Dimension Reduction for Tensor Classification
This article develops a sufficient dimension reduction method for high dimensional regression with tensor predictors, which extends the conventional vector-based dimension reduction model. It proposes a tensor dimension reduction model that assumes that a response depends on some low-dimensional representation of tensor predictors through an unspecified link function. A sequential iterative dimension reduction algorithm (SIDRA) that effectively utilizes the tensor structure is proposed to estimate the parameters. The SIDRA generalizes the method in Zhong and Suslick (2012), which proposes an iterative estimation algorithm for matrix classification. Preliminary studies demonstrate that the tensor dimension reduction model is a rich and flexible framework for high dimensional tensor regression, and SIDRA is a powerful and computationally efficient method.
KeywordsDimension Reduction Tensor Structure Tensor Classification Misclassification Error Simple Vectorization
This work was supported by one National Science Foundation grant DMS 1107029 to PZ and two National Science Foundation grant DMS 1120256 and DMS 1228288 and one National Institutes of Health grant R01 DK062777 to WZ.
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