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

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