Mosaicplots
and Variations
Heike Hofmann
IOWA STATE UNIVERSITY
1
Outline
Construction of Mosaicplots
Associations and Mosaics
Variations:
Doubledecker plots, Fluctuation diagrams,
Same-Bin-Size displays
Generalisations
2
The Titanic Data
3
The Titanic Data
4
The Titanic Data
5
Mosaics
hierarchically built
area-based plots
default: “slice & dice”
order of variables matters
limiting factors: #variables, screen space
6
Properties of Mosaics
Class
First
Second
Third
Crew
Survived
P( Survival = yes | Class = First )
No
181.3 pt
Yes
P( Class = First )
47.7 pt
7
Properties of Mosaics
Class
First
Second
Third
Crew
Survived
P( Survival = yes | Class = First )
No
181.3 pt
Yes
P( Class = First )
47.7 pt
7
Associations
m11
m21
}d
m12
m22
no interaction
some interaction
}d
stronger interaction
8
Associations
m11
m21
}d
m12
m22
no interaction
X and Y
independent
some interaction
}d
stronger interaction
<=>
8
Associations
m11
m21
}d
}d
m12
m22
no interaction
X and Y
independent
some interaction
stronger interaction
<=>
(Hofmann 2000)
8
Associations
m11
m21
}d
}d
m12
m22
no interaction
X and Y
independent
some interaction
stronger interaction
<=>
(Hofmann 2000)
significance of interaction depends on number of cases
8
Higher-Order Interactions
Y
a1
c1
b1
a2
b2
d1
c2
d2
X
Z
Under control group constraints:
9
High-D Associations
Y
H
H
Z
Z
X
interaction: H*Z | X, Y
(Z ordinal)
10
Variations
Changes to properties of default mosaics
slice & dice build
area proportional to cell value
space-filling plot
11
Doubledecker Plot
splits in horizontal direction only
Survived
no
Double Decker Plot of Sex and Class
yes
Sex
Class
female
male
Crew
1st
2nd
3rd
highlighting: heights proportional to cond. probability
loose: relationship between Sex and Class
12
Same-Bin-Size Diagram
All rectangles have the same size
Highlighting gives conditional probabilities
highlighted: x2bar > 9
width
0-3
4
5
6
7-15
A
B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Letter
13
Fluctuation Diagram
Start from Same-Bin-Size display,
shrink each rectangle according to value of
corresponding cell
loose: screen space,
high sensitivity to aspect ratio
gain: comparisons along axes in two directions
14
Fluctuation Diagram
SES and IQ have positive association
SES (socio-economic status)
low
lower
middle
upper
middle
high
IQ
low
lower
middle
upper
middle
high
15
Fluctuation Diagram
SES and IQ have positive association
SES (socio-economic status)
low
lower
middle
College Plans
upper
middle
high
IQ
low
No
Yes
lower
middle
upper
middle
high
Either SES or IQ propel positive college plans
16
Fluctuation Diagram
Correlation
Matrix:
Monthly
Temperatures
over six years
in 576 locations
J F M A M J J A SO N D J F M A M J J A SO N D J F M A M J J A SO N D
J
F
M
A
M
J
J
A
S
O
N
D
J
F
M
A
M
J
J
A
S
O
N
D
J
F
M
A
M
J
J
A
S
O
N
D
17
Fluctuation Diagram
Data Matrix visualization
overall percentages
Ash
Fat
deviations from row averages
Lactose Protein Water
Ash
Fat
Lactose Protein Water
BISON
BUFFALO
CAMEL
CAT
DEER
DOG
DOLPHIN
DONKEY
ELEPHANT
FOX
GUINEA PIG
HIPPO
HORSE
LLAMA
MONKEY
MULE
ORANGUTAN
PIG
RABBIT
RAT
REINDEER
SEAL
SHEEP
WHALE
ZEBRA
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Fluctuation Diagram
Ash
Fat
Lactose
Protein
Water
HORSE
Cluster 1
ORANGUTAN
MONKEY
DONKEY
MULE
HIPPO
CAMEL
Cluster 2
ZEBRA
BISON
LLAMA
BUFFALO
FOX
SHEEP
ELEPHANT
Cluster 3
GUINEA
PIG
CAT
DOG
Cluster 5 Cluster 4
RAT
RABBIT
DEER
REINDEER
WHALE
SEAL
DOLPHIN
