We introduce new dictionary learning methods for tensor-variate data of any order. We represent each data item as a sum of Kruskal decomposed dictionary atoms within the framework of beta-process factor analysis (BPFA). Our model is nonparametric and can infer the tensor-rank of each dictionary atom. This Kruskal-Factor Analysis (KFA) is a natural generalization of BPFA. We also extend KFA to a deep convolutional setting and develop online learning methods. We test our approach on image processing and classification tasks achieving state of the art results for 2D & 3D inpainting and Caltech 101. The experiments also show that atom-rank impacts both overcompleteness and sparsity.
Revised: May 2, 2017 |
Published: April 20, 2017
Citation
Stevens A.J., Y. Pu, Y. Sun, G. Spell, and L. Carin. 2017.Tensor-Dictionary Learning with Deep Kruskal-Factor Analysis. In Proceedings of the 20th International Conference on Artificial Intelligence and Statistics (AISTATS 2017), April 20-22, 2017, Fort Lauderdale, Florida, 54, 121-129. Cambridge:Proceedings of Machine Learning Research Press.PNNL-SA-121675.