A Block-Jacobi Algorithm for Non-Symmetric Joint Diagonalization of Matrices

Shen, Hao; Kleinsteuber, Martin

doi:10.1007/978-3-319-22482-4_37

Latent Variable Analysis and Signal Separation

2015

DOI: 10.1007/978-3-319-22482-4_37

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A Block-Jacobi Algorithm for Non-Symmetric Joint Diagonalization of Matrices

Hao Shen

Martin Kleinsteuber

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2017

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“…The original version of the paper considered tensor diagonalization through generalized Jacobi (Givens) rotations [34]. An algorithm for two-sided diagonalization of order-3 tensor was proposed in a conference paper [43]. An algorithm for three-sided diagonalization of order-3 tensor was proposed in [44].…”

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Non-orthogonal tensor diagonalization

2017

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Tensor diagonalization means transforming a given tensor to an exactly or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices along selected dimensions of the tensor. It is generalization of approximate joint diagonalization (AJD) of a set of matrices. In particular, we derive (1) a new algorithm for symmetric AJD, which is called two-sided symmetric diagonalization of order-three tensor, (2) a similar algorithm for non-symmetric AJD, also called general two-sided diagonalization of an order-3 tensor, and (3) an algorithm for three-sided diagonalization of order-3 or order-4 tensors. The latter two algorithms may serve for canonical polyadic (CP) tensor decomposition, and they can outperform other CP tensor decomposition methods in terms of computational speed under the restriction that the tensor rank does not exceed the tensor multilinear rank. Finally, we propose (4) similar algorithms for tensor block diagonalization, which is related to the tensor block-term decomposition.

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Non-orthogonal tensor diagonalization

2017

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A Block-Jacobi Algorithm for Non-Symmetric Joint Diagonalization of Matrices

Cited by 1 publication

References 13 publications

Non-orthogonal tensor diagonalization

Non-orthogonal tensor diagonalization

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