Tensor decompositions for Face Recognition

Automatic Face Recognition has become increasingly important in the past few years due to its several applications in daily life, such as in social media platforms and security services. Numerical linear algebra tools such as the SVD (Singular Value Decomposition) have been extensively used to allow machines to automatically process images in the recognition and classification contexts. On the other hand, several factors such as expression, view angle and illumination can significantly affect the image, making the processing more complex. To cope with these additional features, multilinear algebra tools, such as high-order tensors are being explored. In this thesis we first analyze tensor calculus and tensor approximation via several dif- ferent decompositions that have been recently proposed, which include HOSVD (Higher-Order Singular Value Decomposition) and Tensor-Train formats. A new algorithm is proposed to perform data recognition for the latter format.