Face Recognition as a Kronecker product equation

Martijn Boussé, Nico Vervliet, Otto Debals, Lieven De Lathauwer


Various parameters influence face recognition such as expression, pose, and illumination. In contrast to matrices, tensors can be used to naturally accommodate for the different modes of variation. The multilinear singular value decomposition (MLSVD) then allows one to describe each mode with a factor matrix and the interaction between the modes with a coefficient tensor. In this paper, we show that each image in the tensor satisfying an MLSVD model can be expressed as a structured linear system called a Kronecker Product Equation (KPE). By solving a similar KPE for a new image, we can extract a feature vector that allows us to recognize the person with high performance. Additionally, more robust results can be obtained by using multiple images of the same person under different conditions, leading to a coupled KPE. Finally, our method can be used to update the database with an unknown person using only a few images instead of an image for each combination of conditions. We illustrate our method for the extended Yale Face Database B, achieving better performance than conventional methods such as Eigenfaces and other tensor-based techniques.

Code description

This package provides experiment files and auxiliary files for the face recognition paper.


M. Boussé, N. Vervliet, O. Debals, L. De Lathauwer, "Face recognition as a Kronecker product equation," in Proceedings of the 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2017, Curacao, Dutch Antilles), pp. 276-280, Dec. 2017.

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This repository can be cited as:
S. Hendrikx, M. Boussé, N. Vervliet, M. Vandecappelle, R. Kenis, and L. De Lathauwer, Tensorlab⁺, Available online, Version of Dec 2022 downloaded from https://www.tensorlabplus.net.