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Parallel Coordinates: Interactive Visualisation for High Dimensions

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Trends in Interactive Visualization

Part of the book series: Advanced Information and Knowledge Processing ((AI&KP))

Abstract

This story is about multidimensional visualization with Parallel Coordinates (abbr. ||-coords) which transform the search for relations in multivariate datasets into a 2-dimensional pattern recognition problem. The discovery process is illustrated by finding:

  • ground features from remote sensing satellite data, and

  • useful rules for gold, foreign currencies and stockmarket trading from a nancial dataset.

A complex dataset with two categories is classified using a geometric classification algorithm based on ||-coords. The minimal set of variables required to state the rule is found and ordered by their predictive value. A visual model of a real country's economy is constructed showing how multivariate relations can be modeled by means of hypersurfaces. Interior points corresponding to feasible economic policies are constructed interactively finding that two sectors unknowingly compete for the same group of workers. An overview of modern ||-coords provides foundational understanding. The representation of an M-dimensional hypersurface is obtained from its (M−1) subsets which are constructed recursively from its points. There are examples of surfaces where convexity can be seen in any dimension as well as non-orientability(as in the Möbius strip), and features like folds, crevices, bumps which are hidden or distorted in other types of displays. This is a prelude of what is on the way: recursive multidimensional interactivity for uncovering the secrets in massive datasets.

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Notes

  1. 1.

    1 The venerable name “Exploratory Data Analysis” EDAis used interchangeably with the currently more fashionable “Visual Data Mining.”.

  2. 2.

    2 MDG'’s Ltd proprietary software -– All Rights Reserved, is used by permission.

  3. 3.

    3 Suggesting that the Landsat Thematic mapper band 4 filters out water though unknown to me.

  4. 4.

    4 I am grateful to Prof. R. Coiffman and group at the Math./CS Depts Yale University for this dataset.

References

  1. Bollobas. B. 1979.Graph Theory. Springer-Verlag, New York,

    MATH  Google Scholar 

  2. A. Chatterjee. Visualizing Multidimensional Polytopes and Topologies for Tolerances. Ph.D. Thesis, Dept. Comp. Sci., Univ. of S. Calif., 1995.

    Google Scholar 

  3. Chatterjee, A. Das, and P. P. Bhattacharya. S. 1993.Visualization in Linear Programming Using Parallel Coordinates. Pattern Recognit, 26–11:1725–1736,

    Article  Google Scholar 

  4. Choi and H. Lee. H. 2005.PCAV: Internet Attack Visualization in Parallel Coordinates, LNCS 3783, Springer-Verlag, New York, 454–466.

    Google Scholar 

  5. T. Chomut. Exploratory Data Analysis in Parallel Coordinates. M.Sc. Thesis, Dept. Comp. Sci. UCLA, 1987.

    Google Scholar 

  6. Cohan and S. M. Yang. D. C. H. 1986.Mobility Analysis in Parallel Coordinates. J. Mech. Mach., 21:63–71,

    Article  Google Scholar 

  7. Desai and A. Walters. L.C. 1991.Graphical Representation of Data Envelopment Analyses: Management Implications from Parallel Axes Representations. Dec. Sci., 22:(2)335–353,

    Article  Google Scholar 

  8. J. Eickemeyer. Visualizing p-ats in N-Space Using Parallel Coordinates. Ph.D. Thesis, Dept. Comp. Sc., UCLA, 1992.

    Google Scholar 

  9. U. M. Fayad, G. P. Piatesky-Shapiro Smyth, and R. Uthurusamy. Advances in Knowledge Discovery and Data Mining. AAAI/MIT Press, Cambridge Mass, 1996.

    Google Scholar 

  10. P. Fiorini and A. Inselberg. Con_guration Space Representation in Parallel Coordinates. IEEE Conf. Rob. & Aut., 1215–1220, 1989.

    Google Scholar 

  11. M. Friendly and al. Milestones in Thematic Cartography. www.math.yorku.ca/scs/SCS/Gallery/milestones/, 2005.

  12. Gennings, C. Dawson, K. S. Carter, and W. H. Myers. R. H. 1990.Interpreting plots of a Multidimensional dose-Response Surface in Parallel Coordinates. Biometrics, 46:719–735,

    Article  Google Scholar 

  13. Harary. F. 1969.Graph Theory. Addison-Wesley, Reading, Mass.,

    Google Scholar 

  14. H. Hauser. Parallel Sets: Visual Analysis of Categorical Data. Proc. IEEE Infovis, 2005.

    Google Scholar 

  15. Helly. J. 1987.Applications of Parallel Coordinates to Complex System Design and Operation. Proc. Nat. Comp. Grap. Assoc. vol. III, 541–546,

    Google Scholar 

  16. C. K. Hung and A. Inselberg. Parallel Coordinate Representation of Smooth Hypersurfaces. USC Tech. Report # CS – 92–531, Univ. of Southern California, Los Angeles, 1992.

