# HierarchyMap: A Novel Approach to Treemap Visualization of Hierarchical Data

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2 Global Journal of Computer Science and Technology Vol. 9 Issue 5 (Ver 2.0), January 2010 P a g e 78 the display space inefficiently as depicted in the Figure 1 below: Fig. 1: Tree diagram for representing Hierarchical Data Structure (Mark Bruls et al., 2000) Fig. 2: TreeMap representing the Hierarchical Data Structure in fig. 1 (Mark Bruls et al., 2000) A treemap as shown in Figure 2 above was developed and introduced to solve the problem of this space usage by using the full display space to visualize the contents of the tree (Johnson and Shneidermann, 1991), (B. Shnerdermann, 1992). As illustrated in Figure 2 above, Slice and Dice treemap algorithm splits the display rectangles along horizontal and vertical lines while recursively traversing a hierarchically structured dataset in top down direction (Shneiderman,1992). Slice- and Dice treemap are very effective when size is the most important feature to be displayed. However, this method also has the problem of creating layouts that contain many rectangles with a high aspect ratio. Therefore, many other treemap layout algorithms have been proposed. In order to overcome this limitations. These include Cluster and Squarified treemap algorithms, Cluster treemap uses a simple recursive algorithm that reduces overall aspect ratios (Wattenberg, 1999), while Squarified treemap algorithm presented the layout of the children in one rectangle as a recursive procedure squarify (Bruls et al., 2000). This procedure lays-out the rectangles in horizontal and vertical rows. When a rectangle is processed, a decision is made between two alternatives, either the rectangle is added to the current row, or the current row is fixed and a new row is started in the remaining subrectangle. This decision depends only on whether adding a rectangle to the row will improve the layout of the current row or not. These methods also have their drawbacks; changes in the data set can cause dramatic discontinuous changes in the layout produced by both cluster treemaps and squarified treemaps. This rapid layout changes also cause an unattractive flickering that draws attention away from other aspects of the visualization and makes it hard to find items on the treemap. Another problem with Cluster and Squarified treemap is that, its layouts fail to preserve order of information as it is done with slice and dice treemap. Many ordered treemap algorithms were introduced to address the limitations in slice-and-dice, Cluster, and Squarified treemap algorithms. The motivating factor here is to seek for the creation of layout in which items that are next to each other in a given order are adjacent in the treemap. Ordered treemaps include Pivot by Split Size, Pivot by Middle, Split and Strip treemap algorithm. These ordered treemaps generally change relatively smoothly under dynamic updates and roughly preserve order, produce rectangles with low aspect ratios compared to that of cluster and squarified treemap (Shneiderman et al. 2002). Pivot- by- middle algorithm selects the pivot to the middle item of the list so as to create a balanced layout. With this idea, this algorithm is not sensitive to changes as Pivot by- Split Size. The pivot is taken to be the item (rectangle) with the largest area. Pivot by-split-size selects the pivot that will split the list into approximately equal total areas. These two algorithms create layouts that roughly preserve order and are relatively efficient, but fail to produce layouts with relatively low aspect ratio. Strip algorithm is a modification of the Squarified treemap algorithm. It works by processing input rectangles in order, laying them out in horizontal or vertical strips of varying thickness. It is efficient in that it produces a layout with better readability than the basic ordered treemap algorithm, and reasonable aspect ratios and stability (Shneiderman et al. 2002). III. METHODS A. Development of HierarchyMap Algorithm The algorithm for the HierarchyMap treemap is as follows: Infotree(treedata nodes) T={t1,t2,t3,.., tn} and a 2- D space divided into four equal rectangles. i. If the number of hierarchical items to be displayed is zero (i.e. T=0), then no display. ii. If the number of hierarchical items to be displayed is 1 (i.e T=1), then Set 2-D space to the item. iii. If the number of items is greater than 1, split the rectangular 2-D space into four equal sizes and recursively divides each of the resultant item into fours until all items in the list are exhausted such that ti T1, tj T2, tk T3, tn Tn : ti ti+1 tj tj+1 tk tk+1... tn tn+1. iv. An attribute of each hierarchical item corresponds to an area of each of the nested rectangles is defined as area( R) in such a manner that their areas correspond to the size of the elements of T1, T2 T3, and T4 where area (R1) area (R2) area (R3)..... area (Rn). The algorithm accepts inputs data in hierarchical form. These input items in their hierarchical order are stored, read

