Simultaneous Matrix Diagonalization : the Overcomplete Case

Keywords

Invertible matrix, Matrix (chemical analysis), Set (abstract data type), Row, Mathematics

References

• Signal Processing based on Multilinear AlgebraLieven De Lathauwer — 1997
• Independent component analysis of largely underdetermined mixturesLieven De Lathauwer, Bart De Moor, Joos Vandewalle — 2003
• Jacobi-Algorithm for Simultaneous Generalized Schur Decomposition in Higher-Order-Only ICALieven De Lathauwer, Joos Vandewalle, Bart De Moor — 1998
• Joint Approximate Diagonalization of Positive Definite Hermitian MatricesDinh Tuan Pham — 2000
• Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decompositionJ. Douglas Carroll, Jih-Jie Chang — 1970
• Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statisticsJoseph B. Kruskal — 1977
• An analytical constant modulus algorithmA.-J. van der Veen, A. Paulraj — 1996
• Joint diagonalization via subspace fitting techniquesA.-J. van der Veen — 2001
• Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multi-model factor analysisRichard A. Harshman — 1970
• Blind separation of instantaneous mixtures of nonstationary sourcesDinh-Tuan Pham, J.-F. Cardoso — 2001
• Blind beamforming for non-gaussian signalsJ.-F. Cardoso, Antoine Souloumiac — 1993
• Blind PARAFAC receivers for DS-CDMA systemsNicholas D. Sidiropoulos, Georgios B. Giannakis, Rasmus Bro — 2000
• A blind source separation technique using second-order statisticsAdel Belouchrani, Karim Abed‐Meraim, J.-F. Cardoso — 1997
• Non-orthogonal joint diagonalization in the least-squares sense with application in blind source separationArie Yeredor — 2002
• Blind source separation based on time-frequency signal representationsAdel Belouchrani, Moeness G. Amin — 1998

Cited by

• Multi-Dimensional Signal Decomposition Techniques for the Analysis of EEG DataMartin Dr.-Ing. Weis — 2015
• MAP-Based Underdetermined Blind Source Separation of Convolutive Mixtures by Hierarchical Clustering and -Norm MinimizationStefan Winter, Walter Kellermann, Hiroshi Sawada — 2007
• Convolutive Separation of I.I.D. Signals Based on Simultaneous Tensors DiagonalizationSaloua Rhioui, Éric Moreau — 2006
• Two Approaches for the Blind Identification of Cyclo-Stationary Signals MixturesSaloua Rhioui, Nadège Thirion-Moreau, Éric Moreau — 2007
• Using High-Order Moments to Estimate Linear Independent Factor ModelsStéphane Bonhomme, Madrid Jean-Marc Robin — 2006
• Bi-Iterative Algorithm for Extracting Independent Components From Array SignalsDa‐Zheng Feng, Hua Zhang, Wei Xing Zheng — 2011
• Alternating Least Squares Identification of Under-Determined Mixtures Based on the Characteristic FunctionM. Rajih, Pierre Comon — 2006
• Joint analysis of multiple datasets by cross-cumulant tensor (block) diagonalizationDana Lahat, Christian Jutten — 2016
• Tensor methods for MIMO decoupling using frequency responseJulian Stoev, Tom Oomen, J. Schoukens — 2016
• Tensor methods for MIMO decoupling and control design using frequency response functionsJulian Stoev, Julien Ertveldt, Tom Oomen — 2017
• Geometric Dataset Distances via Optimal TransportDavid Alvarez-Melis, Nicolò Fusi — 2020
• Common EOFs: a tool for multi-model comparison and evaluationAbdel Hannachi, Kathrin Finke, Nickolay T. Trendafilov — 2022
• Chapter 10. Underdetermined Blind Source Separation Using Acoustic ArraysShoji Makino, S. Araki, Stefan Winter and — 2010
• Blind Identification of Noisy UnderDetermined Mixtures Based on Multiple Order Derivatives of the Characteristic FunctionM. Rajih, P. Comon — 2006
• A comparison of two distinct approaches to the blind identification problem of underdetermined mixtures of cyclo-stationary signals with unknown cyclic frequenciesSaloua Rhioui, N. Thirion-Moreau, E. Moreau — 2006

Related papers

• Higher-order power method - application in independent component analysisLieven De Lathauwer, Pierre Comon, Bart De Moor — 1995
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• Blind source separation by higher-order singular value decompositionLieven De Lathauwer, Bart De Moor, Joos Vandewalle — 1994
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