Interpretable Projection Pursuit

Published in: Laboratory for Computational Statistics, no. 106 (Stanford, CA : Stanford University, Oct. 1989)

by Sally C. Morton

Read More

Access further information on this document at

This article was published outside of RAND. The full text of the article can be found at the link above.

The goal of this thesis is to modify projection pursuit by trading accuracy for interpretability. The modification produces a more parsimonious and understandable model without sacrificing the structure which projection pursuit seeks. The method retains the nonlinear versatility of projection pursuit while clarifying the results. Following an introduction which outlines the dissertation, the first and second chapters contain the technique as applied to exploratory projection pursuit and projection pursuit regression respectively. The interpretability of a description is measured as the simplicity of the coefficients which define its linear projections. Several interpretability indices for a set of vectors are defined based on the ideas of rotation in factor analysis and entropy. The two methods require slightly different indices due to their contrary goals. A roughness penalty weighting approach is used to search for a more parsimonious description, with interpretability replacing smoothness. The computational algorithms for both interpretable exploratory projection pursuit and interpretable projection pursuit regression are described. In the former case, a rotationally invariant projection index is needed and defined. In the latter, alterations in the original algorithm are required. Examples of real data are considered in each situation. The third chapter deals with the connections between the proposed modification and other ideas which seek to produce more interpretable models. The modification as applied to linear regression is shown to be analogous to a nonlinear continuous method of variable selection. It is compared with other variable selection techniques and is analyzed in a Bayesian context. Possible extensions to other data analysis methods are cited and avenues for future research are identified. The conclusion addresses the issue of sacrificing accuracy for parsimony in general. An example of calculating the tradeoff between accuracy and interpretability due to a common simplifying action, namely rounding the binwidth for a histogram, illustrates the applicability of the approach.

This report is part of the RAND Corporation External publication series. Many RAND studies are published in peer-reviewed scholarly journals, as chapters in commercial books, or as documents published by other organizations.

Our mission to help improve policy and decisionmaking through research and analysis is enabled through our core values of quality and objectivity and our unwavering commitment to the highest level of integrity and ethical behavior. To help ensure our research and analysis are rigorous, objective, and nonpartisan, we subject our research publications to a robust and exacting quality-assurance process; avoid both the appearance and reality of financial and other conflicts of interest through staff training, project screening, and a policy of mandatory disclosure; and pursue transparency in our research engagements through our commitment to the open publication of our research findings and recommendations, disclosure of the source of funding of published research, and policies to ensure intellectual independence. For more information, visit

The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.