This document contains summaries of various techniques for visually representing data with 1, 2, 3 or more variables. It begins with examples of encoding univariate data using techniques like bar graphs and histograms. It then discusses ways to encode bivariate data, such as scatterplots and linked histograms. Finally, it explores some options for visually encoding trivariate and higher-dimensional data, including bubble plots and maps. The document serves as an overview of fundamental data visualization concepts and techniques.
Patient Counselling. Definition of patient counseling; steps involved in pati...
Information visualization: representation
1. Information visualization lecture 3
representation
Katrien Verbert
Department of Computer Science
Faculty of Science
Vrije Universiteit Brussel
katrien.verbert@vub.ac.be
06/03/14
pag. 1
2. 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
y
=
3.00
+
0.500x
for
each
data
set
06/03/14
pag. 2
5. Overview
• Encoding of value
– Univariate data
– Bivariate data
– Trivariate data
– Hypervariate data
• Encoding of relation
– Lines
– Maps and diagrams
06/03/14
pag. 5
6. Relations
30
MPG
Price £k
10 - 12
35
12 14
12 -- 14
40
16 - 18
Part of this car purchase interface identifies a relation
06/03/14
pag. 6
7. Relations
Interaction to identify a doctor highlights the hospital beds under his or her
care, and vice versa: an example of brushing
06/03/14
pag. 7
8. Overview
• Encoding of value
– Univariate data
– Bivariate data
– Trivariate data
– Hypervariate data
• Encoding of relation
– Lines
– Maps and diagrams
06/03/14
pag. 8
9. A single number
The
original
aircraX
al8meter,
responsible
for
many
accidents
06/03/14
pag. 9
23. histogram of ordinal data
£200k
£100k
Monday
Tuesday
Wednesday
Thursday
Friday
06/03/14
pag. 23
24. Overview
• Encoding of value
– Univariate data
– Bivariate data
– Trivariate data
– Hypervariate data
• Encoding of relation
– Lines
– Maps and diagrams
06/03/14
pag. 24
30. time series
(a)
(b)
(c)
(d)
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
pag. 30
Source:
Courtesy
of
Harry
Hochheiser
06/03/14
36. Time series
Representa8on
of
the
level
of
ozone
concentra8on
above
Los
Angeles
over
a
period
of
ten
years
06/03/14
pag. 36
37. Linked histogram
(a)
(b)
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;
06/03/14
pag. 37
38. Linked histogram
upper and lower
limits placed on
Price define a subset
of houses which are
coded red on both
histograms
06/03/14
pag. 38
40. Semantic zoom reveals data about a
second attribute
60
50
Price
(£K)
40
Ford
Nissan
VW
40
35
Merc
Jag
Jag
30
3
0
Ford
SEAT
20
10
06/03/14
pag. 40
41. Qualitative understanding of data
A
representa8on
of
Australia
and
New
Zealand
on
a
conven8onal
map
06/03/14
pag. 41
42. Qualitative understanding of data
Australia
New
Zealand
A
representa8on
of
Australia
and
New
Zealand
indica8ng
that
some
aIribute
of
New
pag. 42
Zealand
is
ten
8mes
its
value
for
Australia
06/03/14
43. 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)
44. Overview
• Encoding of value
– Univariate data
– Bivariate data
– Trivariate data
– Hypervariate data
• Encoding of relation
– Lines
– Maps and diagrams
06/03/14
pag. 44
45. Does house A cost more than C?
D
Price
C
B
Bedrooms
A
Time
06/03/14
pag. 45
48. Cognitive overload? Interaction solution
The
highligh8ng
of
houses
in
one
plane
is
brushed
into
the
remaining
planes
06/03/14
pag. 48
49. Trivariate data
July ʻ97
Sept ʻ97
Nov ʻ97
Month
Jan ʻ98
of
Production
(MOP)
Mar ʻ98
May ʻ98
2
4
6
8
10
Months in service (MIS)
12
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
pag. 49
06/03/14
indicates
the
number
of
faults
reported
for
a
given
MOP
and
MIS
50. Trivariate data
Treble
Bass
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
06/03/14 pag. 50
51. Maps to represent trivariate data
A
representa8on
of
the
popula8on
of
major
ci8es
in
England,
Wales
and
Scotland.
Circle
area
is
propor8onal
to
popula8on
pag. 51
06/03/14
52. Also non-static representations of data
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Circles
change
in
size
as
the
decades
are
animated,
so
that
sudden
changes
in
popula8on
‘pop
out’
06/03/14
pag. 52
54. Overview
• Encoding of value
– Univariate data
– Bivariate data
– Trivariate data
– Hypervariate data
• Encoding of relation
– Lines
– Maps and diagrams
06/03/14
pag. 54
55. Simple scatterplot of bivariate data
Number
of
bedrooms
A
B
Price
A
simple
scaIerplot
represen8ng
the
price
and
number
of
bedrooms
associated
with
two
houses
06/03/14
pag. 55
58. Parallel coordinates
A
B
C
D
E
F
G
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
pag. 58
06/03/14
between
B
and
E,
and
the
correla8on
between
C
and
G,
are
not
59. Parallel coordinates
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
pag. 59
Source:
Harri
Siirtola
06/03/14
62. Star plot for comparison
Bob’s
performance
Tony’s
performance
06/03/14
pag. 62
63. 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
64. The
automa8c
display
of
addi8onal
detail
following
the
selec8on
of
narrower
limits
on
years
of
produc8on
and
film
length
65. Histogram
A
histogram
represen8ng
the
prices
of
a
collec8on
of
houses.
