Multilinear principal component analysis

Multilinear extension of principal component analysis

Multilinear principal component analysis (MPCA) is a multilinear extension of principal component analysis (PCA) that is used to analyze M-way arrays, also informally referred to as "data tensors". M-way arrays may be modeled by linear tensor models, such as CANDECOMP/Parafac, or by multilinear tensor models, such as multilinear principal component analysis (MPCA) or multilinear independent component analysis (MICA). The origin of MPCA can be traced back to the tensor rank decomposition introduced by Frank Lauren Hitchcock in 1927; to the Tucker decomposition; and to Peter Kroonenberg's "3-mode PCA" work. In 2000, De Lathauwer et al. restated Tucker and Kroonenberg's work in clear and concise numerical computational terms in their SIAM paper entitled "Multilinear Singular Value Decomposition", (HOSVD) and in their paper "On the Best Rank-1 and Rank-(R1, R2, ..., RN ) Approximation of Higher-order Tensors".

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