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Structure revealing techniques based on parallel coordinates plot

VISUAL COMPUTER 2012年第6-8期28卷 541-551页

作者： Zhao, Xin Kaufman, Arie SUNY Stony Brook Dept Comp Sci Stony Brook NY 11794 USA

parallel coordinates plot (PCP) is an excellent tool for multivariate visualization and analysis, but it may fail to reveal inherent structures for complex and large datasets. Therefore, polyline clustering and coordinate sorting are inevitable for the accurate data exploration and analysis. In this paper, we propose a suite of novel clustering and dimension sorting techniques in PCP, to reveal and highlight hidden trend and correlation information of polylines. Spectrum theory is first introduced to specifically design clustering and sorting techniques for a clear view of clusters in PCP. We also provide an efficient correlation based sorting technique to optimize the ordering of coordinates to reveal correlated relations, and show how our view-range metrics, generated based on the aggregation constraints, can be used to make a clear view for easy data perception and analysis. Experimental results generated using our framework visually represent meaningful structures to guide the user, and improve the efficiency of the analysis, especially for the complex and noisy data.

关键词： parallel coordinates plot Dimension sorting optimization Visual representation

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Bifocal parallel coordinates plot for Multivariate Data Visualization 13

Bifocal Parallel Coordinates Plot for Multivariate Data Visu...

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13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP) and International Conference on Information Visualization Theory and Applications (IVAPP)

作者： Kaur, Gurminder Karki, Bijaya B. Louisiana State Univ Sch Elect Engn & Comp Sci Baton Rouge LA 70803 USA

ISBN: (纸本)9789897583063

Visualization of multivariate data using parallel coordinates plot (PCP) becomes overwhelming as the number of dimensions/variables increases beyond one dozen or so. Here we propose bifocal parallel coordinates plot (BPCP) based on the focus + context approach. BPCP splits vertically the overall rendering into the focus and context regions whose sizes can be adjusted to optimize the use of the available space. The focus area maps a few selected dimensions of interest, referred to as priority axes, at sufficiently wide spacing. The remaining dimensions are represented in the context area in a compact way so as to retain useful information and provide the data continuity. The focus display can be further enhanced with various options, such as axes overlays, scatterplot, and nested juxtaposed PCPs. In order to accommodate an arbitrarily large number of dimensions, the context display supports multi-level stacked view, each PCP level mapping a subset of the context axes. With flexible interactivity, BPCP can manage the priority axes and data rendering with respect to the corresponding dimensions to support exploratory visualization while providing useful context on the same visualization display.

关键词： parallel coordinates plot Multivariate Data High Dimensions Information Visualization Focus plus Context

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parallel coordinates plotting as a Method in Process Control Hazard Identification

Parallel Coordinates Plotting as a Method in Process Control...

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IEEE Systems and Information Engineering Design Symposium (SIEDS)

作者： Comfort, James R. Warner, Thomas R. Vargo, Erik P. Bass, Ellen J. Univ Virginia Syst & Informat Engn Dept Charlottesville VA 22903 USA

ISBN: (纸本)9781457704475

Abnormal events in process plants waste billions of dollars annually. Taking advantage of plant operators' perceptual capabilities in the hazard identification process could enhance the aiding provided by other decision support systems. parallel coordinate plotting allows the visualization of multidimensional data by making apparent geometric patterns that exist in the data sets. This work investigates the use of parallel coordinate plotting in anomalous process control applications. Approaches utilizing the software packages CVE and CPM as decision support tools are explored. These approaches with CVE and CPM are carried out in a case study on historical plant processing data. CVE is used to identify normal plant operating conditions and construct a "best operating zone" that can be loaded into CPM. CPM can then read in real-time or historical data and indicate (i.e, generate alarms) if the plant is leaving normal operating conditions and also recommend mitigation strategies to return the plant to normal operating conditions. CPM's alarms are evaluated as an effective method for determining the onset of a hazard event. Advantages and limitations of CVE and CPM as a decision support are identified through the case study. The results are discussed in the context of the static case study and the need for simulations is highlighted.

