  Principal component analysis (PCA) is an unsupervised method for learning
low-dimensional features with orthogonal projections. Multilinear PCA methods
extend PCA to deal with multidimensional data (tensors) directly via
tensor-to-tensor projection or tensor-to-vector projection (TVP). However,
under the TVP setting, it is difficult to develop an effective multilinear PCA
method with the orthogonality constraint. This paper tackles this problem by
proposing a novel Semi-Orthogonal Multilinear PCA (SO-MPCA) approach. SO-MPCA
learns low-dimensional features directly from tensors via TVP by imposing the
orthogonality constraint in only one mode. This formulation results in more
captured variance and more learned features than full orthogonality. For better
generalization, we further introduce a relaxed start (RS) strategy to get
SO-MPCA-RS by fixing the starting projection vectors, which increases the bias
and reduces the variance of the learning model. Experiments on both face (2D)
and gait (3D) data demonstrate that SO-MPCA-RS outperforms other competing
algorithms on the whole, and the relaxed start strategy is also effective for
other TVP-based PCA methods.
