Tensor vs Matrix Methods: Robust Tensor Decomposition under Block Sparse Perturbations

Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient ascent (a variant of the tensor power method), and hard thresholding of the residual. We prove convergence to the globally optimal solution under natural incoherence conditions on the low rank component, and bounded level of sparse perturbations. We compare our method with natural baselines which apply robust matrix PCA either to the {\em flattened} tensor, or to the matrix slices of the tensor. Our method can provably handle a far greater level of perturbation when the sparse tensor is block-structured. This naturally occurs in many applications such as the activity detection task in videos. Our experiments validate these findings. Thus, we establish that tensor methods can tolerate a higher level of gross corruptions compared to matrix methods

Rapport d'activite 1990-1992 - Centre de spectrometrie nucleaire et de spectrometrie de masse

SIGLEAvailable at INIST (FR), Document Supply Service, under shelf-number : 14741, issue : a.1985/7 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Osmium dithiophosphates. Synthesis, X-ray crystal structure, spectroscopic and electrochemical properties

The reactions of ammonium salt of dialkyldithiophosphate ligands, (RO)2PS2 −NH4 + (R=Me/Et) with (NH4)2OsIVBr6 in methanol solvent and under dinitrogen atmosphere result in one-electron paramagnetic tris complexes, {(RO)2PS2}3OsIII (1a–1b) in the solid state. The molecular structure of one complex (1a) has been determined by single-crystal X-ray diffraction. It shows the expected pseudo-octahedral geometry with reasonable strain due to the presence of four-membered chelate rings. The reflectance spectra of the solid complexes display two broad bands in the range 552–484 nm and in the solid-state complexes exhibit one isotropic EPR signal at 77 K. Although the complexes 1a–1b are found to be stable in the solid state, in solution state the complexes are transformed selectively into the diamagnetic and electrically non-conducting metal–metal bonded dimeric species [{(RO)2PS2}3OsIII–OsIII{S2P(OR)2}3]. The formation of dimeric species in the solution state is authenticated by the electrospray mass spectrum of one representative complex where R=Et (1b). In dichloromethane solution the complexes show two moderately strong sulfur to osmium charge-transfer transitions in the visible region and two strong ligand based transitions in the UV region. The complexes exhibit successive two oxidations correspond to OsIV–OsIV/OsIII–OsIII and OsV–OsV/OsIV–OsIV processes near 0.8 and 1.9 V versus SCE, respectively. One reductive couple corresponds to the OsIII–OsIII/OsII–OsII couple has been observed near −0.6 V. Electrochemically generated oxidized species [{(RO)2PS2}3OsIV–OsIV{S2P(OR)2}3]2+ display lowest energy ligand to metal charge-transfer transition near 550 nm which has observed to be reasonably red shifted as compared to that of the parent trivalent species. On the other hand electrochemically generated reduced species [{(RO)2PS2}3OsII–OsII{S2P(OR)2}3]2− are found to be unstable even on coulometric time scale.© Elsevie

Ruthenium dithiophosphates: synthesis, X-ray crystal structure, spectroscopic and electrochemical properties

The reactions of ammonium salts of dialkyldithiophosphate ligands, (RO)2PS2−NH4+ (R=Me/Et), with RuIIICl3·3H2O in methanol solvent and under N2 atmosphere result in one-electron paramagnetic tris complexes {(RO)2PS2}3RuIII (1) in the solid state. The molecular structures of both complexes were determined by single-crystal X-ray diffraction. This shows the expected pseudo-octahedral geometry with reasonable strain due to the presence of a four-membered chelate ring. The reflectance spectra of the solid complexes display two bands in the range 596–476 nm and in the solid state the complexes exhibit one isotropic EPR signal at 77 K. Although the complexes 1 are stable in the solid state, in solution the complexes are transformed selectively into the diamagnetic and electrically non-conducting sulfur-bridged dimetallic species [{(RO)2PS2}2RuIV(μ-S)2RuIV{S2P(OR)2}2]. The formation of dimeric species in the solution state is authenticated by the electrospray mass spectrum of one representative complex where R=Et (1b). In dichloromethane solution the complexes show two moderately strong sulfur to ruthenium charge-transfer transitions in the range 514–419 nm, and two strong ligand based transitions in the UV region. The complexes exhibit two successive reversible reductions in the ranges 1.01→0.91 V and −0.44→−0.49 V versus SCE corresponding to RuIV–RuIV/RuIII–RuIII and RuIII–RuIII/RuII–RuII couples respectively. Electrochemically or chemically generated first step reduced complexes [{(RO)2PS2}2RuIII(μ-S)2RuIII{S2P(OR)2}2]2− display two ligand to metal charge-transfer transitions in the visible region and in the complexes the two one-electron paramagnetic metal centers (low-spin RuIII, t2g5, S=1/2) are antiferromagnetically coupled. The second step reduced species [{(RO)2PS2}2RuII(μ-S)2RuII{S2P(OR)2}2]4− are observed to be very unstable.© Elsevie