High-dimensional classification has become an increasingly important problem. In this paper we propose a “Multivariate Adaptive Stochastic Search” (MASS) approach which first reduces the dimension of the data space and then applies a standard classification method to the reduced space. One key advantage of MASS is that it automatically adjusts to mimic variable selection type methods, such as the Lasso, variable combination methods, such as PCA, or methods that combine these two approaches. The adaptivity of MASS allows it to perform well in situations where pure variable selection or variable combination methods fail. Another major advantage of our approach is that MASS can accurately project the data into very low-dimensional non-linear, as well as linear, spaces. MASS uses a stochastic search algorithm to select a handful of optimal projection directions from a large number of random directions in each iteration. We provide some theoretical justification for MASS and demonstrate its strengths on an extensive range of simulation studies and real world data sets by comparing it to many classical and modern classification methods.
"A multivariate adaptive stochastic search method for dimensionality reduction in classification." Ann. Appl. Stat. 4 (1) 340 - 365, March 2010. https://doi.org/10.1214/09-AOAS284