A Multidimensional Principal Component Analysis via the C-Product Golub–Kahan–SVD for Classification and Face Recognition

Mustapha Hached, Khalide Jbilou, Christos Koukouvinos and Marilena Mitrouli
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Mustapha Hached: University of Lille, CNRS, UMR 8524—Laboratoire Paul Painlevé, F-59000 Lille, France
Khalide Jbilou: Laboratoire LMPA, 50 rue F. Buisson, ULCO, 62228 Calais, France
Christos Koukouvinos: Department of Mathematics, National Technical University of Athens, Zografou, 15773 Athens, Greece
Marilena Mitrouli: Department of Mathematics, National and Kapodistrian University of Athens Panepistimiopolis, 15784 Athens, Greece

Mathematics, 2021, vol. 9, issue 11, 1-17

Abstract: Face recognition and identification are very important applications 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. Indeed, the most demanding part of the computational effort in recognition or identification problems resides in the training process. 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 it 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.

Keywords: cosine product; Golub–Kahan algorithm; Krylov subspaces; PCA; SVD; tensors (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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