The
contribu8on
of
one
house
is
pag. 65
06/03/14
shown
in
yellow
66. Limits on Price identify a subset of
houses, coded green
06/03/14
pag. 66
68. Linked histograms
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
pag. 68
06/03/14
green
if
the
the
limit
is
extended
to
include
it
69. Linked histograms
Even
if
no
houses
sa8sfy
all
aIribute
limits,
black
houses,
which
fail
only
one
limit,
provide
pag. 69
06/03/14
guidance
as
to
the
effect
of
relaxing
limits
70. Linked histograms
An
AIribute
Explorer
representa8on
of
three
dimensions
of
communica8on
data
captured
during
pag. 70
an
emergency
services
exercise,
suppor8ng
interac8ve
explora8on
by
an
analyst
06/03/14
72. Details of the Titanic disaster
Class
Survived
No
Yes
No
Yes
No
Yes
No
Yes
Age
Gender
Adult
Male
Child
Adult
Child
Female
1st
2nd
3rd
Crew
118
57
0
5
4
140
0
1
154
14
0
11
13
80
0
13
387
75
35
13
89
76
17
14
670
192
0
0
3
20
0
0
06/03/14
pag. 72
73. Steps
to
create
mosaic
plot
325 285
706
885
First Second
2201
Third
Crew
(a)
(b)
Survived
Female
Female
Died
Survived
Male
Male
Died
Adult
[Friendly,
2000]
Child
First Second
Third
(d)
Crew
First Second
Third
(c)
Crew
80. Some criticism
No evidence for pre-attentive nature
[Morris et al. 1999]
Src:
hIp://joshualedwell.typepad.com/usability_blog/files/final_vizualiza8on.pdf
06/03/14
pag. 80
81. Multidimensional icons representing eight
attributes of a dwelling
house
£400,000
garage
central heating
four bedrooms
good repair
large garden
Victoria 15 mins
flat
£300,000
no garage
central heating
two bedrooms
poor repair
small garden
Victoria 20 mins
houseboat
£200,000
no garage
no central heating
three bedrooms
good repair
no garden
Victoria 15 mins
06/03/14
pag. 81
82. Object visibility: each object is represented
as a single and coherent visual entity
Representa8ons
suppor8ve
of
object
visibility
06/03/14
pag. 82
87. Overview
• Encoding of value
– Univariate data
– Bivariate data
– Trivariate data
– Hypervariate data
• Encoding of relation
– Lines
– Maps and diagrams
06/03/14
pag. 87
88. Relation
Relation (n): a logical or natural association between two or
more things; relevance of one to another; connection.
06/03/14
pag. 88
89. A simple symbol indicates the relationship
of marriage
John
Smith
Mary
Robinson
06/03/14
pag. 89
94. Picts
Northumbria
Mercia
West Saxon
South Saxon
Isle of Wight
Kent
Britons
550
600
650
700
Years AD
The
incidence
of
warfare
in
early
Anglo-‐Saxon
England
between
550
AD
and
700
AD.
Red
indicates
the
aggressor,
green
the
aIacked
06/03/14
pag. 94
96. Useful?
(b)
(a)
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
06/03/14
pag. 96
97. 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
106. Flow map diagram
Migration from Colorado, migration from Norway and Latvia, whisky exports from Scotland.
Verbeek,
K.,
Buchin,
K.,
&
Speckmann,
B.
(2011).
Flow
map
layout
via
spiral
trees.
IEEE
06/03/14
transac8ons
on
visualiza8on
and
computer
graphics,
17(12),
2536-‐2544.
pag. 106
112. Social networks
The
social
choices
of
fourth
grade
students
(aXer
Moreno,
1934)
06/03/14
pag. 112
113. (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
114. Overview
• Encoding of value
– Univariate data
– Bivariate data
– Trivariate data
– Hypervariate data
• Encoding of relation
– Lines
– Maps and diagrams
06/03/14
pag. 114
117. A Venn diagram representation of the
attributes of 24 hotels
Swimming
pool
Figure
3.83
Golf
Restaurant
06/03/14
pag. 117
118. InfoCrystal
Price
*
Number of
bedrooms
Garden
size
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
06/03/14 pag. 118
not
number
of
bedrooms
127. Construction of a Tree Map
The
Tree
Forma8on
of
the
Tree
Map
The
Tree
Map
06/03/14
pag. 127
128. Slide and dice construction
Tree
Tree Map
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
06/03/14 pag. 128
129. Tree map display of an author’s collection
of reports
Source:
Courtesy
of
Ben
Shneiderman
06/03/14
pag. 129
130. Map of the market
hIp://www.marketwatch.com/tools/stockresearch/marketmap
06/03/14
pag. 130
135. Tree map
pros and cons
Pros
Cons
Color + Area
(2 attributes)
Hierarchy/Structure
hard to convey
aspect ratios
Slide
adapted
from
Michael
Porath
06/03/14
pag. 135
143. Hyperbolic tree
A
sketch
illustra8on
of
the
hyperbolic
browser
representa8on
of
a
tree.
The
further
away
a
node
is
from
the
06/03/14 pag. 143
root
node,
the
closer
it
is
to
its
superordinate
node,
and
the
area
it
occupies
decreases
144. Nodes can typically be moved into center
position
(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
06/03/14 pag. 144
150. 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 kdimensional space graphically. Journal of the American
Statistical Association, 68(342), 361-368.
06/03/14
pag. 150
152. Team project milestones
1.
2.
3.
4.
5.
due
27
Feb.
Form teams
due
13
March
Project proposal
due
3
April
Intermediate presentation
Final presentation
Short report
22
May
due
29
May
06/03/14
pag. 152
153. 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 ;-)
06/03/14
pag. 153