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Scalable Visual Comparison of Biological Trees and Sequences
Tamara Munzner
University of British Columbia
Department of Computer Science
Imager
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Outline
• Accordion Drawing– information visualization technique
• TreeJuxtaposer– tree comparison
• SequenceJuxtaposer– sequence comparison
• PRISAD– generic accordion drawing framework
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Accordion Drawing• rubber-sheet navigation
– stretch out part of surface, the rest squishes
– borders nailed down– Focus+Context technique
• integrated overview, details
– old idea• [Sarkar et al 93],
[Robertson et al 91]
• guaranteed visibility– marks always visible– important for scalability – new idea
• [Munzner et al 03]
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Guaranteed Visibility
• marks are always visible• easy with small datasets
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Guaranteed Visibility Challenges
• hard with larger datasets
• reasons a mark could be invisible
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Guaranteed Visibility Challenges
• hard with larger datasets
• reasons a mark could be invisible– outside the window
• AD solution: constrained navigation
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Guaranteed Visibility Challenges
• hard with larger datasets
• reasons a mark could be invisible– outside the window
• AD solution: constrained navigation
– underneath other marks• AD solution: avoid 3D
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Guaranteed Visibility Challenges
• hard with larger datasets
• reasons a mark could be invisible– outside the window
• AD solution: constrained navigation
– underneath other marks• AD solution: avoid 3D
– smaller than a pixel• AD solution: smart culling
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Guaranteed Visibility: Small Items
• Naïve culling may not draw all marked items
GV no GV
Guaranteed visibilityof marks
No guaranteed visibility
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Guaranteed Visibility: Small Items
• Naïve culling may not draw all marked items
GV no GV
Guaranteed visibilityof marks
No guaranteed visibility
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Outline
• Accordion Drawing– information visualization technique
• TreeJuxtaposer
– tree comparison
• SequenceJuxtaposer– sequence comparison
• PRISAD– generic accordion drawing framework
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Phylogenetic/Evolutionary Tree
M Meegaskumbura et al., Science 298:379 (2002)
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Common Dataset Size Today
M Meegaskumbura et al., Science 298:379 (2002)
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Future Goal: 10M node Tree of Life
David Hillis, Science 300:1687 (2003)
Plants
Protists
Fungi
Animals
You arehere
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Paper Comparison: Multiple Trees
focus
context
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TreeJuxtaposer• side by side comparison of evolutionary trees • [video]
– video/software downloadable from http://olduvai.sf.net/tj
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TJ Contributions• first interactive tree comparison system
– automatic structural difference computation– guaranteed visibility of marked areas
• scalable to large datasets– 250,000 to 500,000 total nodes– all preprocessing subquadratic– all realtime rendering sublinear
• scalable to large displays (4000 x 2000)
• introduced – guaranteed visibility, accordion drawing
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Structural Comparison
rayfinned fish
lungfish
salamander
frog
mammal
turtle
bird
crocodile
lizard
snake
rayfinned fish
bird
lungfish
salamander
frog
mammal
turtle
snake
lizard
crocodile
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Matching Leaf Nodes
rayfinned fish
lungfish
salamander
frog
mammal
turtle
bird
crocodile
lizard
snake
rayfinned fish
bird
lungfish
salamander
frog
mammal
turtle
snake
lizard
crocodile
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Matching Leaf Nodes
rayfinned fish
lungfish
salamander
frog
mammal
turtle
bird
crocodile
lizard
snake
rayfinned fish
bird
lungfish
salamander
frog
mammal
turtle
snake
lizard
crocodile
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Matching Leaf Nodes
rayfinned fish
lungfish
salamander
frog
mammal
turtle
bird
crocodile
lizard
snake
rayfinned fish
bird
lungfish
salamander
frog
mammal
turtle
snake
lizard
crocodile
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Matching Interior Nodes
rayfinned fish
lungfish
salamander
frog
mammal
turtle
bird
crocodile
lizard
snake
rayfinned fish
bird
lungfish
salamander
frog
mammal
turtle
snake
lizard
crocodile
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Matching Interior Nodes
rayfinned fish
lungfish
salamander
frog
mammal
turtle
bird
crocodile
lizard
snake
rayfinned fish
bird
lungfish
salamander
frog
mammal
turtle
snake
lizard
crocodile
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Matching Interior Nodes
rayfinned fish
lungfish
salamander
frog
mammal
turtle
bird
crocodile
lizard
snake
rayfinned fish
mammal
lungfish
salamander
frog
bird
turtle
snake
lizard
crocodile
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Matching Interior Nodes
rayfinned fish
lungfish
salamander
frog
mammal
turtle
bird
crocodile
lizard
snake
rayfinned fish
bird
lungfish
salamander
frog
mammal
turtle
snake
lizard
crocodile
?
