Tensor is a multidimensional array which is an extension of matrix that arises frequently in our daily life such as video, microarray data, EEG data, ctc. Tensor factorization can be considered higher-order gencralization of matrix SVD or PCA, but they also have much differences, such as NP essential of deciding higher-order tensor rank, non-optimal property of higher-order tensor factorization. There are still many other tensor factorizations, such as block-oriented decomposition, DEDICOM, CANDELINC.  Tensor factorizations have wide applications in data reconstruction, cluster analysis,  compression etc.