Combining variable selection with dimensionality reduction

TL;DR: This paper bridges the gap between variable selection methods and dimensionality reduction algorithms by applying variable selection followed bydimensionality reduction, and the resulting algorithm benefits from complex features as variable selection algorithms do, and at the same time enjoys the benefits of Dimensionality reduction.

Abstract: This paper bridges the gap between variable selection methods (e.g., Pearson coefficients, KS test) and dimensionality reduction algorithms (e.g., PCA, LDA). Variable selection algorithms encounter difficulties dealing with highly correlated data, since many features are similar in quality. Dimensionality reduction algorithms tend to combine all variables and cannot select a subset of significant variables. Our approach combines both methodologies by applying variable selection followed by dimensionality reduction. This combination makes sense only when using the same utility function in both stages, which we do. The resulting algorithm benefits from complex features as variable selection algorithms do, and at the same time enjoys the benefits of dimensionality reduction.