Eigenvalues of Quaternion Tensors with Applications to Color Video Processing

This paper studies the eigenvalues of quaternion tensors and their applications. Firstly, we investigate the definitions and properties of the left and right eigenvalues of the quaternion tensors. Then we establish the quaternion tensor Lanczos method to calculate the eigenvalues and eigentensors of a Hermitian quaternion tensor and the principal component analysis for the quaternion tensor. Moreover, we present the k -means method for quaternion tensor and use it to color video clustering. Finally, we conducted experiments to prove the effectiveness of the proposed theory and algorithms.