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Matrix compression along isogenic blocks

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Matrix compression along isogenic blocks. / Belton, Alexander; Guillot, Dominique; Khare, Apoorva et al.
In: Acta Scientiarum Mathematicarum, Vol. 88, No. 1-2, 31.08.2022, p. 417-448.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Belton, A, Guillot, D, Khare, A & Putinar, M 2022, 'Matrix compression along isogenic blocks', Acta Scientiarum Mathematicarum, vol. 88, no. 1-2, pp. 417-448. https://doi.org/10.1007/s44146-022-00023-0

APA

Belton, A., Guillot, D., Khare, A., & Putinar, M. (2022). Matrix compression along isogenic blocks. Acta Scientiarum Mathematicarum, 88(1-2), 417-448. https://doi.org/10.1007/s44146-022-00023-0

Vancouver

Belton A, Guillot D, Khare A, Putinar M. Matrix compression along isogenic blocks. Acta Scientiarum Mathematicarum. 2022 Aug 31;88(1-2):417-448. doi: 10.1007/s44146-022-00023-0

Author

Belton, Alexander ; Guillot, Dominique ; Khare, Apoorva et al. / Matrix compression along isogenic blocks. In: Acta Scientiarum Mathematicarum. 2022 ; Vol. 88, No. 1-2. pp. 417-448.

Bibtex

@article{be58613e4a494199ae134234959235be,
title = "Matrix compression along isogenic blocks",
abstract = "A matrix-compression algorithm is derived from a novel isogenic block decomposition for square matrices. The resulting compression and inflation operations possess strong functorial and spectral-permanence properties. The basic observation that Hadamard entrywise functional calculus preserves isogenic blocks has already proved to be of paramount importance for thresholding large correlation matrices. The proposed isogenic stratification of the set of complex matrices bears similarities to the Schubert cell stratification of a homogeneous algebraic manifold. An array of potential applications to current investigations in computational matrix analysis is briefly mentioned, touching concepts such as symmetric statistical models, hierarchical matrices and coherent matrix organization induced by partition trees.",
author = "Alexander Belton and Dominique Guillot and Apoorva Khare and Mihai Putinar",
year = "2022",
month = aug,
day = "31",
doi = "10.1007/s44146-022-00023-0",
language = "English",
volume = "88",
pages = "417--448",
journal = "Acta Scientiarum Mathematicarum",
issn = "0001-6969",
publisher = "University of Szeged",
number = "1-2",

}

RIS

TY - JOUR

T1 - Matrix compression along isogenic blocks

AU - Belton, Alexander

AU - Guillot, Dominique

AU - Khare, Apoorva

AU - Putinar, Mihai

PY - 2022/8/31

Y1 - 2022/8/31

N2 - A matrix-compression algorithm is derived from a novel isogenic block decomposition for square matrices. The resulting compression and inflation operations possess strong functorial and spectral-permanence properties. The basic observation that Hadamard entrywise functional calculus preserves isogenic blocks has already proved to be of paramount importance for thresholding large correlation matrices. The proposed isogenic stratification of the set of complex matrices bears similarities to the Schubert cell stratification of a homogeneous algebraic manifold. An array of potential applications to current investigations in computational matrix analysis is briefly mentioned, touching concepts such as symmetric statistical models, hierarchical matrices and coherent matrix organization induced by partition trees.

AB - A matrix-compression algorithm is derived from a novel isogenic block decomposition for square matrices. The resulting compression and inflation operations possess strong functorial and spectral-permanence properties. The basic observation that Hadamard entrywise functional calculus preserves isogenic blocks has already proved to be of paramount importance for thresholding large correlation matrices. The proposed isogenic stratification of the set of complex matrices bears similarities to the Schubert cell stratification of a homogeneous algebraic manifold. An array of potential applications to current investigations in computational matrix analysis is briefly mentioned, touching concepts such as symmetric statistical models, hierarchical matrices and coherent matrix organization induced by partition trees.

U2 - 10.1007/s44146-022-00023-0

DO - 10.1007/s44146-022-00023-0

M3 - Journal article

VL - 88

SP - 417

EP - 448

JO - Acta Scientiarum Mathematicarum

JF - Acta Scientiarum Mathematicarum

SN - 0001-6969

IS - 1-2

ER -