Ordered and Quantum Treemaps: Making Effective Use of 2D Space to Display Hierarchies'

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Ordered and Quantum Treemaps Making Effective
Use of 2D Space to Display Hierarchies.

• By Bederson, B.B., Shneiderman, B., and
  Wattenberg, M.
• ACM Transactions on Graphics (TOG) , October 2002.

Layla Shahamat Kenny Weiss March 8, 2005
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Outline

• Motivation
• Main Ideas
• Related Work
• Demo
• Treemap 4.0
• Quantum Treemaps
• Demo
• Photomesa
• Concluding Remarks

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Motivation
What information do you get from this tree? How
about more realistic bigger trees?
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Motivation

• Displaying large hierarchical information
  structures
• First Spark!Solving 1990s common problem of
  displaying filled hard disk in order to achieve
  goals such as
• Displaying the file system in a compact way
• Better utilization of available pixels
• Visually appealing
• Informative, easy to browse, easy to read

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Treemap Development

• Treemap - Novel idea and design of the algorithm
  was developed by

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What is a treemap?

• Space-filling visualization method to represent
  large hierarchical structures of quantitative
  data.
• The Key idea is creating the nested rectangles
  that make up the layout.

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Treemap Algorithm Overview

• Each node in the tree hierarchy has a name, and
  an associated size.
• Treemap is constructed via recursive subdivision
  of the initial rectangle
• The direction of the subdivision alternates per
  level between horizontally and vertically.
• The area of each rectangle in the treemap is
  proportional to the size of that particular node.
• Aspect ratio of a rectangle is the maximum of
  width/height and height/width.

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Different types of Treemaps
Quantum
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Slice and Dice Algorithm

• Creates rectangles with high aspect ratio
• As a result hard to see skinny rectangles
• 6

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Areas 6, 6, 4, 3, 2, 2, 1
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6
4
2
2
3
6
4
4
horizontal 16/1
Vertical 36/1
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Cluster (Map of Market)
http//www.smartmoney.com/marketmap
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Cluster Treemap Squarified Treemap

• Drawbacks
• Rapid Dramatic changes in the layout resulting
  from change in data
• Second by second updates
• Flickering
• Ignoring the order of the data (e.g.
  alphabetical)
• Switching between vertical and horizontal squares
• Harder to locate data or see patterns

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Ordered Treemap

• Algorithm change smoothly under dynamic updates.
• Produces rectangles with low aspect ratio. Higher
  readability
• Solves the problem of ordered data such as
  alphabetical indexed data

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Ordered Treemap Algorithm
Rp
R3 (gt Rp) (gt R2)
R1 (lt Rp)
R2 (gt Rp) (lt R3)
Rp Size, Middle, Split-Size
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Ordered Treemap AlgorithmPivot by size Algorithm

• Inspired byQuickSort
• If the number of items lt 4, lay them out in R,
  stop.
• Let P, the pivot, be the item with the largest
  size.
• Divide R into 4 rectangles, R1,Rp,R2,R3
• Divide the items in the list, except p items,
  into 3 lists L1,L2,L3
• All L1 indexes are less than p.
• All the items in L2 have smaller indexes than the
  ones in L3 (L2.index lt L3.index)
• Repeat until items lt 4.

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Different types of Ordered Treemaps

• All these algorithm preserve the ordering of the
  index of the items.
• Pivot-by-size O(nn)
• Pivot-by-middle O(nlogn) worst case
• Pivot-by-split-size

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Strip Treemap Overview

• Modification of Squarified Treemap Alg.
• Preserves Order.
• Eliminating the final skinny strip by developing
  look ahead strip
• Better readability than the ordered treemap
  Algorithm.
• Average Run time O(sqrt(n))

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Strip Treemap Algorithm

• Creates an empty strip called current strip.
• Adds a rectangle to the current strip
• If average aspect ratio increases, remove the
  rectangle from the strip
• Create a new strip
• add the rectangle
• If average aspect ratio decreases
• or stays the same, add the rectangle to the
  current strip.

