2021
DOI: 10.3390/math9111249
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A Multidimensional Principal Component Analysis via the C-Product Golub–Kahan–SVD for Classification and Face Recognition

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 som… Show more

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Cited by 11 publications
(6 citation statements)
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“…In the case of tensors, harmonic Ritz lateral slices furnish approximations of eigenvectors of  H ⋆  associated with harmonic Ritz tubes of  H ⋆ . The harmonic Ritz tubes θj of  H ⋆  associated with the partial tensor tridiagonalization defined in (14) are the eigentubes of the generalized eigenvalue problem ( (…”
Section: Augmentation By Harmonic Ritz Lateral Slicesmentioning
confidence: 99%
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“…In the case of tensors, harmonic Ritz lateral slices furnish approximations of eigenvectors of  H ⋆  associated with harmonic Ritz tubes of  H ⋆ . The harmonic Ritz tubes θj of  H ⋆  associated with the partial tensor tridiagonalization defined in (14) are the eigentubes of the generalized eigenvalue problem ( (…”
Section: Augmentation By Harmonic Ritz Lateral Slicesmentioning
confidence: 99%
“…Using this identification, PCA for third‐order tensors that represent color images is structurally very similar to PCA for matrices that represent grayscale images. The latter is described in Reference 14.…”
Section: Multidimensional Principal Component Analysis For Facial Rec...mentioning
confidence: 99%
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