In this paper, we propose a novel space partitioning strategy for implicit hierarchy visualization such that the new plot not only has a tidy layout similar to the treemap, but also is flexible to data changes similar to the Voronoi treemap. To achieve this, we define a new distance function and neighborhood relationship between sites so that space will be divided by axis-aligned segments. Then a sweepline+skyline based heuristic algorithm is proposed to allocate the partitioned spaces to form an orthogonal Voronoi diagram with orthogonal rectangles. To the best of our knowledge, it is the first time to use a sweepline-based strategy for the Voronoi treemap. Moreover, we design a novel strategy to initialize the diagram status and modify the status update procedure so that the generation of our plot is more effective and efficient. We show that the proposed algorithm has an O(nlog(n)) complexity which is the same as the state-of-the-art Voronoi treemap. To this end, we show via experiments on the artificial dataset and real-world dataset the performance of our algorithm in terms of computation time, converge rate, and aspect ratio. Finally, we discuss the pros and cons of our method and make a conclusion.
Non-rectangular treemaps are also designed in the literature. Jigsaw map has nicely shaped regions and stable layout by considering Hilbert curves or H curves @cite_7 . They generate irregular shapes which are not easy to be compared with. A modification then was proposed by splitting the space into rectangles @cite_32 . To relax rectangular constraint, angular treemaps describe a divide-and-conquer method to partition the space into various shapes @cite_13 . Besides that, the treemap layout that produces irregular nested shapes by subdividing the Gosper curve @cite_28 was also proposed.
@cite_28 @cite_13 @cite_32 @cite_7
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A recent line of treemap research has focused on layout algorithms that optimize properties such as stability, preservation of ordering information, and aspect ratio of rectangles. No ideal treemap layout algorithm has been found, and so it is natural to explore layouts that produce nonrectangular regions. This note describes a connection between space-filling visualizations and the mathematics of space-filling curves, and uses that connection to characterize a family of layout algorithms which produce nonrectangular regions but enjoy geometric continuity under changes to the data and legibility even for highly unbalanced trees. Space-filling visualization techniques have proved their capability in visualizing large hierarchical structured data. However, most existing techniques restrict their partitioning process in vertical and horizontal direction only, which cause problem with identifying hierarchical structures. This paper presents a new space-filling method named Angular Treemaps that relax the constraint of the rectangular subdivision. The approach of Angular Treemaps utilizes divide and conquer paradigm to visualize and emphasize large hierarchical structures within a compact and limited display area with better interpretability. Angular Treemaps generate various layouts to highlight hierarchical sub-structure based on user's preferences or system recommendations. It offers flexibility to be adopted into a wider range of applications, regarding different enclosing shapes. Preliminary usability results suggest user's performance by using this technique is improved in locating and identifying categorized analysis tasks. Space-filling techniques seek to use as much as possible the visual space to represent a dataset, splitting it into regions that represent the data elements. Amongst those techniques, Treemaps have received wide attention due to its simplicity, reduced visual complexity, and compact use of the available space. Several different Treemap algorithms have been proposed, however the core idea is the same, to divide the visual space into rectangles with areas proportional to some data attribute or weight. Although pleasant layouts can be effectively produced by the existing techniques, most of them do not take into account relationships that might exist between different data elements when partitioning the visual space. This violates the distance-similarity metaphor, that is, close rectangles do not necessarily represent similar data elements. In this paper, we propose a novel approach, called Neighborhood Treemap (Nmap), that seeks to solve this limitation by employing a slice and scale strategy where the visual space is successively bisected on the horizontal or vertical directions and the bisections are scaled until one rectangle is defined per data element. Compared to the current techniques with the same similarity preservation goal, our approach presents the best results while being two to three orders of magnitude faster. The usefulness of Nmap is shown by two applications involving the organization of document collections and the construction of cartograms illustrating its effectiveness on different scenarios. This paper presents work in progress on a new technique for visu- alising and manipulating large hierarchies. The information slices approach compactly visualises hierarchical structures using a series of semi-circular discs. The technique is described in the context of our early experience with a prototype file system visualiser based on information slices. Over the last few years, the emerging field of information visuali- sation has resulted in a numerous techniques for helping visualise and make sense of large information spaces (10). Among these are several techniques for visualising and interacting with large hierar- chies which go beyond the traditional approach taken in 2d scrolling browsers such as the Windows Explorer. Treemaps (6, 9) are space-filling visualisations of hierarchies based on successive horizontal and vertical subdivision of screen rectangles. The area of each rectangle is proportional to some at- tribute of the underlying hierarchy such as the (total) size of each subtree. Xdu (4) is a utility for the X window system which displays a graphical disk usage for Unix file systems. Rectangles are stacked from left to right as the directory tree is descended. The current di- rectory is represented by the leftmost rectangle, which is the entire height of the window. Subdirectories are represented by neighbour- ing rectangles in the next column, whose height are proportional to the size of each subdirectory. The hyperbolic browser (7) uses a focus and context technique based on hyperbolic geometry. A hierarchy is laid out uniformly on the hyperbolic plane and then mapped to the unit disc for display on screen. Nodes in the centre of the disc are largest and nodes are assigned progressively less space towards the perimeter of the disc. Cheops (3) is based on multiple re-use of overlaid triangles in the display. Working top-down, the selection of a node (triangle) at a particular level designates that node's children are to be represented