Turn off MathJax
Article Contents
CHENG Guanghui, MIAO Jifei, LI Wenrui. Two Jacobi-like algorithms for the general joint diagonalization problem with applications to blind source separation[J]. Chinese Journal of Electronics. doi: 10.1049/cje.2019.00.102
Citation: CHENG Guanghui, MIAO Jifei, LI Wenrui. Two Jacobi-like algorithms for the general joint diagonalization problem with applications to blind source separation[J]. Chinese Journal of Electronics. doi: 10.1049/cje.2019.00.102

Two Jacobi-like algorithms for the general joint diagonalization problem with applications to blind source separation

doi: 10.1049/cje.2019.00.102
Funds:  This work is supported by the National Natural Science Foundation of China (No.11671023).
More Information
  • Author Bio:

    was born in Jilin, China, in 1979. He received the Ph.D. degree in applied mathematics from University of Electronic Science and Technology of China, Sichuan, China, in 2008. He is currently a professor with University of Electronic Science and Technology of China, Sichuan, China. His current research interests include matrix computation, matrix and tensor decomposition, signal processing and image processing. (Email: ghcheng@uestc.edu.cn)

    was born in Sichuan, China, in 1992. Jifei Miao received the M.S. degree in the School of Mathematical Sciences, University of Electronic Science and Technology of China, Sichuan, China. He is pursuing the Ph.D. degree in the University of Macau, Macau, China. His current research interests include quaternion algebra, matrix and tensor calculations, image and signal processing (Email: jifmiao@163.com)

    was born in Sichuan, China, in 1999. He received the B.S. degree in the School of Information and Software Engineering, University of Electronic Science and Technology of China, Sichuan, China. His current research interests include matrix decomposition and machine learning. (Email: 944683243@qq.com)

