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Using tours to visually investigate properties of new projection pursuit indexes with application to problems in physics

Author

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  • Ursula Laa

    (Monash University
    Monash University)

  • Dianne Cook

    (Monash University)

Abstract

Projection pursuit is used to find interesting low-dimensional projections of high-dimensional data by optimizing an index over all possible projections. Most indexes have been developed to detect departure from known distributions, such as normality, or to find separations between known groups. Here, we are interested in finding projections revealing potentially complex bivariate patterns, using new indexes constructed from scagnostics and a maximum information coefficient, with a purpose to detect unusual relationships between model parameters describing physics phenomena. The performance of these indexes is examined with respect to ideal behaviour, using simulated data, and then applied to problems from gravitational wave astronomy. The implementation builds upon the projection pursuit tools available in the R package, tourr, with indexes constructed from code in the R packages, binostics, minerva and mbgraphic.

Suggested Citation

  • Ursula Laa & Dianne Cook, 2020. "Using tours to visually investigate properties of new projection pursuit indexes with application to problems in physics," Computational Statistics, Springer, vol. 35(3), pages 1171-1205, September.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:3:d:10.1007_s00180-020-00954-8
    DOI: 10.1007/s00180-020-00954-8
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    References listed on IDEAS

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    1. Ju Ahn & Heike Hofmann & Dianne Cook, 2003. "A Projection Pursuit Method on the multidimensional squared Contingency Table," Computational Statistics, Springer, vol. 18(3), pages 605-626, September.
    2. Huang, Bei & Cook, Dianne & Wickham, Hadley, 2012. "tourrGui: A gWidgets GUI for the Tour to Explore High-Dimensional Data Using Low-Dimensional Projections," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 49(i06).
    3. Loperfido, Nicola, 2018. "Skewness-based projection pursuit: A computational approach," Computational Statistics & Data Analysis, Elsevier, vol. 120(C), pages 42-57.
    4. F. Ferraty & A. Goia & E. Salinelli & P. Vieu, 2013. "Functional projection pursuit regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 293-320, June.
    5. Simon N. Wood & Natalya Pya & Benjamin Säfken, 2016. "Smoothing Parameter and Model Selection for General Smooth Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1548-1563, October.
    6. Posse, Christian, 1995. "Projection pursuit exploratory data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 20(6), pages 669-687, December.
    7. Eun-Kyung Lee & Dianne Cook & Sigbert Klinke & Thomas Lumley, 2005. "Projection Pursuit for Exploratory Supervised Classification," SFB 649 Discussion Papers SFB649DP2005-026, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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    Cited by:

    1. Ursula Laa & Dianne Cook & Andreas Buja & German Valencia, 2020. "Hole or grain? A Section Pursuit Index for Finding Hidden Structure in Multiple Dimensions," Monash Econometrics and Business Statistics Working Papers 17/20, Monash University, Department of Econometrics and Business Statistics.
    2. Nicola Loperfido, 2023. "Kurtosis removal for data pre-processing," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(1), pages 239-267, March.

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