000222948 001__ 222948
000222948 005__ 20181202195915.0
000222948 02470 $$2ArXiv$$aarXiv:1611.04835
000222948 037__ $$aCONF
000222948 245__ $$aMultilinear Low-Rank Tensors on Graphs & Applications
000222948 260__ $$c2016
000222948 269__ $$a2016
000222948 336__ $$aConference Papers
000222948 520__ $$aWe propose a new framework for the analysis of low- rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the classical low-rank SVD for matrices and multi- linear SVD for tensors. Then, building on this novel decomposition we construct a general class of convex optimization problems for approximately solving low-rank tensor inverse problems, such as tensor Robust PCA. The whole frame- work is named as “Multilinear Low-rank tensors on Graphs (MLRTG)”. Our theoretical analysis shows: 1) MLRTG stands on the notion of approximate stationarity of multi- dimensional signals on graphs and 2) the approximation error depends on the eigen gaps of the graphs. We demonstrate applications for a wide variety of 4 artificial and 12 real tensor datasets, such as EEG, FMRI, BCI, surveillance videos and hyperspectral images. Generalization of the tensor concepts to non-euclidean domain, orders of magnitude speed-up, low-memory requirement and significantly enhanced performance at low SNR are the key aspects of our framework.
000222948 700__ $$0248142$$aShahid, Nauman$$g232886
000222948 700__ $$0(EPFLAUTH)264158$$aGrassi, Francesco$$g264158
000222948 700__ $$0240428$$aVandergheynst, Pierre$$g120906
000222948 8564_ $$uhttps://arxiv.org/abs/1611.04835$$zURL
000222948 8564_ $$s11183654$$uhttps://infoscience.epfl.ch/record/222948/files/cvpr_arxiv.pdf$$yPreprint$$zPreprint
000222948 8560_ $$falain.borel@epfl.ch
000222948 909C0 $$0252392$$pLTS2$$xU10380
000222948 909CO $$ooai:infoscience.tind.io:222948$$pconf$$pSTI$$pGLOBAL_SET
000222948 917Z8 $$x232886
000222948 917Z8 $$x232886
000222948 937__ $$aEPFL-CONF-222948
000222948 973__ $$aEPFL$$rREVIEWED
000222948 980__ $$aCONF