Orthogonal Nonnegative Tucker Decomposition
This work addresses tensor decomposition for nonnegative data in domains such as image analysis, but it appears incremental as it builds on existing Tucker decomposition methods.
The paper tackles the problem of decomposing nonnegative tensor data by proposing an orthogonal nonnegative Tucker decomposition (ONTD), and numerical results demonstrate its effectiveness in applications like face recognition and hyperspectral unmixing.
In this paper, we study the nonnegative tensor data and propose an orthogonal nonnegative Tucker decomposition (ONTD). We discuss some properties of ONTD and develop a convex relaxation algorithm of the augmented Lagrangian function to solve the optimization problem. The convergence of the algorithm is given. We employ ONTD on the image data sets from the real world applications including face recognition, image representation, hyperspectral unmixing. Numerical results are shown to illustrate the effectiveness of the proposed algorithm.