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A common thread in various approaches for model reduction, clustering, feature extraction, classification, and blind source separation (BSS) is to represent the original data by a lower-dimensional approximation obtained via matrix or tensor (multiway array) factorizations or decompositions. The notion of matrix/tensor factorizations arises in a wide range of important applications and each matrix/tensor factorization makes different assumptions regarding component (factor) matrices and their underlying structures. So choosing the appropriate one is critical in each application domain. Approximate low-rank matrix and tensor factorizations play fundamental roles in enhancing the data and extracting latent (hidden) components.