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parallel coordinates for Multidimensional Data Visualization: Basic Concepts

COMPUTING IN SCIENCE & ENGINEERING 2015年第3期17卷 70-76页

作者： Heinrich, Julian Weiskopf, Daniel CSIRO Digital Prod Clayton Vic Australia Univ Stuttgart Stuttgart Germany

parallel coordinates provide a flexible and effective way of showing multidimensional data. The authors describe basic concepts, geometric models, and their use in visualization.

关键词： data visualisation parallel processing geometric models multidimensional data visualization parallel coordinates Data management Data visualization Scientific computing Visualization Visualization data plots multidimensional data scientific computing

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parallel coordinates in three dimensions and sharp spectral isoperimetric inequalities

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RICERCHE DI MATEMATICA 2022年第1期71卷 41-52页

作者： Vikulova, Anastasia V. LD Landau Inst Theoret Phys Pr Ak Semenova 1a Chernogolovka 142432 Russia

In this paper we show how the method of parallel coordinates can be extended to three dimensions. As an application, we prove the conjecture of Antunes et al. (Adv Calc Var 10:357-380, 2017) that "the ball maximises the first Robin eigenvalue with negative boundary parameter among all convex domains of equal surface area" under the weaker restriction that the boundary of the domain is diffeomorphic to the sphere and convex or axiconvex. We also provide partial results in arbitrary dimensions.

关键词： Robin Laplacian Negative boundary parameter Eigenvalue optimisation parallel coordinates

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parallel coordinates - A TOOL FOR VISUALIZING MULTIDIMENSIONAL GEOMETRY

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1ST IEEE CONF ON VISUALIZATION ( VISUALIZATION 90 )

作者： INSELBERG, A DIMSDALE, B IBM Scientific Center Los Angeles CA USA

A methodology for visualizing analytic and synthetic geometry in RN is presented. It is based on a system of parallel coordinates which induces a nonprojective mapping between N-dimensional and two-dimensional sets. H... 详细信息

ISBN: (纸本)0818620838

A methodology for visualizing analytic and synthetic geometry in R^N is presented. It is based on a system of parallel coordinates which induces a nonprojective mapping between N-dimensional and two-dimensional sets. Hypersurfaces are represented by their planar images which have some geometrical properties analogous to the properties of the hypersurface that they represent. A point ← → line duality when N = 2 generalizes to lines and hyperplanes enabling the representation of polyhedra in R^N. The representation of a class of convex and non-convex hypersurfaces is discussed, together with an algorithm for constructing and displaying any interior point. The display shows some local properties of the hypersurface and provides information on the point's proximity to the boundary. Applications are discussed.

关键词： MULTIDIMENSIONAL GEOMETRY VISUALIZATION parallel coordinates STATISTICAL GRAPHICS

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parallel coordinates-based Visual Analytics for Materials Property 10

Parallel Coordinates-based Visual Analytics for Materials Pr...

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14th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP) / 10th International Conference on Information Visualization Theory and Applications (IVAPP)

作者： Bhattarai, Diwas Zhang, Jian Karki, Bijaya B. Louisiana State Univ Sch Elect Engn & Comp Sci Baton Rouge LA 70803 USA

ISBN: (纸本)9789897583544

Because of major advances in experimental and computational techniques, materials data are abundant even for specific classes of materials such as magma-forming silicate melts. A given material property M can be posed as a complex multivariate data problem. The relevant variables or dimensions are the values of the property itself, the factors which influence the property (pressure P, temperature T, multicomponent composition X), and meta data information I. Here we present an innovative visual analytics system for the melt viscosity (eta), which can be represented by M (eta, P, T, X-1, X-2, ..., I-1, I-2, ...). Our system consists of a viscosity data store along with a web-based visualization support. In particular, we enrich the parallel coordinates plot with non-standard features, such as derived axes/sub-axes, dimension merging, binary scaling, and nested plot. It offers many insights of relevance to underlying physics, data modeling, and guiding future experiments/computations. Other material properties such as density can be incorporated as new attributes and corresponding new axes in the plot. Our aim is to collect all published data on various melt properties and develop a framework supporting database, visualization and modelling functions.

