Spatially Ordered Treemaps

Existing treemap layout algorithms suffer to some extent from poor or inconsistent mappings between data order and visual ordering in their representation, reducing their cognitive plausibility. While attempts have been made to quantify this mismatch, and algorithms proposed to minimize inconsistency, solutions provided tend to concentrate on one-dimensional ordering. We propose extensions to the existing squarified layout algorithm that exploit the two-dimensional arrangement of treemap nodes more effectively. Our proposed spatial squarified layout algorithm provides a more consistent arrangement of nodes while maintaining low aspect ratios. It is suitable for the arrangement of data with a geographic component and can be used to create tessellated cartograms for geovisualization. Locational consistency is measured and visualized and a number of layout algorithms are compared. CIELab color space and displacement vector overlays are used to assess and emphasize the spatial layout of treemap nodes. A case study involving locations of tagged photographs in the Flickr database is described

Augmenting citation chain aggregation with article maps

Presentation slides available at: https://www.gesis.org/fileadmin/upload/kmir2014/paper4_slides.pdfThis paper presents Voyster, an experimental system that combines citation chain aggregation (CCA) and spatial-semantic maps to support citation search. CCA uses a three-list view to represent the citation network surrounding a ‘pearl’ of known relevant articles, whereby cited and citing articles are ranked according to number of pearl relations. As the pearl grows, this overlap score provides an effective proxy for relevance. However, when the pearl is small or multi-faceted overlap ranking provides poor discrimination. To address this problem we augment the lists with a visual map, wherein articles are organized according to their content similarity. We demonstrate how the article map can help the user to make relevant choices during the early stages of the search pro-cess and also provide useful insights into the thematic structure of the local citation network

HierarchyMap: A Novel Approach to Treemap Visualization of Hierarchical Data

The HierarchyMap describes a novel approach for Treemap Visualization method for representing large volume of hierarchical information on a 2-dimensional space. HierarchyMap algorithm is a new ordered treemap algorithm. Results of the implementation of HierarchyMap treemap algorithm show that it is capable of representing several thousands of hierarchical data on 2-dimensional space on a computer and Portable Device Application (PDA) screens while still maintaining the qualities found in existing treemap algorithms such as readability, low aspect ratio, reduced run time, and reduced number of thin rectangles. The HierarchyMap treemap algorithm is implemented in Java programming language and tested with dataset of Departmental and Faculty systems of Universities, Family trees, Plant and Animal taxonomy structure

QuizMap: Open social student modeling and adaptive navigation support with TreeMaps

In this paper, we present a novel approach to integrate social adaptive navigation support for self-assessment questions with an open student model using QuizMap, a TreeMap-based interface. By exposing student model in contrast to student peers and the whole class, QuizMap attempts to provide social guidance and increase student performance. The paper explains the nature of the QuizMap approach and its implementation in the context of self-assessment questions for Java programming. It also presents the design of a semester-long classroom study that we ran to evaluate QuizMap and reports the evaluation results. © 2011 Springer-Verlag Berlin Heidelberg

Fat Polygonal Partitions with Applications to Visualization and Embeddings

Let $\mathcal{T}$ be a rooted and weighted tree, where the weight of any node is equal to the sum of the weights of its children. The popular Treemap algorithm visualizes such a tree as a hierarchical partition of a square into rectangles, where the area of the rectangle corresponding to any node in $\mathcal{T}$ is equal to the weight of that node. The aspect ratio of the rectangles in such a rectangular partition necessarily depends on the weights and can become arbitrarily high. We introduce a new hierarchical partition scheme, called a polygonal partition, which uses convex polygons rather than just rectangles. We present two methods for constructing polygonal partitions, both having guarantees on the worst-case aspect ratio of the constructed polygons; in particular, both methods guarantee a bound on the aspect ratio that is independent of the weights of the nodes. We also consider rectangular partitions with slack, where the areas of the rectangles may differ slightly from the weights of the corresponding nodes. We show that this makes it possible to obtain partitions with constant aspect ratio. This result generalizes to hyper-rectangular partitions in $\mathbb{R}^d$. We use these partitions with slack for embedding ultrametrics into $d$-dimensional Euclidean space: we give a $\mathop{\rm polylog}(\Delta)$-approximation algorithm for embedding $n$-point ultrametrics into $\mathbb{R}^d$ with minimum distortion, where $\Delta$ denotes the spread of the metric, i.e., the ratio between the largest and the smallest distance between two points. The previously best-known approximation ratio for this problem was polynomial in $n$. This is the first algorithm for embedding a non-trivial family of weighted-graph metrics into a space of constant dimension that achieves polylogarithmic approximation ratio.Comment: 26 page

Configuring Hierarchical Layouts to Address Research Questions

We explore the effects of selecting alternative layouts in hierarchical displays that show multiple aspects of large multivariate datasets, including spatial and temporal characteristics. Hierarchical displays of this type condition a dataset by multiple discrete variable values, creating nested graphical summaries of the resulting subsets in which size, shape and colour can be used to show subset properties. These 'small multiples' are ordered by the conditioning variable values and are laid out hierarchically using dimensional stacking. Crucially, we consider the use of different layouts at different hierarchical levels, so that the coordinates of the plane can be used more effectively to draw attention to trends and anomalies in the data. We argue that these layouts should be informed by the type of conditioning variable and by the research question being explored. We focus on space-filling rectangular layouts that provide data-dense and rich overviews of data to address research questions posed in our exploratory analysis of spatial and temporal aspects of property sales in London. We develop a notation ('HiVE') that describes visualisation and layout states and provides reconfiguration operators, demonstrate its use for reconfiguring layouts to pursue research questions and provide guidelines for this process. We demonstrate how layouts can be related through animated transitions to reduce the cognitive load associated with their reconfiguration whilst supporting the exploratory process