    Google Scholar 

  17. Hung and C. K. Inselberg. A. 2007.Description of Surfaces in Parallel Coordinates by Linked Planar Regions, Mathematics of Surfaces XII, 177–208, LNCS 4647. Springer-Verlag, New York,

    Google Scholar 

  18. A. Inselberg. N-Dimensional Graphics. LASC Tech. Rep. G320-2711, 140. IBM, 1981.

    Google Scholar 

  19. A. Inselberg. Parallel Coordinates for Multidimensional Displays. Proc. IEEE Conf. on Spatial Infor., Sioux Falls, SD, 312–324. IEEE Comp. Soc., Los Alamitos, CA, 1984.

    Google Scholar 

  20. A. Inselberg. Intelligent Instrumentation and Process Control. Proc. 2nd IEEE Conf. on AI Appl., 302–307. IEEE Comp. Soc., Los Alamitos, CA, 1985.

    Google Scholar 

  21. Inselberg. A. 1985.The Plane with Parallel Coordinates. Visual Computer, 1:69–97,

    Article  MATH  Google Scholar 

  22. A. Inselberg. Discovering Multi-Dimensional Structure with Parallel Coordinates (Invited Paper). In Proc. of ASA. Stat. Graphics 1–16. Amer. Stat. Assoc., 1989.

    Google Scholar 

  23. Inselberg. A. 2008.Parallel Coordinates: VISUAL Multidimensional Geometry and its Applications. Springer, New York,

    Google Scholar 

  24. A. Inselberg and T. Avidan. The Automated Multidimensional Detective. In Proc. of IEEE Information Visualization ‘99, 112–119. IEEE Comp. Soc., Los Alamitos, CA, 1999.

    Google Scholar 

  25. A. Inselberg and B. Dimsdale. Parallel Coordinates: A Tool for Visualizing Multi-Dimensional Geometry. Proc. of IEEE Conf. on Visualization, 361–378. IEEE Comp. Soc., Los Alamitos, CA, 1990.

    Google Scholar 

  26. Inselberg, A. Reif, and M. Chomut. T. 1987.Convexity Algorithms in Parallel Coordinates. J. ACM, 34:765–801,

    Article  MathSciNet  Google Scholar 

  27. A. Inselberg, M. Boz, and B. Dimsdale. Planar Conict Resolution Algorithm for Air-Traffic Control and the One-Shot Problem, in IBM PASC Tech. Rep. G320–3559. IBM Palo Alto Scientific Center, 1991.

    Google Scholar 

  28. Jones. C. 1996.Visualization and Optimization. Kluwer Academic Publishers, Boston,

    MATH  Google Scholar 

  29. T. Matskewich, A. Inselberg, and M. Bercovier. Approximated Planes in Parallel Coordinates. Proc. of Geom. Model. Conf., St. Malo, Vanderbilt Univ. Press, 257–266, 2000.

    Google Scholar 

  30. T. M. Mitchell. Machine Learning. McGraw-Hill, New York , 1997.

    Google Scholar 

  31. J. R. Quinlan. C4.5: Programs for Machine Learning. Morgan Kaufman, San Francisco 1993.

    Google Scholar 

  32. J. Rivero and A. Inselberg. Extension al Analisis del Espacio De Fase de Systemas Dinamicos por las Coordinadas Parallelas. Proc. VII Systems EngrWorkshop, Santiago, Chile, 1984.

    Google Scholar 

  33. C. Schmid and H. Hinterberger. Comparative Multivariate Vis. Across Conceptually Different Graphic Displays. In Proc. of 7th SSDBM. IEEE Comp. Soc., Los Alamitos, CA, 1994.

    Google Scholar 

  34. Tufte. E. R. 1983.The Visual Display of Quantitative Information. Graphic Press, Connecticut,

    Google Scholar 

  35. Tufte. E. R. 1990.Envisioning Information. Graphic Press, Connecticut,

    Google Scholar 

  36. Tufte. E. R. 1996.Visual Explanation. Graphic Press, Connecticut,

    Google Scholar 

  37. M. O. Ward. XmdvTool: Integrating Multiple Methods for Visualizing Multivariate Data. Proc. IEEE Conf. on Vis., CA, 326–333. IEEE Comp. Soc., Los Alamitos, CA, 1994.

    Google Scholar 

  38. Wegman. E. 1990.Hyperdimensional Data Analysis Using Parallel Coordinates. J. Amer. Stat. Assoc., 85:664–675,

    Article  Google Scholar 

  39. Yang. L. 2005.Prunning & Visualizing Generalized Association Rules in Parallel Coordinates. IEEE Knowledge Data Eng., 15:(1)60–70,

    Article  Google Scholar 

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Acknowledgements

I am very grateful to David Adjiashvili who wrote the magnificent interactive software displaying the ||-coords representation of surfaces as seen in Figs. 3.25–3.30. Also I thank the two anonymous referees for their constructive and helpful suggestions.

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  1. Alfred Inselberg
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    Inselberg, A. (2009). Parallel Coordinates: Interactive Visualisation for High Dimensions. In: Liere, R., Adriaansen, T., Zudilova-Seinstra, E. (eds) Trends in Interactive Visualization. Advanced Information and Knowledge Processing. Springer, London. https://doi.org/10.1007/978-1-84800-269-2_3

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    • DOI: https://doi.org/10.1007/978-1-84800-269-2_3

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    • Online ISBN: 978-1-84800-269-2

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