Orthogonal Nonnegative Tucker Decomposition
Junjun Pan, Michael K. Ng, Ye Liu, Xiongjun Zhang, Hong Yan
Abstract
In this paper, we study 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, and hyperspectral unmixing. Numerical results are shown to illustrate the effectiveness of the proposed algorithm.
Topics & Concepts
MathematicsAugmented Lagrangian methodTucker decompositionConvergence (economics)Karush–Kuhn–Tucker conditionsDecompositionTensor decompositionRelaxation (psychology)Representation (politics)Image (mathematics)Tensor (intrinsic definition)Applied mathematicsMathematical optimizationAlgorithmArtificial intelligenceComputer sciencePure mathematicsPsychologyLawEconomicsPoliticsBiologyEconomic growthPolitical scienceSocial psychologyEcologyTensor decomposition and applicationsSparse and Compressive Sensing TechniquesAdvanced Neuroimaging Techniques and Applications