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Previous Work
• tree comparison– RF distance [Robinson and Foulds 81]– perfect node matching [Day 85]– creation/deletion [Chi and Card 99]– leaves only [Graham and Kennedy 01]
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Similarity Score: S(m,n)
{ }{ } 3
2)()(
)()(),( ==
∪∩
=FE,D,
FE,
nm
nmnm
LL
LLS
{ }FE,D,n =)(L{ }FE,m =)(L
T1 T2A
B
C
D
E
F
A
C
B
D
F
Em n
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Best Corresponding Node
• – computable in O(n log2 n)– linked highlighting
T1 T2A
B
C
D
E
F
A
C
B
D
F
Em BCN(m) = n
1/32/3
2/6
00
0
0
0
0
1/2
1/2
)),(( vSv margmax)mBCN(2T∈=
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• – Matches intuition
1≠))BCN(,( whichfor Nodes vvS
Marking Structural DifferencesT1 T2A
B
C
D
E
F
A
C
B
D
F
Em n
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Outline
• Accordion Drawing– information visualization technique
• TreeJuxtaposer– tree comparison
• SequenceJuxtaposer– sequence comparison
• PRISAD– generic accordion drawing framework
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Genomic Sequences• multiple aligned sequences of DNA• now commonly browsed with web apps
– zoom and pan with abrupt jumps– previous work
• Ensembl [Hubbard 02], UCSC Genome Browser [Kent 02], NCBI [Wheeler 02]
• investigate benefits of accordion drawing– showing focus areas in context– smooth transitions between states– guaranteed visibility for globally visible
landmarks
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SequenceJuxtaposer
• comparing multiple aligned gene sequences• provides searching, difference calculation• [video]
– video/software downloadable from http://olduvai.sf.net/tj
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Searching
• search for motifs– protein/codon search– regular expressions supported
• results marked with guaranteed visibility
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Differences
• explore differences between aligned pairs– slider controls difference threshold in realtime
• results marked with guaranteed visibility
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SJ Contributions• fluid tree comparison system
– showing multiple focus areas in context– guaranteed visibility of marked areas
• thresholded differences, search results
• scalable to large datasets– 2M nucleotides– all realtime rendering sublinear
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Outline
• Accordion Drawing– information visualization technique
• TreeJuxtaposer– tree comparison
• SequenceJuxtaposer– sequence comparison
• PRISAD– generic accordion drawing framework
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Goals of PRISAD
• generic AD infrastructure– tree and sequence applications
• PRITree is TreeJuxtaposer using PRISAD• PRISeq is SequenceJuxtaposer using PRISAD
• efficiency– faster rendering: minimize overdrawing– smaller memory footprint
• correctness– rendering with no gaps: eliminate overculling
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PRISAD Navigation
• generic navigation infrastructure– application independent– uses deformable grid– split lines
• Grid lines define object boundaries
– horizontal and vertical separate• Independently movable
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Split line hierarchy
• data structure supports navigation, picking, drawing• two interpretations
– linear ordering
– hierarchical subdivision
A B C D E F
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PRISAD Architecture
world-space discretization• preprocessing
• initializing data structures• placing geometry
screen-space rendering• frame updating
• analyzing navigation state• drawing geometry
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World-space Discretization
interplay between infrastructure and application
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• application-specific layout of dataset– non-overlapping objects
• initialize PRISAD split line hierarchies– objects aligned by split lines
Laying Out & Initializing
A A C C
A T T T68
12
34 5
97
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4
2
• application-specific layout of dataset– non-overlapping objects
• initialize PRISAD split line hierarchies– objects aligned by split lines
Laying Out & Initializing
A A C C
A T T T68
12
34 5
97
4
5
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Gridding
• each geometric object assigned its four encompassing split line boundaries
A A C C
A T T T
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Mapping
• PRITree mapping initializes leaf references– bidirectional O(1) reference between leaves and
split lines
13
468
25
973
4
12
5
84
95
63
52
21 Map
68
25
9
Split line Leaf index
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Screen-space Rendering
control flow to draw each frame
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Partitioning
• partition object set into bite-sized ranges– using current split line screen-space positions
• required for every frame
– subdivision stops if region smaller than 1 pixel• or if range contains only 1 object
1234
5
[1,2]
[3,4]
[5]
{ [1,2], [3,4], [5] }
Queue of ranges
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Seeding
• reordering range queue result from partition– marked regions get priority in queue
• drawn first to provide landmarks
1234
5
[1,2]
[3,4]
[5]
{ [1,2], [3,4], [5] }
{ [3,4], [5], [1,2] }
ordered queue
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Drawing Single Range
• each enqueued object range drawn according to application geometry– selection for trees– aggregation for sequences
