Here we attach all the quality metrics pipelines for all the papers from the taxonomy presented in Section 4.1 and summarized in Table 4.2 that are not part of the examples of this section. We ordered them in the same order that the papers are presented in the taxonomy’s table.
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Figure A.4: Pipeline for“A Projection Pursuit Algorithm for Exploratory Data Analysis”by Fried-man and Tukey [54]: (A) different 2D linear, but not axis-parallel, data projections are computed and evaluated by the quality metric; (B) the best projection direction is chosen by the quality metric, called “usefulness” index, that measures the quality of a projection axis and varies the projection direction so that the index is maximized.
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Figure A.5: Pipeline for “A Rank-by-Feature Framework for Interactive Exploration of Multidi-mensional Data” by Seo and Shneiderman [126]: (A) generation of projections and each 1D and 2D projection is evaluated/ranked by a quality metric selected by theuser; (B) best projections are presented; (C) present ranking scores in a color coded grid (“Score Overview”), as well as an color-coded “Ordered List” for each projection. The userselects one view in the list or grid, and can also change dimension axes and then the view adapts. Please note: here we have a visualization of dimensions and quality metric scores, that are highly interactive, rather than a static projection of data records.
A.3. Quality Metrics Pipelines for the Literature Review 157
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Figure A.6: Pipeline for “Finding and Visualizing Relevant Subspaces for Clustering High-Dimensional Astronomical Data Using Connected Morphological Operators” by Ferdosi et al. [52]:
(A) generation of projections, all above 3D are reduced with PCA; the user can change the smooth-ing parameter, what influences the number of projections; (B) evaluate each view; the user can select the view to inspect.
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Figure A.7: Pipeline for“Graph-Theoretic Scagnostics” by Wilkinson et al. [151]: (A) generation of projections; (B) all 2D views are ranked by several metrics; (C) once the metrics have been computed, they are used to create the SPLOM (rows and columns are the metrics) - projections are mapped as data points.
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Figure A.8: Pipeline for “Selecting good views of high-dimensional data using class consistency”
by Sips et al. [129]: (A) all 2D projections are ranked with the quality metric; (B) each view is associated with a quality metric computed in A; (C) view transformation decides which scatterplot to highlight (fade out) depending on the quality values and the set threshold.
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Figure A.9: Pipeline for“Coordinating computational and visual approaches for interactive feature selection and multivariate clustering” by Guo [59]: (A) all 2D projections are evaluated with the
“minimum conditional entropy (MCE)”; (B) original dimensions are clustered to find an ordering according to their MCE value; (C) matrix ordered according to dimension clustering. The user can 1) select, add to, or subtract from a variable subset that is analyzed further; 2) move the threshold bar for the connecting edges, and clusters are automatically extracted and colored; 3) interact to link, brush and select elements.
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Figure A.10: Pipeline for“Exploring High-D Spaces with Multiform Matrices and Small Multiples”
by MacEachren et al. [98]: (A) automatic selection of potentially interesting subspaces of variables;
the user can also manually select subspaces; (B) all 2D plots are ranked with a quality metric (conditional entropy based); (C) the matrix view is colored and ordered according to the quality metric value. The user can select a dimension subset to be visualized with other visualization techniques.
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Figure A.11: Pipeline for “Improving the Visual Analysis of High-dimensional Datasets Using Quality Measures” by Albuquerque et al. [8] for Jigsaw Maps: (A) mapping of dimension to 2D displays; (B) all 2D plots are ranked with a quality metric to select the best.
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Figure A.12: Pipeline for “Improving the Visual Analysis of High-dimensional Datasets Using Quality Measures” by Albuquerque et al. [8] for RadVis: (A) all views are ranked with a quality metric; (B) dimensions are ordered according to quality values.
A.3. Quality Metrics Pipelines for the Literature Review 159
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Figure A.13: Pipeline for “Improving the Visual Analysis of High-dimensional Datasets Using Quality Measures” by Albuquerque et al. [8] for Table Lens: (A) quality metric is computed on the data (B) user can select an area, marking dimensions and records; the view is than transformed according to the user interaction; (C) colors are mapped according to the quality metrics values for outliers and correlation.
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Figure A.14: Pipeline for“Pragnostics: Screen-Space Metrics for Parallel Coordinates”by Dasputa and Kosara [43]: (A) all 2D views are evaluated according to the metrics; (B) the best pairs are selected to compute the best ordering of dimensions. Theusercan also influence this decision by selecting interesting plots.
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Figure A.15: Pipeline for“Combining automated analysis and visualization techniques for effective exploration of high-dimensional data” by Tatu et al. [133] for HDM: (A) all 2D data tables are evaluated according to the 1D-HDM; (B) create the bestnD visible on the 2D plot (with PCA), evaluated by the 2D-HDM.
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Figure A.16: Pipeline for“High-Dimensional Visual Analytics: Interactive Exploration Guided by Pairwise Views of Point Distributions” by Wilkinson et al. [152]: (A) generation of projections;
(B) all 2D views are evaluated according to quality metric; (C) a sorted/highlighted view is created using the metrics. The usercan navigate trough the ranked list, and sort and highlight plots in this and the SPLOM view.
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Figure A.17: Pipeline for “Clutter Reduction in Multi-Dimensional Data Visualization Using Di-mension Reordering” by Peng et al. [112]: (A) quality metric is computed on the data; (B) quality metric calculated also dependent on the visual abstraction; (C) best visual mapping (ordering) decided based on metric values.
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Figure A.18: Pipeline for “Similarity Clustering of Dimensions for an Enhanced Visualization of Multidimensional Data” by Ankerst et al. [9]: (A) quality metric is computed on the data;
(B) quality metric calculated also dependent on the visual abstraction; (C) best visual mapping (ordering) decided based on metric values.
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Figure A.19: Pipeline for “Quality Metrics for 2D Scatterplot Graphics: Automatically Reducing Visual Clutter” by Bertini and Santucci [24]: (A) quality metric is computed on the data density and screen density and compared; (B) projection and sampling based on metric values.
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Figure A.20: Pipeline for “A Screen Space Quality Method for Data Abstraction” by Johansson and Cooper [80]: (A) sampled and original data tables are associated to quality metric computed on the views of sampled and original data; (B) the values are used to decide upon the sampling rate.
A.3. Quality Metrics Pipelines for the Literature Review 161
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Figure A.21: Pipeline for“Enabling Automatic Clutter Reduction in Parallel Coordinate Plots” by Ellis and Dix [48]: (A) pixel occlusion is measured in the view space; theusercan move a window (lens) and sampling and measuring occlusion is done only in this window (B) the values of the quality metric are used to decide upon the sampling rate.
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Figure A.22: Pipeline for “Pixnostics: Towards Measuring the Value of Visualization” by Schnei-dewind et al. [120]: (A) a subset of dimensions is selected with standard mining techniques; (B) alternative mappings of selected data are evaluated on the screen space; (C) and (D) based on the quality value the best subset and mapping is determined. The user can decide to fix map some data features to visual features manually.