

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Ben Shneiderman hIp://www.youtube.com/watch?v=og7bzN0DhpI

(watch 12:20 – 15:49 )

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Anscombe's quartet

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Overview

•  Encoding of value –  Univariate data –  Bivariate data –  Trivariate data –  Hypervariate data

•  Encoding of relation –  Lines – Maps and diagrams

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Part of this car purchase interface identifies a relation

Relations

10 - 12 12 - 14 16 - 18£kPrice

MPG 30 35 40

12 - 14

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Interaction to identify a doctor highlights the hospital beds under his or her care, and vice versa: an example of brushing

Relations

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Overview

•  Encoding of value – Univariate data –  Bivariate data –  Trivariate data –  Hypervariate data


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A single number

The original aircraX al8meter, responsible for many accidents

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Representation of the view of an altimeter

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An altimeter representation easily assumed to be the same as shown on the previous slide

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Change blindness

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Change blindness

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Change blindness

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2000

1600

2200

182000

stop1200

1400

A modern aircraft altimeter

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Single number: second example

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Each dot represents the price of a car

A collection of numbers

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60

50

40

30

20

10

Price (£K)

Box plot

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Box plot

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1 –20 20–30 30–40 40–50 50–60

Price (£K)

2

4

6

8

1 –20 20–30 30–40 40–50 50–60

Price (£K)

2

4

6

8

histogram

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10 - 12 12 - 14 16 - 18£kPrice

bargram

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Nissan Ford Ferrari MG Cadillac

Bargram of categorical data

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Monday Tuesday Wednesday Thursday Friday

£100k

£200k

histogram of ordinal data

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Overview



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Anscombe's quartet

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Scatterplot

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Time series

Android Ac8va8ons per day, measured on the first of each month

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Time series

Android Ac8va8ons per day, measured on the first of each month

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Stock data

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Four views of a 8me-‐series query tool. (a) An overview of the en8re data set; (b) a single 8me-‐box limits the display to items with prices between $70 an $250 during days 1 to 4; (c) an addi8onal constraint selects items with prices between $70 and $95 during days 7 to 12; (d) yet another constraint concerns prices between $90 and $115 for days 15 to 18 Source: Courtesy of Harry Hochheiser

(a) (b)

(c) (d)

time series

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Overview of the entire data set

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time-box limits the display to items with prices between $70 an $250 during days 1 to 4

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additional constraint selects items with prices between $70 and $95 during days 7 to 12

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yet another constraint concerns prices between $90 and $115 for days 15 to 18

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Student activity meter

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Representa8on of the level of ozone concentra8on above Los Angeles over a period of ten years

Time series

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Price Number ofbedrooms

(a)

(b)

(c)

(d)

imposed limits

imposed limits

Linked histogram

the price and number of bedrooms associated with a collection of houses are represented by separate histograms a single house is represented once on each histogram;

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Linked histogram

upper and lower limits placed on Price define a subset of houses which are coded red on both histograms

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Linked histogram

Interpretation is enhanced by ‘ranging down’ the colour-coded houses, especially if exploration involves the dynamic alteration of limits

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60

50

20

10

Price (£K)

40

30

40

3 0

35

Ford

Nissan

VW Merc

Jag

Jag

Ford

SEAT

Semantic zoom reveals data about a second attribute

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A representa8on of Australia and New Zealand on a conven8onal map

Qualitative understanding of data

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A representa8on of Australia and New Zealand indica8ng that some aIribute of New Zealand is ten 8mes its value for Australia

Australia

NewZealand

Qualitative understanding of data

In the State of the World Atlas, magnifica8on encoding is used to give a first impression of popula8on densi8es. Note the reduced ‘size’ of Canada and Australia when compared with a conven8onal map Source: Smith (1999)

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Overview



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Price

Time

BedroomsAB

C

D

Does house A cost more than C?

