Although widely used, Multilinear PCA (MPCA), one of the leading multilinear analysis methods, still suffers from four major drawbacks. First, it is very sensitive to outliers and noise. Second, it is unable to cope with missing values. Third, it is computationally expensive since MPCA deals with large multi-dimensional datasets. Finally, it is unable to maintain the local geometrical structures due to the averaging process. This paper proposes a novel approach named Compressed Submanifold Multifactor Analysis (CSMA) to solve the four problems mentioned above. Our approach can deal with the problem of missing values and outliers via SVD-L1. The Random Projection method is used to obtain the fast low-rank approximation of a given multifactor dataset. In addition, it is able to preserve the geometry of the original data. Our CSMA method can be used efficiently for multiple purposes, e.g. noise and outlier removal, estimation of missing values, biometric applications. We show that CSMA method can achieve good results and is very efficient in the inpainting problem as compared to [1], [2]. Our method also achieves higher face recognition rates compared to LRTC, SPMA, MPCA and some other methods, i.e. PCA, LDA and LPP, on three challenging face databases, i.e. CMU-MPIE, CMU-PIE and Extended YALE-B.