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 Layla Shahamat Kenny 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 4 Areas 6, 6, 4, 3, 2, 2, horizontal 16/1Vertical 36/1

Cluster (Map of Market)

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 RpRp R 1 (< R p ) R 2 (> R p ) (< R 3 ) R 3 (> R p ) (> R 2 ) R p = {Size, Middle, Split-Size}

Ordered Treemap Algorithm Pivot 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 Experiment Design  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 Treemaps Problem  Input size of elements is fixed Similar Images  Pictures  Pages  Grouping Integral multiples of fixed input  Search Meaningful categories Ordered layout

Quantum Treemaps Procedure  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 x Change width Wide layout Change 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