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PRITree Range Drawing
• select suitable leaf in each range
• draw path from leaf to the root– ascent-based tree drawing
– efficiency: minimize overdrawing • only draw one path per range
1234
5
[3,4]{ [3,4], [5], [1,2] }
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Rendering Dense Regions
– correctness: eliminate overculling• bad leaf choices would result in misleading gaps
– efficiency: maximize partition size to reduce rendering• too much reduction would result in gaps
Intended rendering Partition size too big
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Rendering Dense Regions
– correctness: eliminate overculling• bad leaf choices would result in misleading gaps
– efficiency: maximize partition size to reduce rendering• too much reduction would result in gaps
Intended rendering Partition size too big
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PRITree Skeleton
• guaranteed visibility of marked subtrees during progressive rendering
first frame: one path per marked group
full scene: entire marked subtrees
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PRISeq Range Drawing: Aggregation
• aggregate range to select box color for each sequence– random select to break ties
A A C C
A T T T
[1,4]
A
T
[1,4]
T T T C T
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PRISeq Range Drawing
• collect identical nucleotides in column– form single box to represent identical objects
• attach to split line hierarchy cache• lazy evaluation
• draw vertical column
A
T
T
T
A
{ A:[1,1], T:[2,3] }
1
2
3
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PRISAD Performance
• PRITree vs. TreeJuxtaposer (TJ)
• synthetic and real datasets
– complete binary trees• lowest branching factor• regular structure
– star trees• highest possible branching factor
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InfoVis Contest Benchmarks• two 190K node trees• directly compare TJ and PT
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OpenDirectory benchmarks• two 480K node trees• too large for TJ, PT results only
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PRITree Rendering Time Performance
TreeJuxtaposer renders all nodes for star trees• branching factor k leads to O(k) performance
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PRITree Rendering Time Performance
TreeJuxtaposer renders all nodes for star trees• branching factor k leads to O(k) performance
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PRITree Rendering Time Performance
InfoVis 2003 Contest dataset• 5x rendering speedup
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PRITree Rendering Time Performance
a closer look at the fastest rendering times
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PRITree Rendering Time Performance
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PRITree handles 4 million nodes in under 0.4 seconds• TreeJuxtaposer takes twice as long to render 1 million nodes
Detailed Rendering Time Performance
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Detailed Rendering Time PerformanceTreeJuxtaposer valley from overculling
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Memory Performancelinear memory usage for both applications
• 4-5x more efficient for synthetic datasets
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Memory Performance1GB difference for InfoVis contest comparison
• marked range storage changes improve scalability
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Performance Comparison
• PRITree vs. TreeJuxtaposer– detailed benchmarks against identical TJ
functionality• 5x faster, 8x smaller footprint• handles over 4M node trees
• PRISeq vs. SequenceJuxtaposer– 15x faster rendering, 20x smaller memory size– 44 species * 17K nucleotides = 770K items– 6400 species * 6400 nucleotides = 40M items
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Future Work
• future work– editing and annotating datasets– PRISAD support for application specific actions
• logging, replay, undo, other user actions
– develop process or template for building applications
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PRISAD Contributions
• infrastructure for efficient, correct, and generic accordion drawing
• efficient and correct rendering – screen-space partitioning tightly bounds overdrawing and
eliminates overculling
• first generic AD infrastructure– PRITree renders 5x faster than TJ– PRISeq renders 20x larger datasets than SJ
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Joint Work• TreeJuxtaposer
– François Guimbretière, Serdar Taşiran, Li Zhang, Yunhong Zhou• SIGGRAPH 2003
• SequenceJuxtaposer– James Slack, Kristian Hildebrand, Katherine St.John
• German Conference on Bioinformatics 2004
• TJC/TJC-Q– Dale Beermann, Greg Humphreys
• EuroVis 2005
• PRISAD– James Slack, Kristian Hildebrand
• IEEE InfoVis Symposium 2005• Information Visualization journal, to appear
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Open Source
• software freely available from http://olduvai.sourceforge.net– SequenceJuxtaposer
olduvai.sf.net/sj– TreeJuxtaposer
olduvai.sf.net/tj– requires Java and OpenGL
• JOGL bindings for TJ, GL4Java for SJ (JOGL coming soon)
• papers, talks, videos also from http://www.cs.ubc.ca/~tmm
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Other Projects
• Focus+Context evaluation– high-level user studies of systems– low-level visual search and memory
• graph drawing
• dimensionality reduction