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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. Outline. Motivation Main Ideas Related Work Demo - PowerPoint PPT Presentation
Citation preview
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 ShahamatKenny Weiss
March 8, 2005
Outline Motivation Main Ideas Related Work Demo
Treemap 4.0 Quantum Treemaps Demo
Photomesa Concluding Remarks
Motivation
What information do you get from this tree?
How about more realistic bigger trees?
Motivation Displaying large hierarchical information
structures First Spark!
Solving 1990’s 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
Treemap Development Treemap - Novel idea and design of the
algorithm was developed by
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.
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.
Different types of Treemaps
Quantum
Slice and Dice Algorithm
Creates rectangles with high aspect ratio As a result hard to see skinny rectangles 6
4Areas
6, 6, 4, 3, 2, 2, 16 6 4 223
664
horizontal 16/1 Vertical 36/1
Cluster (Map of Market)
http://www.smartmoney.com/marketmap
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
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
Ordered Treemap Algorithm
Rp
R1(< Rp) R2
(> Rp)(< R3)
R3(> Rp)(> R2)
Rp = {Size, Middle, Split-Size}
Ordered Treemap AlgorithmPivot by size Algorithm Inspired byQuickSort If the number of items <= 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 < L3.index) Repeat until items <= 4.
Different types of Ordered Treemaps All these algorithm preserve the ordering of the
index of the items. Pivot-by-size O(n*n) Pivot-by-middle O(nlogn) worst case Pivot-by-split-size
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))
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.
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
Monte Carlo Trials ExperimentDesign The data constantly gets updated. For each experiment ran 100 trials of 100
steps each. 3 different collections of data
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.
Static Stock Market Experiment Data: 535 publicly traded companies High aspect ratios are due to the outliers in the
data
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
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.
Treemap Demo
Quantum TreemapsProblem
Input size of elements is fixed Similar Images
Pictures Pages
Grouping Integral multiples of fixed input
Search Meaningful categories Ordered layout
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
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
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
Element Aspect Ratio Aspect ratio (AR) doesn’t affect layout algorithm
Can stretch out starting box by inverse of aspect ratio
• Visually has same effect
Ragged Edges QST
distribute space along width to fix ragged edge
General case distribute globally
Left and Bottom edges may be ragged
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
x
xChangewidth
Wide layoutChange
height
Comparison
QT has better average aspect ratio, but wastes more space than ordinary treemap
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
Demo
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