Visual analysis of high dimensional point clouds using topological landscapes

Oesterling, Patrick; Heine, Christian; Jänicke, Heike; Scheuermann, Gerik

doi:10.1109/pacificvis.2010.5429601

Cited by 24 publications

(24 citation statements)

References 23 publications

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“…The Safari Interface [10] plotted number of connected components for different time steps and isovalues and provided pop-up renderings of isosurfaces as the mouse hovered over the plot. More recently, topological landscapes [22,9,16] used a terrain as proxy representation for the contour tree. Related work on topological volume rendering [23] displayed the transfer function directly on the contour tree.…”

Section: Design Galleriesmentioning

confidence: 99%

Topological Galleries: A High Level User Interface for Topology Controlled Volume Rendering

MacCarthy¹,

Carr²,

Weber³

2011

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Existing topological interfaces to volume rendering are limited by their reliance on sophisticated knowledge of topology by the user. We extend previous work by describing topological galleries, an interface for novice users that is based on the design galleries approach. We report three contributions: an interface based on hierarchical thumbnail galleries to display the containment relationships between topologically identifiable features, the use of the pruning hierarchy instead of branch decomposition for contour tree simplification, and drag-and-drop transfer function assignment for individual components. Initial results suggest that this approach suffers from limitations due to rapid drop-off of feature size in the pruning hierarchy. We explore these limitations by providing statistics of feature size as function of depth in the pruning hierarchy of the contour tree.

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Section: Design Galleriesmentioning

confidence: 99%

Topological Galleries: A High Level User Interface for Topology Controlled Volume Rendering

MacCarthy¹,

Carr²,

Weber³

2011

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“…To achieve this, we use a topology-based projection which critically depends on a single parameter which has to be found by interacting with the visualization. This interactive analysis [17] supports the user to iteratively find the desired parameter, and therefore the desired information. In the end, since clustering information leads to only coarse insights, we deem our data layout as an initial point for further exploration.…”

Section: Work Was Supported By the Us Department Of Energy Under Comentioning

confidence: 99%

“…For, e.g., clustering purposes, a meaningful scalar function should also be defined in the void part of a data set (where there are no vertices) in order to appropriately separate dense regions from regions of low density. Therefore, Oesterling et al [17] focus on the appropriate construction of a point set's scalar function, supported by a neighborhood description by means of the Gabriel graph [7], instead of deriving a manifold from the function. In the end, their 3-D data layout reflects the topology of the data's approximated density function, realized by the topological landscape metaphor [24], a 3-D terrain which has the same topology as the input data set.…”

Section: Related Workmentioning

confidence: 99%

“…In order to avoid this second projection error, the intermediate space could be analyzed directly, instead of considering the point cloud in either the original m-dimensional space or in the 2-D/ 3-D space. Oesterling et al [17] describe a method to analyze a point cloud's structure in higher dimensions followed by a topology-based projection to obtain a 3-D layout of the data which describes the structure in the original space. The basic idea is to describe the point cloud's structure indirectly by constructing a scalar function which appropriately reflects the data distribution in terms of density.…”

Section: Approximating a Point Cloud's Topologymentioning

confidence: 99%

“…Due space limitations, we refer to [17] and [24] for further information, since they introduce and explain a number of other concepts unrelated to the contributions of this work.…”

Section: Approximating a Point Cloud's Topologymentioning

confidence: 99%

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Two-stage framework for a topology-based projection and visualization of classified document collections

Oesterling

Scheuermann

Teresniak

et al. 2010

2010 IEEE Symposium on Visual Analytics Science and Technology

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Figure 1: Island-like visualization of a document point cloud's topological structure. By sharing similar dimensions, documents accumulate in subspaces of the high dimensional information space. Considering dimensions as words, clusters are assumed to describe topics, i.e., islands, in the final visualization. ABSTRACTDuring the last decades, electronic textual information has become the world's largest and most important information source available. People have added a variety of daily newspapers, books, scientific and governmental publications, blogs and private messages to this wellspring of endless information and knowledge. Since neither the existing nor the new information can be read in its entirety, computers are used to extract and visualize meaningful or interesting topics and documents from this huge information clutter.In this paper, we extend, improve and combine existing individual approaches into an overall framework that supports topological analysis of high dimensional document point clouds given by the well-known tf-idf document-term weighting method. We show that traditional distance-based approaches fail in very high dimensional spaces, and we describe an improved two-stage method for topology-based projections from the original high dimensional information space to both two dimensional (2-D) and three dimensional (3-D) visualizations. To show the accuracy and usability of this framework, we compare it to methods introduced recently and apply it to complex document and patent collections.

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