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A

B C

D

Price

Bedrooms

Scatterplot matrix

Interac8on can offer solu8on A projec8on of the data, allowing comparison of Price and Bedrooms values

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Scatterplot matrix

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The highligh8ng of houses in one plane is brushed into the remaining planes

Cognitive overload? Interaction solution

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A representa8on of reported product failure, based on month of produc8on (MOP) of the failed product, and total months in service (MIS) before the fault occurred. The radius of each circle indicates the number of faults reported for a given MOP and MIS

MonthofProduction(MOP)

2 4 6 8 10 12Months in service (MIS)

July ʻ97

Sept ̒ 97

Nov ʻ97

Jan ʻ98

Mar ʻ98

May ʻ98

Trivariate data

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Circles indicate the extent of the effect of a component on some property of the circuit, and change in size as the frequency cycles up and down the range from bass to treble

Treble

Bass

Trivariate data

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A representa8on of the popula8on of major ci8es in England, Wales and Scotland. Circle area is propor8onal to popula8on

Maps to represent trivariate data

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Circles change in size as the decades are animated, so that sudden changes in popula8on ‘pop out’

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

Also non-static representations of data

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hIp://www.youtube.com/watch?v=hVimVzgtD6w

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Overview

•  Encoding of value –  Univariate data –  Bivariate data –  Trivariate data – Hypervariate data


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A simple scaIerplot represen8ng the price and number of bedrooms associated with two houses

A

B

Price

Numberofbedrooms

Simple scatterplot of bivariate data

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An alterna8ve representa8on to the scaIerplot in which the two aIribute scales are presented in parallel, thereby requiring two points to represent each house

Price Numberofbedrooms

06/03/14 pag. 57 To avoid ambiguity the pair of points represen8ng a house are joined and labelled

Price Numberofbedrooms

A

BLabels

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A parallel coordinate plot for six objects, each characterised by seven aIributes. The trade-‐off between A and B, and the correla8on between B and C, are immediately apparent. The trade-‐off between B and E, and the correla8on between C and G, are not

A B C D E F G

Parallel coordinates

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A parallel coordinate plot representa8on of a collec8on of cars, in which a range of the aIribute Year has been selected to cause all those cars manufactured during that period to be highlighted Source: Harri Siirtola

Parallel coordinates

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Student activity meter

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Sport

Literature

Mathematics

Physics

History

Geography

Art

Chemistry

Star plot

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Bob’s performance Tony’s performance

Star plot for comparison

A scaIerplot enhanced by addi8onal and selec8ve encoding, allowing the selec8on of a film on the basis of type, dura8on, year of produc8on and other aIributes

The automa8c display of addi8onal detail following the selec8on of narrower limits on years of produc8on and film length

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A histogram represen8ng the prices of a collec8on of houses. The contribu8on of one house is shown in yellow

Histogram

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Limits on Price identify a subset of houses, coded green

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Houses defined by the limits on Price are coded green in other aIribute histograms

Linked histograms

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Green coding applies only to houses which sa8sfy all aIribute limits. Houses which fail one limit are coded black, so if a black house is posi8oned outside a limit it will turn green if the the limit is extended to include it

Linked histograms

06/03/14 pag. 69 Even if no houses sa8sfy all aIribute limits, black houses, which fail only one limit, provide guidance as to the effect of relaxing limits

Linked histograms

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An AIribute Explorer representa8on of three dimensions of communica8on data captured during an emergency services exercise, suppor8ng interac8ve explora8on by an analyst

Linked histograms

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Linked histogram

Details in lecture 6: case studies

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Survived Age GenderClass

1st 2nd 3rd Crew

NoYesNoYesNoYesNoYes

Adult

Child

Adult

Child

Male

Female

118 57 0 5 4140 0 1

154 14 0 11 13 80 0 13

387 75 35 13 89 76 17 14

670192 0 0 3 20 0 0

Details of the Titanic disaster

2201 885706285325

First Second Third Crew

Female

Male

First Second Third Crew

Female

Male

Adult

First Second Third CrewChild

Survived

Died

Survived

Died

(a) (b)

(c)(d)

[Friendly, 2000]

Steps to create mosaic plot

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Mosaic plot

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Friendly’s webslte

hIp://www.datavis.ca/gallery/

06/03/14 pag. 76 Chernoff Faces allow aIribute values to be encoded in the features of cartoon faces (Chernoff 1973)

Icons

Michael Porath

Example

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Some criticism

No evidence for pre-attentive nature [Morris et al. 1999]

