Jacobi Angles for Simultaneous Diagonalization

By Jean-François Cardoso, Antoine Souloumiac. 1996

Subfields: Mathematical Optimization, Numerical Methods & Scientific Computing

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Citations in the corpus

Beyond CCA: Moment Matching for Multi-View Models (2016, neutral): “Therefore, the workhorses of the method of moments in similar context — orthogonal diagonalization algorithms, such as the tensor power method (Anandkumar et al., 2014), and orthogonal joint diagonalization (Bunse-Gerstner et al., 1993; Cardoso & Souloumiac, 1996) — are not applicable.”
Rethinking LDA: Moment Matching for Discrete ICA (2015, neutral): “Importantly, a fast implementation [23] of the orthogonal joint diagonalization algorithm from [24] was proposed, which is based on closed-form iterative Jacobi updates (see, e.”
On the interpretation of weight vectors of linear models in multivariate neuroimaging (2014, methodology): “For each BSS dataset, independent component analysis was carried out using joint approximate diagonalization (JADE, Cardoso & Souloumiac, 1996), where we used the original code provided by the authors.”
Tensor Factorization via Matrix Factorization (2015, unknown): “We sweep over all i < j, compute the best angle θ in closed form using the formula proposed by Cardoso and Souloumiac [25] to obtain Bt, and then update each Ml by BtMlB > t .”
Towards a general independent subspace analysis (2006, methodology): “Indeed, in the conjecture it is required to use the Jacobi-update algorithm from [5], but this is not necessary, and we can prove the conjecture partially: We want to show that JD implies JBD up to permutation, i.”
Handbook of Blind Source Separation: Independent Component Analysis and Applications (2010, background): “…of vector a traceA trace of matrix A detA determinant of matrix A meana arithmetic average of component of vector a š(ν) Fourier transform of process s(t) ⊗ Kronecker product between matrices ⊗ tensor product •j contraction over index j krank{A} Kruskal’s k-rank of matrix A Contents Glossary 3”
Simultaneous Diagonalization With Similarity Transformation for Non-Defective Matrices (2006, background): “The extension to the complex case is not difficult [7, 9].”
Multimodal Manifold Analysis by Simultaneous Diagonalization of Laplacians (2015, unknown): “Cardoso and Soloumiac [21] show that for a rotation matrix Rθ as in (6), the rotation angle θ minimizing ∑m i=1 off(R T θ LiRθ) can be computed as follows: Let G = ∑m i=1 h(Li)h(Li) , where h(L) = (lii − ljj , lij + lji), and let α = g11 − g22 and β = g12 +g22.”
Measure Transformed Independent Component Analysis (2013, methodology): “The OAJD (Flury and Gautschi, 1986; Cardoso and Souloumiac, 1996) seeks a unitary matrix V̂ ∈ Rp×p, such that V̂Σ̂ (um) Ẑ V̂ T , m = 1, . . . ,M are “as diagonal as possible” by, once again, minimizing a deviation measure from diagonality.”
Blind Source Separation and Independent Component Analysis: A Review (2005, methodology): “Find a unitary joint diagonalizer V of {Mx(kr, τj)} using the joint approximate diagonalization method in [23], which satisfies V T Mx(kr, τj)V = Λr,j , (28)”
Jacobi Algorithm for the Best Low Multilinear Rank Approximation of Symmetric Tensors (2013, methodology): “Jacobi-based algorithms in the literature [9, 18, 17, 5, 6, 37] are designed to solve problems in the framework of ICA or in relation to PARAFAC/CANDECOMP.”