关键词： parallel coordinates Multivariate Visual Analytics Materials Property Viscosity Data

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Angle-uniform parallel coordinates

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Computational Visual Media 2023年第3期9卷 495-512页

作者： Kaiyi Zhang Liang Zhou Lu Chen Shitong He Daniel Weiskopf Yunhai Wang School of Computer Science and Technology Shandong UniversityQingdao 266237China National Institute of Health Data Science Peking UniversityBeijing 100191China Visualization Research Center(VISUS) University of Stuttgart70569 StuttgartGermany

We present angle-uniform parallel coordinates,a data-independent technique that deforms the image plane of parallel coordinates so that the angles of linear relationships between two variables are linearly mapped along the horizontal axis of the parallel coordinates *** being a common method for visualizing multidimensional data,parallel coordinates are ineffective for revealing positive correlations since the associated parallel coordinates points of such structures may be located at infinity in the image plane and the asymmetric encoding of negative and positive correlations may lead to unreliable *** address this issue,we introduce a transformation that bounds all points horizontally using an angleuniform mapping and shrinks them vertically in a structure-preserving fashion;polygonal lines become smooth curves and a symmetric representation of data correlations is *** further propose a combined subsampling and density visualization approach to reduce visual clutter caused by *** method enables accurate visual pattern interpretation of data correlations,and its data-independent nature makes it applicable to all multidimensional *** usefulness of our method is demonstrated using examples of synthetic and real-world datasets.

关键词： parallel coordinates multidimensional data deformation correlations

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On the usability of three-dimensional display in parallel coordinates: Evaluating the efficiency of identifying two-dimensional relationships

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INFORMATION VISUALIZATION 2014年第1期13卷 29-41页

作者： Johansson, Jimmy Forsell, Camilla Cooper, Matthew Linkoping Univ C Res SE-60174 Norrkoping Sweden

In recent years, several different attempts have been made to extend the well-known technique of parallel coordinates using a three-dimensional display. This article presents an evaluation that investigates the performance of the three-dimensional parallel coordinates technique and compares it with standard, two-dimensional parallel coordinates for analysis of two-dimensional relationships. Three-dimensional parallel coordinates, based on parallel planes instead of parallel axes, have been used for many years within the information visualization community for a variety of applications. Despite its quite common use, no formal evaluation detailing its usefulness for different tasks has been conducted. The evaluation presented in this article is the first step towards determining the usefulness of this type of three-dimensional parallel coordinates. The study compared three-dimensional parallel coordinates, using two different axis configurations commonly seen in the literature, with standard two-dimensional parallel coordinates for identification of two-dimensional relationships between variables in multivariate data. This type of task and the relationships to be judged are known to be well supported by two-dimensional parallel coordinates and multi-relational three-dimensional parallel coordinates. The results show that for identification of two-dimensional relationships, two-dimensional parallel coordinates are superior to the three-dimensional extensions, in terms of both response time and accuracy. Subjective opinions were also in favour of two-dimensional parallel coordinates. This study adds to the much-needed body of work examining the usability of three-dimensional representations in information visualization and for what tasks and data a proposed method is or is not appropriate.

关键词： Information visualization evaluation usability parallel coordinates 3D parallel coordinates

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Real-time detection of lines using parallel coordinates and CUDA

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JOURNAL OF REAL-TIME IMAGE PROCESSING 2014年第1期9卷 205-216页

作者： Havel, Jiri Dubska, Marketa Herout, Adam Josth, Radovan Brno Univ Technol Graph FIT Brno 61266 Czech Republic

The Hough transform is a well-known and popular algorithm for detecting lines in raster images. The standard Hough transform is rather slow to be usable in real time, so different accelerated and approximated algorithms exist. This study proposes a modified accumulation scheme for the Hough transform, using a new parameterization of lines "PClines". This algorithm is suitable for computer systems with a small but fast read-write memory, such as today's graphics processors. The algorithm requires no floating-point computations or goniometric functions. This makes it suitable for special and low-power processors and special-purpose chips. The proposed algorithm is evaluated both on synthetic binary images and on complex real-world photos of high resolutions. The results show that using today's commodity graphics chips, the Hough transform can be computed at interactive frame rates, even with a high resolution of the Hough space and with the Hough transform fully computed.

