Papers › Sequential and Simultaneous Distance-based Dimension Reduction
Sequential and Simultaneous Distance-based Dimension Reduction
Yijin Ni, Chuanping Yu, Andy Ko, Xiaoming Huo
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This paper introduces a method called Sequential and Simultaneous Distance-based Dimension Reduction (S²D²R) that performs simultaneous dimension reduction for a pair of random vectors based on Distance Covariance (dCov). Compared with Sufficient Dimension Reduction (SDR) and Canonical Correlation Analysis (CCA)-based approaches, S²D²R is a model-free approach that does not impose dimensional or distributional restrictions on variables and is more sensitive to nonlinear relationships. Theoretically, we establish a non-asymptotic error bound to guarantee the performance of S²D²R. Numerically, S²D²R performs comparable to or better than other state-of-the-art algorithms and is computationally faster. All codes of our S²D²R method can be found on Github, including an R package named S2D2R.
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