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Abstract
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Many high dimensional classi?cation techniques have been proposed in the literature based on sparse linear discriminant analysis (LDA). To e?ciently use them, sparsity of linear classi?ers is a prerequisite. However, this might not be readily available in many applications and rotations of data are required to create the needed sparsity. In this paper, we propose a surprisingly simple rotation to create the required sparsity. The basic idea is to use the principal components of the sample covariance matrix of the pooled samples or its simple variants to rotate the data ?rst and to then apply an existing high dimensional classi?er. This rotate-and-solve procedure can be combined with any existing classi?ers, and is robust against the sparse level of the true model. We show that this rotation does create the sparsity needed for high dimensional classi?cations. The methodological power is demonstrated by a number of simulation and real data examples and the improvements of our method over some popular high dimensional classi?cation rules are clearly shown. Extensions of the proposed rotate-and-solve procedure and possible future work will be presented at the end.
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