20
10
1
# clusters
19
Multiple Barcharts
Vehicle
4 -wheeledvehicles
Bicycles
Mot orcycles
Pedest rians
Age
Gender
0 -1 0
1 0 -2 0 2 0 -3 0 3 0 -5 0
Female
50+
0 -1 0
1 0 -2 0 2 0 -3 0 3 0 -5 0
50+
Male
Barcharts in each panel
-> Mosaicplots area special case of Trellis displays
20
Multiple Barcharts
Vehicle
Male
4−wheeled−vehicles
4 -wheeledvehicles
Male
Bicycles
Male
Motorcycles
Male
Pedestrians
15000
10000
5000
Bicycles
Observed
0
Female
4−wheeled−vehicles
15000
Female
Bicycles
Female
Motorcycles
Female
Pedestrians
0−10 10−20 20−30 30−50 50+
0−10 10−20 20−30 30−50 50+
Mot orcycles
10000
5000
0
Pedest rians
0−10 10−20 20−30 30−50 50+
Age
Gender
0 -1 0
0−10 10−20 20−30 30−50 50+
1 0 -2 0 2 0 -3 0 3 0 -5 0
Female
50+
0 -1 0
1 0 -2 0 2 0 -3 0 3 0 -5 0
50+
Male
Barcharts in each panel
-> Mosaicplots area special case of Trellis displays
20
Some Generalisations
Mosaics are special cases of
Trellis Displays
type of display is more flexible
Treemaps
different variables in same level of hierarchy
21
Treemap - construction
eicosenoic
< 6.5
!6.5
linoleic
< 951
palmitoleic
!951
Apulia
< 1053.5
!95.5 < 95.5
stearic
Calabria
North
Sardinia
< 264.5
Apulia
AT&T Labs - Research
linoleic
Sicily
Visualizing Trees and Forests, Simon Urbanek
22
22
Treemap - construction
eicosenoic
< 6.5
!6.5
linoleic
< 951
palmitoleic
!951
Apulia
< 1053.5
!95.5 < 95.5
stearic
Calabria
North
Sardinia
< 264.5
Apulia
AT&T Labs - Research
linoleic
Sicily
Visualizing Trees and Forests, Simon Urbanek
23
23
Treemap - construction
eicosenoic
< 6.5
!6.5
linoleic
< 951
palmitoleic
!951
Apulia
< 1053.5
!95.5 < 95.5
stearic
Calabria
North
Sardinia
< 264.5
Apulia
AT&T Labs - Research
linoleic
Sicily
Visualizing Trees and Forests, Simon Urbanek
24
24
Treemap - construction
eicosenoic
< 6.5
!6.5
linoleic
< 951
palmitoleic
!951
Apulia
< 1053.5
!95.5 < 95.5
stearic
Calabria
North
Sardinia
< 264.5
Apulia
AT&T Labs - Research
linoleic
Sicily
Visualizing Trees and Forests, Simon Urbanek
25
25
Treemap - construction
eicosenoic
< 6.5
!6.5
linoleic
< 951
palmitoleic
!951
Apulia
< 1053.5
!95.5 < 95.5
stearic
Calabria
North
Sardinia
< 264.5
Apulia
AT&T Labs - Research
linoleic
Sicily
Visualizing Trees and Forests, Simon Urbanek
26
26
Treemap - construction
eicosenoic
< 6.5
!6.5
linoleic
< 951
palmitoleic
!951
Apulia
< 1053.5
!95.5 < 95.5
stearic
Calabria
North
Sardinia
< 264.5
Apulia
AT&T Labs - Research
linoleic
Sicily
Visualizing Trees and Forests, Simon Urbanek
27
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Treemaps in the
Infovis Community
Voronoi Treemap
Circle Treemap
Figure 10: Enhanced AW Voronoi Treemap layout of 4075 nodes at
10 hierarchy levels (a brighter color indicates a lower hierarchy level)
Figure 11: Enhanced PW Voronoi Treemap layout of 16288 nodes at
7 hierarchy levels (a brighter color indicates a lower hierarchy level)
become very large. Thus, with regard to computation time, other
Treemap layout algorithms outperform this method by far. This
problem is diminished by using distributed computing environ-
[6] Qiang Du and Xiaoqiang Wang. Centroidal voronoi tessellation based
algorithms for vector fields visualization and segmentation. In Proceedings of the IEEE Visualization, pages 43–50. IEEE Computer So-
Balzer et al. 2005
Kai Wetzel, 2005
28
Thank you!
Comments? Questions?
Software: Manet (all mosaic variations),
Mondrian (most),
iplots 2.0 (some)
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