Face recognition is used in different fields and is considered as a difficult problem due to different factors, such as lighting, image angle, face expression, which significantly affect clasification process of an image. Multilinear algebra enables us to sort images in an object considering multiple categories and offers mathematical framework for dealing with these objects (tensors). We present the idea of face recognition with linear algebra using singular value decomposition. Further, we define basics of multilinear algebra, describe higher order singular value decomposition, extension of the matrix singular value decomposition, and usefulness of this decomposition in data mining. We explain how to use higher order singular value decomposition on a tensor that is constructed of face images considering three categories, and show results on an example using the Extended Yale Face Database B database.
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