Src: hIp://joshualedwell.typepad.com/usability_blog/files/final_vizualiza8on.pdf

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Multidimensional icons representing eight attributes of a dwelling

house£400,000garagecentral heatingfour bedroomsgood repairlarge gardenVictoria 15 mins

flat£300,000no garagecentral heatingtwo bedroomspoor repairsmall gardenVictoria 20 mins

houseboat£200,000no garageno central heatingthree bedroomsgood repairno gardenVictoria 15 mins

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Representa8ons suppor8ve of object visibility

Object visibility: each object is represented as a single and coherent visual entity

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Infocanvas

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Attribute correlation

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Object correlation

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Overview



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Relation

Relation (n): a logical or natural association between two or more things; relevance of one to another; connection.

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John Smith

MaryRobinson

A simple symbol indicates the relationship of marriage

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Social networks

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John Stingy Bank

1930 Bentley

Lines indicate relationship

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YX1

X2

X3

Arrows indicate unique unilateral functional relations

y=f(x)

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Colour indicates a relation

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The incidence of warfare in early Anglo-‐Saxon England between 550 AD and 700 AD. Red indicates the aggressor, green the aIacked

PictsNorthumbriaMerciaWest SaxonSouth SaxonIsle of WightKentBritons

Years AD

550 600 650 700

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Insight into even a short list of telephone calls (a) is enhanced by their node-‐link representa8on (b), especially if disconnected subsets can be iden8fied (c)

(a) (b) (c)

Originator Receiver

ACIBFGIBKGKCD

HLMEHIBMBBEJC

AB

C

D

E

F

GI

J

K

L

M

H

B

EK

G I

M

A H

FJ C

L D

Lines

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A representa8on of mortgage ac8vity: (a) lenders, proper8es (houses), buyers, etc. are represented by small radial segments of an annulus as shown in (b), and their rela8onships denoted by straight lines

(a)

(b)

Useful?

A threshold has been imposed to suppress the display of normal behaviour. As a result, unusual behaviour is revealed by the paIerns formed by the lines

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hIp://seekshreyas.com/beerviz/

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hIp://visualiza8on.geblogs.com/visualiza8on/network/

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Chord diagram

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An ‘association’ style chart depicting the African bombings

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Source: Courtesy i2 Ltd.

Part of a ‘timeline’ style chart depicting the Kennedy assassination

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Sankey diagram

hIp://bost.ocks.org/mike/sankey/

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Remember this one?

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Flow map diagram

Verbeek, K., Buchin, K., & Speckmann, B. (2011). Flow map layout via spiral trees. IEEE transac8ons on visualiza8on and computer graphics, 17(12), 2536-‐2544.

Migration from Colorado, migration from Norway and Latvia, whisky exports from Scotland.

06/03/14 pag. 107 Harry Beck’s original London Underground map Source: © Transport for London

Most familiar use of lines?

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Source: © Transport for London

The Underground map in use prior to the introduction of Harry Beck’s map

Differences? Easier to use?

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Journey time?

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hIp://www.london-‐tubemap.com/journey_8mes.php

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hIp://www.tom-‐carden.co.uk/p5/tube_map_travel_8mes/applet/

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The social choices of fourth grade students (aXer Moreno, 1934)

Social networks

(a) Social choices among department store employees (b) Social choices among department store employees, with marital status encoded (c) Social choices among department store employees, with age range encoded (blue <30, 30 <yellow <40, red >40) Source: L.C. Freeman

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Overview



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Facili8es offered by eight hotels

ABCDEFG

Swimming Pool

GolfCourse Restaurant

Hotels

Maps and diagrams

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Swimming pool

Golf

Restaurant

A

B

C

D

E

F

G

Venn diagram

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Figure 3.83

Swimming pool Golf

Restaurant

A Venn diagram representation of the attributes of 24 hotels

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The development leading from a Venn diagram to an InfoCrystal. The InfoCrystal illustrated allows visual queries to be made concerning price, garden size and number of bedrooms. The asterisk represents houses sa8sfying criteria on Price and garden size but not number of bedrooms

Price

Garden size

Number of bedrooms

*

InfoCrystal

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Swimming Pool

45

8

0

2

41

Golf

Restaurant

An Infocrystal representation of the hotel data

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Cluster map

06/03/14 pag. 121 A cluster map representa8on of 24 hotels, each described by four aIributes Source: Courtesy ChrisLaan Fluit, Aduna

Cluster map

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TalkExplorer

Details in lecture 6: case studies

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designated root node

parent of A

sibling of A

child of A

leaf nodes

Aleaf nodes

Tree representations

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Tree visualizations

hIp://www.informa8k.uni-‐koeln.de/ls_juenger/research/vbctool/

Problems?

