In information visualization and computing, treemapping is a method for displaying hierarchical data using nested figures, usually rectangles. Contents 1 Main idea 2 Tiling algorithms 3 Rectangular treemaps 4 Convex treemaps 4.1
5 Other treemaps 6 History 7 See also 8 References 9 External links Main idea[edit] Treemaps display hierarchical (tree-structured) data as a set of nested rectangles. Each branch of the tree is given a rectangle, which is then tiled with smaller rectangles representing sub-branches. A leaf node's rectangle has an area proportional to a specified dimension of the data. Often the leaf nodes are colored to show a separate dimension of the data. When the color and size dimensions are correlated in some way with the tree structure, one can often easily see patterns that would be difficult to spot in other ways, such as if a certain color is particularly relevant. A second advantage of treemaps is that, by construction, they make efficient use of space. As a result, they can legibly display thousands of items on the screen simultaneously. Tiling algorithms[edit] To create a treemap, one must define a tiling algorithm, that is, a way to divide a region into sub-regions of specified areas. Ideally, a treemap algorithm would create regions that satisfy the following criteria: A small aspect ratio - ideally close to one. Regions with a small aspect ratio (i.e, fat objects) are easier to perceive.[1] Preserve some sense of the ordering in the input data. Change to reflect changes in the underlying data. Unfortunately, these properties have an inverse relationship. As the aspect ratio is optimized, the order of placement becomes less predictable. As the order becomes more stable, the aspect ratio is degraded.[example needed] Rectangular treemaps[edit] To date, six primary rectangular treemap algorithms have been developed: Treemap algorithms[2] Algorithm Order Aspect ratios Stability BinaryTree partially ordered high stable Mixed Treemaps[3] ordered lowest stable Ordered and Quantum[4] partially ordered medium medium stability Slice And Dice[citation needed] ordered very high stable Squarified[5] unordered[further explanation needed] lowest medium stability Strip ordered medium medium stability Convex treemaps[edit] Rectangular treemaps have the disadvantage that their aspect ratio might be arbitrarily high in the worst case. As a simple example, if the tree root has only two children, one with weight 1 / n displaystyle 1/n and one with weight 1 − 1 / n displaystyle 1-1/n , then the aspect ratio of the smaller child will be n displaystyle n , which can be arbitrarily high. To cope with this problem, several algorithms have been proposed that use regions that are general convex polygons, not necessarily rectangular. Convex treemaps were developed in several steps, each step improved the upper bound on the aspect ratio. The bounds are given as a function of n displaystyle n - the total number of nodes in the tree, and d displaystyle d - the total depth of the tree. 1. Onak and Sidiropoulos[6] proved an upper bound of O ( ( d log n ) 17 ) displaystyle O((dlog n )^ 17 ) . 2. De-Berg and Onak and Sidiropoulos[7] improve the upper bound to O ( d + log n ) displaystyle O(d+log n ) , and prove a lower bound of Ω ( d ) displaystyle Omega (d) . 3. De-Berg and Speckmann and van-der-Weele[8] improve the upper bound to O ( d ) displaystyle O(d) , matching the theoretical lower bound. For the special case where the depth is 1, they present an algorithm that uses only four classes of 45-degree-polygons (rectangles, right-angled triangles, right-angled trapezoids and 45-degree pentagons), and guarantees an aspect ratio of at most 34/7. The latter two algorithms operate in two steps (greatly simplified for clarity): A. The original tree is converted to a binary tree: each node with more than two children is replaced by a sub-tree in which each node has exactly two children. B. Each region representing a node (starting from the root) is divided to two, using a line that keeps the angles between edges as large as possible. It is possible to prove that, if all edges of a convex polygon are separated by an angle of at least ϕ displaystyle phi , then its aspect ratio is O ( 1 / ϕ ) displaystyle O(1/phi ) . It is possible to ensure that, in a tree of depth d displaystyle d , the angle is divided by a factor of at most d displaystyle d , hence the aspect ratio guarantee.
For the special case where the depth is 1, they present an algorithm that uses only rectangles and L-shapes, and the aspect ratio is at most 2 + 2 / 3 ≈ 3.15 displaystyle 2+2/ sqrt 3 approx 3.15 ; the internal nodes use only rectangles with aspect ratio at most 1 + 3 ≈ 2.73 displaystyle 1+ sqrt 3 approx 2.73 . Other treemaps[edit]
Voronoi Treemaps[9] - based on
Treemap of Benin's exports by product category, 2009. The Product Exports Treemaps are one of the most recent applications of these kind of visualizations, developed by the Harvard-MIT Observatory of Economic Complexity See also[edit] Disk space analyzer Information visualization List of countries by economic complexity, which includes a list of Products Exports Treemaps. Marimekko Chart, a similar concept with one level of explicit hierarchy. References[edit] ^ Kong, N; Heer, J; Agrawala, M (2010). "Perceptual Guidelines for
Creating Rectangular Treemaps". IEEE Transactions on Visualization and
Computer Graphics. 16 (6): 990. doi:10.1109/TVCG.2010.186.
PMID 20975136.
^ a b Ben Shneiderman;
External links[edit] Wikimedia Commons has media related to Treemaps. Treemap Art Project produced exhibit for the National Academies in
Washington, DC
An article by
v t e Visualization of technical information Fields Biological data visualization
Chemical imaging
Crime mapping
Data visualization
Educational visualization
Flow visualization
Geovisualization
Information visualization
Mathematical visualization
Medical imaging
Molecular graphics
Product visualization
Scientific visualization
Software visualization
Technical drawing
Image types Chart Diagram Engineering drawing Graph of a function Ideogram Map Photograph Pictogram Plot Schematic Statistical graphics Table Technical drawings Technical illustration User interface People Jacques Bertin Stuart Card Thomas A. DeFanti Michael Friendly George Furnas Pat Hanrahan Nigel Holmes Christopher R. Johnson Manuel Lima Alan MacEachren Jock D. Mackinlay Michael Maltz Bruce H. McCormick Miriah Meyer Charles Joseph Minard Rudolf Modley Gaspard Monge Tamara Munzner Otto Neurath Florence Nightingale Hanspeter Pfister Clifford A. Pickover William Playfair Karl Wilhelm Pohlke Adolphe Quetelet George G. Robertson Arthur H. Robinson Lawrence J. Rosenblum Ben Shneiderman Edward Tufte Fernanda Viégas Ade Olufeko Howard Wainer Martin Wattenberg Bang Wong Related topics Cartography Chartjunk Computer graphics in computer science Graph drawing Graphic design Graphic organizer Imaging science Information graphics Information science Mental visualisation Misleading graph Neuroimaging Patent drawing Scientific modelling Spatial analysis Visual analytics Visual perception Volume cartograph |