关键词： Line detection parallel coordinates CUDA implementation Hough transform Real-time detection

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Scalable Multivariate Volume Visualization and Analysis Based on Dimension Projection and parallel coordinates

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IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2012年第9期18卷 1397-1410页

作者： Guo, Hanqi Xiao, He Yuan, Xiaoru Peking Univ Key Lab Machine Percept Minist Educ Beijing 100871 Peoples R China Peking Univ Sch EECS Beijing 100871 Peoples R China Peking Univ Ctr Computat Sci & Engn Beijing 100871 Peoples R China

In this paper, we present an effective and scalable system for multivariate volume data visualization and analysis with a novel transfer function interface design that tightly couples parallel coordinates plots (PCP) and MDS-based dimension projection plots. In our system, the PCP visualizes the data distribution of each variate (dimension) and the MDS plots project features. They are integrated seamlessly to provide flexible feature classification without context switching between different data presentations during the user interaction. The proposed interface enables users to identify relevant correlation clusters and assign optical properties with lassos, magic wand, and other tools. Furthermore, direct sketching on the volume rendered images has been implemented to probe and edit features. With our system, users can interactively analyze multivariate volumetric data sets by navigating and exploring feature spaces in unified PCP and MDS plots. To further support large-scale multivariate volume data visualization and analysis, Scalable Pivot MDS (SPMDS), parallel adaptive continuous PCP rendering, as well as parallel rendering techniques are developed and integrated into our visualization system. Our experiments show that the system is effective in multivariate volume data visualization and its performance is highly scalable for data sets with different sizes and number of variates.

关键词： Multivariate volume transfer function parallel coordinates dimension projection user-interface design parallel visualization

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Visual clustering in parallel coordinates

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COMPUTER GRAPHICS FORUM 2008年第3期27卷 1047-1054页

作者： Zhou, Hong Yuan, Xiaoru Qu, Huamin Cui, Weiwei Chen, Baoquan Hong Kong Univ Sci & Technol Dept Comp Sci & Engn Hong Kong Hong Kong Peoples R China Peking Univ Sch EECS Beijing Peoples R China Peking Univ Key Lab Machine Percept Minist Educ Beijing Peoples R China Chinese Acad Sci Shenzhen Inst Adv Technol Beijing 100864 Peoples R China

parallel coordinates have been widely applied to visualize high-dimensional and multivariate data, discerning patterns within the data through visual clustering. However, the effectiveness of this technique on large data is reduced by edge clutter In this paper, we present a novel framework to reduce edge clutter, consequently improving the effectiveness of visual clustering. We exploit curved edges and optimize the arrangement of these curved edges by minimizing their curvature and maximizing the parallelism of adjacent edges. The overall visual clustering is improved by adjusting the shape of the edges while keeping their relative order The experiments on several representative datasets demonstrate the effectiveness of our approach.

关键词： parallel coordinates visual clustering multi-variate data visualization clutter reduction

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Visual Analysis of Multidimensional Big Data: A Scalable Lightweight Bundling Method for parallel coordinates

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IEEE TRANSACTIONS ON BIG DATA 2023年第1期9卷 106-117页

作者： Cui, Wenqiang Strazdins, Girts Wang, Hao Norwegian Univ Sci & Technol Dept ICT & Nat Sci N-6009 Alesund Norway Norwegian Univ Sci & Technol Dept Comp Sci N-2815 Gjovik Norway

Varied edge bundling methods have been used to reduce visual clutter in parallel coordinates plots (PCP). However, existing edge-bundled PCP do not scale well for visual analysis of multidimensional big data and often overplot the bundles in the area near the axes. In this study, we propose a scalable lightweight bundling method to support visual analysis of multidimensional big data in PCP. It helps the users discover trends and detect outliers in the data by bundling the edges between each two adjacent axes independently. We integrate human judgments into the two-dimensional data binning by novel interactions to accelerate the clustering process of the data. We use the frequency-based representation to render the clusters as histogram-like bundles to reveal the distribution of the data and eliminate the overplotting of the bundles. Based on our method, we build a lightweight web-based visual analytics system for exploring multidimensional big data in PCP. The scalability analysis of our method shows that its clustering time increases linearly with the size of the data. Its rendering time is independent of the size of the data. It can cluster and visualize 1 million data records with 6 dimensions in about 1 second in web-based visualization without pre-computation of the data or hardware-accelerated rendering. We conduct two case studies and a user study to compare our method with classic PCP and two state-of-the-art edge-bundled PCP. The results show that our method is more efficient and effective for visually analyzing multidimensional big data.

关键词： Data visualization Big Data Rendering (computer graphics) Image edge detection Clutter Visual analytics Scalability parallel coordinates edge bundling visual analytics big data visualization anomaly detection

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