关键词： CPM alarm CVE Data visualization Decision support systems Hazards Process control Real time systems Software packages data visualisation decision support system decision support systems hazards historical plant processing data industrial plants mitigation strategy multidimensional data visualization parallel coordinates plot process control process control hazard identification process plant production engineering computing software package software packages

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A useful tool for computation and interpretation of trading-off solutions through pareto-optimal front in the field of experimental designs for mixtures

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CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS 2016年 158卷 210-217页

作者： Sanchez, M. S. Ortiz, M. C. Sarabia, L. A. Univ Burgos Dept Math & Computat Plaza Misael Banuelos S-N Burgos Spain Univ Burgos Dept Chem Analyt Chem Plaza Misael Banuelos S-N Burgos Spain

An algorithmic implementation is presented to deal with several responses in mixtures problems, without theoretical limits on the number of responses or on the factors to be blended. Also, constrained and unconstrained domains are handled, as well as domains with both mixtures and discrete variables. Besides, an alternative way of interpreting the results coming from the experimental design for mixtures is presented. It is based on the parallel coordinates plots for visualization in more than the usual three-dimensional Cartesian diagrams or the simplex mixture spaces for at most four experimental factors. Specifically, this is done in cases in which more than one experimental response should be handled, tackling the conflict by estimating trading-off solutions via the computation of the pareto-optimal front, which is fully explored with the parallel coordinates plots. The procedure is shown by two case-studies, taken from the literature. The first one deals with several factors in a constrained experimental domain when trying to optimize a detergent by taking into account two severely conflicting characteristics. The second one is about five chemical components blended with different dosage levels for getting a concrete strong enough, experimental results that are re-evaluated by posing a unique blocked design for analysing the data. The joint use of the pareto-optimal front for mixtures designs and the parallel coordinates plots for its visualization provide the researcher a deeper understanding of the problem under study to make accurate decisions.

关键词： Mixtures designs Scheffe designs Pareto optimal front Genetic algorithms parallel coordinates plot

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Flexible Linked Axes for Multivariate Data Visualization

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IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2011年第12期17卷 2310-2316页

作者： Claessen, Jarry H. T. van Wijk, Jarke J. Eindhoven Univ Technol NL-5600 MB Eindhoven Netherlands

Multivariate data visualization is a classic topic, for which many solutions have been proposed, each with its own strengths and weaknesses. In standard solutions the structure of the visualization is fixed, we explore how to give the user more freedom to define visualizations. Our new approach is based on the usage of Flexible Linked Axes: The user is enabled to define a visualization by drawing and linking axes on a canvas. Each axis has an associated attribute and range, which can be adapted. Links between pairs of axes are used to show data in either scatterplot- or parallel coordinates plot-style. Flexible Linked Axes enable users to define a wide variety of different visualizations. These include standard methods, such as scatterplot matrices, radar charts, and PCPs [11];less well known approaches, such as Hyperboxes [1], TimeWheels [17], and many-to-many relational parallel coordinate displays [14];and also custom visualizations, consisting of combinations of scatterplots and PCPs. Furthermore, our method allows users to define composite visualizations that automatically support brushing and linking. We have discussed our approach with ten prospective users, who found the concept easy to understand and highly promising.

关键词： Multivariate data visualization scatterplot parallel coordinates plot

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DSPCP: A Data Scalable Approach for Identifying Relationships in parallel coordinates

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IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2018年第3期24卷 1301-1315页

作者： Hoa Nguyen Rosen, Paul Univ Utah Sci Comp & Imaging Inst Salt Lake City UT 84112 USA Univ S Florida Dept Comp Sci & Engn Tampa FL 33620 USA

parallel coordinates plots (PCPs) are a well-studied technique for exploring multi-attribute datasets. In many situations, users find them a flexible method to analyze and interact with data. Unfortunately, using PCPs becomes challenging as the number of data items grows large or multiple trends within the data mix in the visualization. The resulting overdraw can obscure important features. A number of modifications to PCPs have been proposed, including using color, opacity, smooth curves, frequency, density, and animation to mitigate this problem. However, these modified PCPs tend to have their own limitations in the kinds of relationships they emphasize. We propose a new data scalable design for representing and exploring data relationships in PCPs. The approach exploits the point/ line duality property of PCPs and a local linear assumption of data to extract and represent relationship summarizations. This approach simultaneously shows relationships in the data and the consistency of those relationships. Our approach supports various visualization tasks, including mixed linear and nonlinear pattern identification, noise detection, and outlier detection, all in large data. We demonstrate these tasks on multiple synthetic and real-world datasets.

