NLS Algorithm for Kronecker-Structured Linear Systems with a CPD Constrained Solution. Boussé, M., Sidiropoulos, N., & Lathauwer, L. D. In *2019 27th European Signal Processing Conference (EUSIPCO)*, pages 1-5, Sep., 2019.

Paper doi abstract bibtex

Paper doi abstract bibtex

In various applications within signal processing, system identification, pattern recognition, and scientific computing, the canonical polyadic decomposition (CPD) of a higher-order tensor is only known via general linear measurements. In this paper, we show that the computation of such a CPD can be reformulated as a sum of CPDs with linearly constrained factor matrices by assuming that the measurement matrix can be approximated by a sum of a (small) number of Kronecker products. By properly exploiting the hypothesized structure, we can derive an efficient non-linear least squares algorithm, allowing us to tackle large-scale problems.

@InProceedings{8902816, author = {M. Boussé and N. Sidiropoulos and L. D. Lathauwer}, booktitle = {2019 27th European Signal Processing Conference (EUSIPCO)}, title = {NLS Algorithm for Kronecker-Structured Linear Systems with a CPD Constrained Solution}, year = {2019}, pages = {1-5}, abstract = {In various applications within signal processing, system identification, pattern recognition, and scientific computing, the canonical polyadic decomposition (CPD) of a higher-order tensor is only known via general linear measurements. In this paper, we show that the computation of such a CPD can be reformulated as a sum of CPDs with linearly constrained factor matrices by assuming that the measurement matrix can be approximated by a sum of a (small) number of Kronecker products. By properly exploiting the hypothesized structure, we can derive an efficient non-linear least squares algorithm, allowing us to tackle large-scale problems.}, keywords = {least squares approximations;linear systems;matrix decomposition;pattern recognition;signal processing;tensors;NLS algorithm;Kronecker-structured linear systems;CPD constrained solution;signal processing;system identification;pattern recognition;scientific computing;canonical polyadic decomposition;higher-order tensor;linearly constrained factor matrices;measurement matrix;nonlinear least squares algorithm;Tensors;Signal processing algorithms;Jacobian matrices;Signal processing;Linear systems;Computational complexity;Matrix decomposition}, doi = {10.23919/EUSIPCO.2019.8902816}, issn = {2076-1465}, month = {Sep.}, url = {https://www.eurasip.org/proceedings/eusipco/eusipco2019/proceedings/papers/1570528074.pdf}, }

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