A projection pursuit approach to variable selection

A variable selection criterion based on projection pursuit is developed, exploiting the attractive property of projection pursuit methods to detect and ignore non informative variables in the cluster analysis context. Importance coefficients are introduced in order to measure the contribution of each variable to the definition of the projection pursuit solution. Each importance coefficient depends on the absolute value of the coefficient associated to each variable in the projection pursuit solution and on the variability of the corresponding variable. The selection criterion consists in retaining those variables which present an importance coefficient greater than a suitably chosen threshold. This is determined considering that in the no structure k-variate case the vectors of importance coefficients are uniformly distributed on the unit k-sphere, The good performances of the proposed method, tested both on real and simulated data, along with its simplicity, make it a valid competitor to the classical variable selection methods. (C) 2001 Elsevier Science B.V. All rights reserved.