关键词： Correlation parallel coordinates plot large data visualization

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New cluster mapping tools for the graphical assessment of non-dominated solutions in multi-objective optimization

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CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS 2012年 114卷 72-86页

作者： Cela, R. Bollain, M. H. Univ Santiago de Compostela Food Res Inst Dept Analyt Chem Nutr & Food Sci Santiago De Compostela Spain

Two new graphical tools for the interpretation of Pareto fronts and the selection of non-dominated solutions produced in multi-objective optimization processes (MOOPs), are presented. The first is a version of the parallel coordinates plots (PCP), modified by combining the PCP with the dendrogram representing the cluster analysis of non-dominated solutions in the decision variable space or in the objective space. A correspondence plot that simplifies interpretation of the above plots has also been developed. The second graphical tool is a cluster map (PFCM), produced by combining the information provided by the dendrograms calculated in the decision and the objective spaces, to provide a two-dimensional plot in which the non-dominated solutions are organized according to both dendrograms: the plot is colored on the basis of any of the objectives or a combination of these objectives when convenient. Two derived graphic tools consisting of a combination of the decision variables and the objectives and the dendrograms produced in the decision and the objective spaces have also been developed. All of these graphical tools are demonstrated with several mathematical functions available in the MOOP-related literature and with a real-world optimization process consisting of the computer-assisted method development of high-performance liquid chromatography. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Cluster maps parallel coordinates plot Pareto front visualization Multi-objective optimization

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Speaking Stata: Paired, parallel, or profile plots for changes, correlations, and other comparisons

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STATA JOURNAL 2009年第4期9卷 621-639页

作者： Cox, Nicholas J. Univ Durham Dept Geog Durham England

Paired, parallel, or profile plots showing the values of two variables may be constructed readily using a combination of graph twoway commands. This column explores the principles and practice of such plot-making, considering both wide and long (panel or longitudinal) data structures in which such data may appear. Applications include analysis of change over time or space and indeed ally kind of correlation or comparison between variables. Such plots may be extended to show numeric values and associated name information.

关键词： gr0041 profile plot parallel coordinates plot parallel line plot pair-link diagram bumps charts barometer charts graphics panel data longitudinal data arrows twoway

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Correlated components

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STAT 2016年第1期5卷 45-56页

作者： Cox, Trevor F. Arnold, David S. Univ Liverpool Dept Mol & Clin Canc Med Liverpool L69 3GL Merseyside England Univ Liverpool Dept Biostat Liverpool L69 3GL Merseyside England Unilever R&D Port Sunlight Bebington CH63 3JW England

Principal components analysis is a much used and practical technique for analysing multivariate data, finding a particular set of linear compounds of the variables under consideration, such that covariances between all pairs are 0. An alternative view is that when the variables are considered as axes in a Cartesian coordinate system, then principal components analysis is the particular orthogonal rotation of the axes that makes all the pairwise covariances equal to 0. It is this view that is taken here, but instead of finding the rotation that makes all covariances equal to 0, an orthogonal rotation is found that maximizes the sum of the covariances. The rotation is not unique, except for the two or three component case, and so another criterion can be used alongside so that it too can also be optimized. The motivation is that two highly correlated components will tend to measure the same latent variable but with interesting differences because of the orthogonality between them. Theory is given for identifying the correlated components as well as algorithms for finding them. Two illustrative examples are provided, one involving gene expression data and the other consumer questionnaire data. Copyright (C) 2016 John Wiley & Sons, Ltd.

关键词： correlated components factor analysis gene expression data parallel coordinates plot principal components

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Searching for the optimum multivariate profile of an ash gourd [Benincasa hispida (Thunb.) Cogn.] genotype

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ACTA PHYSIOLOGIAE PLANTARUM 2011年第2期33卷 463-468页

作者： Sanwal, S. K. Kozak, Marcin Verma, Med Ram Indian Inst Vegetable Res Varanasi 221305 Uttar Pradesh India Warsaw Univ Life Sci Fac Agr & Biol Dept Expt Design & Bioinformat PL-02776 Warsaw Poland ICAR Res Complex NEH Reg Div Agr Econ & Stat Barapani 793103 Meghalaya India

Ash gourd is an important vegetable especially in the Indo-China region, but also in America and Africa. It is a monotypic genus, and its genetic pool is considered little diverse, which makes breeding of good ash gourd cultivars difficult. A pool of 56 genotypes, of which 10 are released cultivars and 46 indigenous lines collected from different parts of India, was studied in a two-year experiment. Various traits are important when breeding new cultivars, so an optimum multivariate performance is studied in this germplasm, with a special focus on traits of the greatest importance, namely fruit yield per plant, flesh thickness, vine length, and number of days to female and male flowering. Such performance is studied for the best-yielding genotypes, and promising genotypes in terms of multivariate performance are selected.

关键词： Genotype selection Multivariate selection parallel coordinates plot Plant breeding

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