This paper surveys many attemps of solving problems of processing multidimensional data by means of projection pursuit (PP) and gives them a common framework. It shows that special procedures as principal components, multidimensional scaling, factor analysis, non-parametric regression, density estimation, and approximation are special cases of PP.
The paper includes: Explanation and discussion of basic concepts and corresponding definitions for PP. Functions classifying projections (projection indices) and their invariance and equivariance properties. Robust multivariate estimators. Application of PP in regression analysis, density approximation and estimation (also its consistency). Connections to tomography and time series analysis. Finite sample version of PP methods and their implementation.
The paper is accompanied by fifteen contributions of twenty two authors discussing some of its points.