Predictive nonlinear biplots: maps and trajectories

Vines, S. K. (2015). Predictive nonlinear biplots: maps and trajectories. Journal of Multivariate Analysis, 140 pp. 47–59.

DOI: https://doi.org/10.1016/j.jmva.2015.04.010

Abstract

When the difference between samples is measured using a Euclidean embeddable dissimilarity function, observations and the associated variables can be displayed on a nonlinear biplot. Furthermore, a nonlinear biplot is predictive if information on variables is added in such a way that it allows the values of the variables to be estimated for points in the biplot. In this paper an r dimensional biplot which maps the predicted value of a variable for every point in the plot, is introduced. Using such maps it is shown that even with continuous data, predicted values do not always vary continuously across the biplot plane. Prediction trajectories that appropriate for summarising such non-continuous prediction maps are also introduced. These prediction trajectories allow information about two or more variables to be estimated even when the underlying predicted values do not vary continuously.

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About

• Item ORO ID
• 42599
• Item Type
• Journal Item
• ISSN
• 0047-259X
• Project Funding Details

• Funded Project Name	Project ID	Funding Body
  Not Set	Not Set	The Open University (OU)

• Keywords
• Euclidean-embeddable dissimilarity function; Nonlinear biplot; normal projection; prediction; prediction region; predictive trajectory
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Depositing User
• Karen Vines