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(a) A tree (b) The corresponding cone tree

(a)

(b)

Alternative: cone trees

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Cam tree: horizontal orientation of cone tree

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The Tree

The Tree Map

Forma8on of the Tree Map

Construction of a Tree Map

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The ‘slice-‐and-‐dice’ construc8on of a Tree Map to obtain leaf nodes represented by rectangles more suited to the inclusion of text and images

Tree

Tree Map

Slide and dice construction

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Tree map display of an author’s collection of reports

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Map of the market hIp://www.marketwatch.com/tools/stockresearch/marketmap

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hIp://www.hivegroup.com/solu8ons/demos/usda.html

hIp://www.ny8mes.com/interac8ve/2008/05/03/business/20080403_SPENDING_GRAPHIC.html?_r=0

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hIp://www.youtube.com/watch?v=og7bzN0DhpI Watch 31:11 – 35:35

Ben Sheiderman on tree maps

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Tree map pros and cons

Pros?

Cons?

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Tree map pros and cons

Pros

Color + Area (2 attributes)

Cons

Hierarchy/Structure hard to convey

aspect ratios

Slide adapted from Michael Porath

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Aspect ratios

Which one is bigger?


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Aspect ratios



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Aspect ratios


make the segments more square!


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Layout Strategies / Algorithms

hIp://hcil2.cs.umd.edu/trs/2001-‐06/2001-‐06.html

Cluster Squarified StripTreemap

Pivot By Middle Pivot By Size


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Sunburst

hIp://bl.ocks.org/mbostock/4063423

hIp://www.th

eguardian.com/new

s/datablog/2012/oct/05/beatle

s-‐charts-‐in

fographics

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hIp://hci.stanford.edu/jheer/files/zoo/

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A sketch illustra8on of the hyperbolic browser representa8on of a tree. The further away a node is from the root node, the closer it is to its superordinate node, and the area it occupies decreases

Hyperbolic tree

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(a)  The repor8ng structure of the employees of a company. (b) One employee of interest,

Rachel Anderson, has been moved towards the centre, revealing her subordinates

Nodes can typically be moved into center position

Representa8on of the Library of Congress by the hyperbolic browser

hIp://ph

ilogb.gith

ub.io/jit/sta8

c/v20/Jit/

Exam

ples/Hypertree/example1.htm

l

hIp://www.autod

eskresearch.com/projects/orgorgchart

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Readings

Chapter 3

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Questions?

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References

•  Christopher J. Morris, David S. Ebert, Penny Rheingans, An Experimental Analysis of the Pre-Attentiveness of Features in Chernoff Faces, Proceedings Applied Imagery Pattern Recognition, pp. 12–17, 1999.

•  Friendly, Michael. Visualizing categorical data. SAS Institute, 2000.

•  Chernoff, H. (1973). The use of faces to represent points in k-dimensional space graphically. Journal of the American Statistical Association, 68(342), 361-368.

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project

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Team project milestones

1.  Form teams 2.  Project proposal 3.  Intermediate presentation 4.  Final presentation 5.  Short report

due 27 Feb.

due 13 March

due 3 April

22 May

due 29 May

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Project proposal

1 page description of your intended project: –  mo8va8on –  which datasets you will use –  current status. If available, first designs. –  problems/ques8ons

due 13 March If you want earlier feedback, send us your proposal earlier ;-)

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Data collection

•  https://docs.google.com/forms/d/1gHwVWHZLzWdSz1F37jA1Gungrl56bT215M6FYW3YqGY/viewform Or

•  bit.ly/N6JTyD

Anonymous! Choose your own ID.

•  Please report your data ;-)

Education

Information visualization: representation