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High-dimensional data refers to data with a large number of variables. Classifying these data is a difficult problem because the enormous number of variables poses challenges to conventional classification methods and renders many classical techniques impractical. A natural solution is to add a dimensionality reduction step before a classification technique is applied. We Propose three methods to deal with this problem: a simulated annealing (SA) based method, a multivariate adaptive stochastic search (MASS) method, and a functional adaptive classification (FAC) method. The third method considers functional predictors. They all utilize stochastic search algorithms to select a handful of optimal transformation directions from a large number of random directions in each iteration. These methods are designed to mimic variable selection type methods, such as the Lasso, or variable combination methods, such as PCA, or a method that combines the two approaches. We demonstrate the strengths of our methods on an extensive range of simulation and real-world studies.

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Siva Tian is an Assistant Professor in the Department of Psychology at the University of Houston. She received her Ph.D. in Quantitative Psychology and an M.S. in Statistics at the University of Southern California.

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