This paper proposes a novel approach named Compressed Submanifold Multifactor Analysis (CSMA) to concisely and precisely deal with multifactor analysis. Compared to the state-of-the-art MPCA method that loses the original local geometry structures of input factors due to the averaging process, our proposed approach can preserve their original geometry. In addition, the fast low-rank approximation of a given dataset with multifactors is also provided using Random Projection to reduce space requirements and give more transparent representation. Our proposed method achieves both fastest running time and highest accuracy in the face recognition problem compared to MPCA and some other multifactor based methods on two challenging databases, i.e. CMU-MPIE and Extended YALE-B.
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