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How Do We Compare?

• Evaluation Metric
• Average aspect Ratio of a treemap layout
• Average aspect ratio is arithmetic average of all
  aspect ratios of all leaf-node rectangles. The
  lowest is 1.Different calculation is possible.
• Layout Distance Change
• Distance function measuring how much rectangles
  move as data gets updated
• Readability how easy it is to locate an item
• Measuring eye motion direction changes

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Monte Carlo Trials ExperimentDesign

• The data constantly gets updated.
• For each experiment ran 100 trials of 100 steps
  each.
• 3 different collections of data

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Monte Carlo Trials Experiment Results

• Slice and Dice Method shows the tradeoff between
  aspect ratio and smooth updates.
• Ordered and Strip treemaps fall in the middle.
• Cluster and squarified treemaps show low aspect
  ratio, large changes.

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Static Stock Market Experiment

• Data 535 publicly traded companies
• High aspect ratios are due to the outliers in the
  data

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User Study of Layout Readability

• 100 rectangles with random size uniform
  distribution.
• Measured the time it took the user to find a
  numerical ID.
• Each subject performed 10 tasks for each 3 alg.
• 20 subjects, 20 female,80 male, 50 student
• Squarified treemap
• longest time to locate an item
• lowest user preference

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User Study of Layout Readability results

• Subject preference was in the same direction as
  the readability metric
• Strip users found the item 60 faster than when
  using squarified treemap.

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Treemap Demo
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Quantum TreemapsProblem

• Input size of elements is fixed
• Similar Images
• Pictures
• Pages
• Grouping
• Integral multiples of fixed input
• Search
• Meaningful categories
• Ordered layout

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Quantum TreemapsProcedure

• Similar to other treemaps
• Input
• List of image groups
• Number elements in each group
• Fixed aspect ratio
• Output
• List of rectangles
• Constraints
• Guaranteed to fit images
• Can have extra space
• Must fit contents into rows and columns

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Fit images into rectangles

• Scale to fit
• Long skinny rectangle
• Visually unattractive
• Slow to scan

• Align content
• Global Grid
• Groups are integral multiples of quanta

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Quantized Strip Treemap

• Difference from normal striptree (ST)
• Rectangle Area Integral multiples of quanta
• Ragged Edges
• Distribute extra space throughout width
• Same complexity as ST
• Up to a constant
• Can use other treemap strategies
• Subtle changes may be necessary

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Element Aspect Ratio

• Aspect ratio (AR) doesnt affect layout algorithm
• Can stretch out starting box by inverse of aspect
  ratio

• Visually has same effect

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Ragged Edges

• QST
• distribute space along width to fix ragged edge
• General case
• distribute globally
• Left and Bottom edges may be ragged

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Horizontal and Vertical Growth

• Grow to match rectangle to quantum ratio
• Experiments show best results when
• Grow width in wide layouts
• Grow height in vertical layouts

x
Wide layout
Change height
x
x
Change width
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Comparison
QT has better average aspect ratio, but wastes
more space than ordinary treemap
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Analysis

• QT works better when groups have more elements
• More flexibility
• Wastes less space (proportionally)
• 1000 elements (30x34), (31x33), (32x32)
• Each element is 0.1
• 5 elements (1x5), (2x3)
• Each element is 20
• Single global grid
• Quantum size
• Usually, if domain requires constant size,other
  considerations are outweighed

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Demo
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Thoughts

• Informative background information on various
  Treemap strategies
• Experiments discuss dynamic ordered data
• Order preservation helps users orient themselves
• Categorical data not discussed
• Photomesa
• Impressive overview of a lot of information
• very nice overview, zoom, filter, details
• GUI works well while loading images
• Zoom is abrupt and pixelated
• Compare to Picasa and Photoshop Album
• TreeMap
• Would be nice if File Mapper offered file
  previews