3 P a g e 79 Vol. 9 Issue 5 (Ver 2.0), January 2010 Global Journal of Computer Science and Technology and lay-out on nested rectangles which make up a treemap on the computer screen. The entire 2-dimensional computer screen is divided first into four equal parts, each of the successive parts is then repeatedly divided into four parts in such a way that the resultant rectangles are grouped according to the nodes level to be represented in the entire hierarchical data. This is to ensure that the order of the items to be displayed is maintained. These items are then linked to each of the resultant rectangles that make up the treemap. Each rectangle that represents the node level of tree data can then clicked repeatedly to display the sub-node elements. Every other nodal rectangle on the treemap could be clicked to display their own sub-node elements in a similar manner. In this process, several thousands of items of information could be displayed and viewed in a single space of 2- dimensional treemap. IV. RESULTS AND DISCUSSION HierarchyMap algorithm is tested with a several number of sample data of the information structures such as University system, Family system, and Animal Taxonomy. The results of this implementation are represented in Figures 3,4 and 5 respectively. Figure 3 shows the treemap appearance with no information, Figure 4 shows the treemap representation of ten different families Structure and the adjustment of each of the rectangles to reduce their aspect ratio, improve their readability, reduction of thin rectangles. Finally, Figure 5 shows the HierarchyMap for the combination of several tree structures capable of displaying thousands of information. It also shows the adjustment change of the rectangles to demonstrate its optimum measures of the three treemap metrics (i.e. aspect ratio, readability, ordering and capability for change) as data is updated. The results of this implementation also shows that this HierarchyMap algorithm is similar to other existing treemaps in that, it lays out hierarchical information on nested rectangles, and added further advantage by making it possible to display very large volume of hierarchical information by continuous clicking of node level rectangle, which we have demonstrated in the implementation. Figure 3: HierarchyMap showing nested rectangles without information

4 Global Journal of Computer Science and Technology Vol. 9 Issue 5 (Ver 2.0), January 2010 P a g e 80 Figure 4: HierarchyMap representing ten different family Structures Figure 5: HierarchyMap representing a combination of several hierarchical Structures.

5 P a g e 81 Vol. 9 Issue 5 (Ver 2.0), January 2010 Global Journal of Computer Science and Technology V. CONCLUSIONS In this work, we developed and implemented a novel treemap called HierarchyMap algorithm, which improved on the limitations of the existing treemap algorithms such as Slice-and-dice, Cluster, Squarified, Strip, etc. and added a new feature, which enable viewing of several thousands of hierarchical information by clicking on any of the nodal rectangles. The result showed that the HierarchyMap treemap algorithm has the capability for adjustment change whenever data are updated; it also improved on readability, preservation of order, low aspect ratio, and reduced number of thin rectangles. The combination of these treemap metrics makes HierarchyMap a promising treemap algorithm for the future. VI. REFERENCES 1) Bruggemann-Klein and D. Wood. Drawing trees nicely with tex. Electronic Publishing, 2(2): , ) Johnson and B. Shneiderman. Treemaps: A spacefilling approach to the Visualization of Hierarchical Information Structures. In Proc. of the 2nd International IEEE Visualization Conference, pages , October ) Shneiderman. Tree visualization with treemaps:a 2-D space-filling approach. ACM Transactions on Graphics, 11(1):92 99, September ) Bruls S., M., Huizing, K., and Van Wijk, J., Squarified treemaps. In Proceedings of the Joint Eurographics and IEEE TCVG Symposium on Visualization (VisSym), ) Bederson, B., Shneiderman, B., and Wattenberg, M Ordered and quantum treemaps: Making effective use of 2D space to display hierarchies. ACM Transactions on Graphics 21, 4, ) D.E. Knuth. Fundamental algorithms. Art of computer programming. Volume 1. Addison-Wesley, Reading, MA, ) G.W. Furnas. Generalized fisheye views. In Proc. of ACM CHI 86, Conference on Human Factors in computing systems, pages 16 23, ) Herman H, Maurer. Data Structures and Programming Techniques. Prentice- All Incorporation ) J. Bingham and S.Sudarsanum. Visualising large hierarchical clusters in Hyperbolic space. Bioinfomatics Chapter 16:pg , Malin Koksal, Visualization of threaded discussions forums on handheld devices, Masters Thesis at NADA, ) Russel Winder and Graham Roberts, Developing Java Software, John Wiley & Sons ) S.K. Card, G.G. Robertson, and J.D. Mackinlay. The information visualizer, an information workspace. In Proc. of ACM CHI 91, Conference on Human Factors in Computing Systems, pages , ) Wattenberg, M Visualizing the stock market. In Extended Abstracts onbhuman Factors in Computing Systems (CHI), ACM Press,

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