  Face recognition and identification is a very important application in
machine learning. Due to the increasing amount of available data, traditional
approaches based on matricization and matrix PCA methods can be difficult to
implement. Moreover, the tensorial approaches are a natural choice, due to the
mere structure of the databases, for example in the case of color images.
Nevertheless, even though various authors proposed factorization strategies for
tensors, the size of the considered tensors can pose some serious issues. When
only a few features are needed to construct the projection space, there is no
need to compute a SVD on the whole data. Two versions of the tensor Golub-Kahan
algorithm are considered in this manuscript, as an alternative to the classical
use of the tensor SVD which is based on truncated strategies. In this paper, we
consider the Tensor Tubal Golub Kahan Principal Component Analysis method which
purpose is to extract the main features of images using the tensor singular
value decomposition (SVD) based on the tensor cosine product that uses the
discrete cosine transform. This approach is applied for classification and face
recognition and numerical tests show its effectiveness.
