Sufficient dimension reduction is a body of theory and methods for reducing the dimensionality of predictors while preserving information on regressions. In this paper we propose a sparse dimension reduction method to perform interpretable dimension reduction. It is designed for situations in...

Given symmetric matrices B,D∈ℝ<Superscript> n×n </Superscript> and a symmetric positive definite matrix W∈ℝ<Superscript> n×n </Superscript>, maximizing the sum of the Rayleigh quotient <Emphasis Type="Bold">x <Superscript>⊤</Superscript> D <Emphasis Type="Bold">x and the generalized Rayleigh quotient <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\frac{\mathbf{x}^{\top}B \mathbf{x}}{\vphantom{\mathrm{I}^{\mathrm{I}}}\mathbf{x}^{\top}W\mathbf{x} }$</EquationSource> </InlineEquation>...</equationsource></inlineequation></emphasis></superscript></emphasis></superscript></superscript>