  • Received Date: 2019-04-01
    Available Online: 2021-11-05
  • We consider the general problem of the approximate joint diagonalization of a set of non-Hermitian matrices. This problem mainly arises in the data model of the joint blind source separation for two datasets. Based on a special parameterization of the two diagonalizing matrices and on adapted approximations of the classical cost function, we establish two Jacobi-like algorithms. They may serve for the canonical polyadic decomposition (CPD) of a third-order tensor, and in some scenarios they can outperform traditional CPD methods. Simulation results demonstrate the competitive performance of the proposed algorithms.
  • loading
  • [1]
    E. Moreau, “A generalization of joint diagonalization criteria for source separation”, IEEE Trans. Signal Processing, Vol.49, No.3, pp.530–541, 2001. doi: 10.1109/78.905873
    [2]
    B. Afsari, “Simple LU and QR based non-orthogonal matrix joint diagonalization”, Independent Component Analysis and Blind Signal Separation, 6th International Conference, Charleston, SC, USA, pp. 1–7, 2006.
    [3]
    P. Tichavsky and A. Yeredor, “Fast approximate joint diagonalization incorporating weight matrices”, IEEE Trans. Signal Processing, Vol.57, No.3, pp.878–891, 2009. doi: 10.1109/TSP.2008.2009271
    [4]
    G. Chabriel, M. Kleinsteuber, E. Moreau, et al., “Joint matrices decompositions and blind source separation: A survey of methods, identification, and applications”, IEEE Signal Process. Mag., Vol.31, No.3, pp.34–43, 2014. doi: 10.1109/MSP.2014.2298045
    [5]
    V. Maurandi and E. Moreau, “A decoupled Jacobi-like algorithm for non-unitary joint diagonalization of complex-valued matrices”, IEEE Signal Process. Lett., Vol.21, No.12, pp.1453–1456, 2014. doi: 10.1109/LSP.2014.2339891
    [6]
    V. Maurandi, E. Moreau and C. DeLuigi, “Jacobi like algorithm for non-orthogonal joint diagonalization of Hermitian matrices”, ICASSP, Florence, Italy, pp. 6196–6200, 2014.
    [7]
    T. Trainini and E. Moreau, “A coordinate descent algorithm for complex joint diagonalization under Hermitian and transpose congruences”, IEEE Trans. Signal Processing, Vol.62, No.19, pp.4974–4983, 2014. doi: 10.1109/TSP.2014.2343948
    [8]
    G.H. Cheng, S.M. Li and E. Moreau, “New Jacobi-like algorithms for non-orthogonal joint diagonalization of Hermitian matrices”, Signal Processing, Vol.128, pp.440–448, 2016. doi: 10.1016/j.sigpro.2016.05.013
    [9]
    D.Z. Feng, X.D. Zhang and Z. Bao, “An efficient multistage decomposition approach for independent components”, Signal Processing, Vol.83, No.1, pp.181–197, 2003. doi: 10.1016/S0165-1684(02)00390-0
    [10]
    B. Afsari and P. S. Krishnaprasad, “Some gradient based joint diagonalization methods for ICA”, Independent Component Analysis and Blind Signal Separation, Fifth International Conference, Granada, Spain, pp. 437–444, 2004.
    [11]
    H.J. Yu and D.S. Huang, “Graphical representation for DNA sequences via joint diagonalization of matrix pencil”, IEEE J. Biomedical and Health Informatics, Vol.17, No.3, pp.503–511, 2013. doi: 10.1109/TITB.2012.2227146
    [12]
    J. F Cardoso and A. Souloumiac, “Blind beamforming for non-gaussian signals”, IEE Proceedings-F, Vol.140, No.6, pp.362–370, 1993.
    [13]
    A. Belouchrani, K. Abed-Meraim, J.F. Cardoso and E. Moulines, “A blind source separation technique using second-order statistics”, IEEE Trans. Signal Processing, Vol.45, No.2, pp.434–444, 1997. doi: 10.1109/78.554307
    [14]
    Y.O. Li, T. Adali, W. Wang and V. D. Calhoun, “Joint blind source separation by multiset canonical correlation analysis”, IEEE Trans. Signal Processing, Vol.57, No.10, pp.3918–3929, 2009. doi: 10.1109/TSP.2009.2021636
    [15]
    V.D. Calhoun and T. Adali, “Multisubject independent component analysis of fmri: a decade of intrinsic networks, default mode, and neurodiagnostic discovery”, IEEE Reviews in Biomedical Engineering, Vol.5, pp.60–73, 2012. doi: 10.1109/RBME.2012.2211076
    [16]
    V.D. Calhoun, T. Adali, G.D. Pearlson and J.J. Pekar, “A method for making group inferences from functional MRI data using independent component analysis”, Human Brain Mapping, Vol.14, No.3, Article No.140, 2001. doi: 10.1002/hbm.1048
    [17]
    J. Laney, K. Westlake, S. Ma, E. Woytowicz, and T. Adali, “Capturing subject variability in data driven FMRI analysis: A graph theoretical comparison”, 48th Annual Conference on Information Sciences and Systems, Princeton, NJ, USA, pp. 1–6, 2014.
    [18]
    A. M. Michael, M. Anderson, et al., “Preserving subject variability in group FMRI analysis: performance evaluation of GICA vs. IVA”, Frontiers in Systems Neuroscience, Vol.8, No.106, Article No.106, 2014.
    [19]
    T. Adali, Y. Levin-Schwartz, and V. D. Calhoun, “Multimodal data fusion using source separation: Two effective models based on ICA and IVA and their properties”, Proceedings of the IEEE, Vol.103, No.9, pp.1478–1493, 2015. doi: 10.1109/JPROC.2015.2461624
    [20]
    X.L. Li, T. Adali, and M. Anderson, “Joint blind source separation by generalized joint diagonalization of cumulant matrices”, Signal Processing, Vol.91, No.10, pp.2314–2322, 2011. doi: 10.1016/j.sigpro.2011.04.016
    [21]
    P. Tichavsky, A. H. Phan, and A. Cichocki, “Non-orthogonal tensor diagonalization”, Signal Processing, Vol.138, pp.313–320, 2017. doi: 10.1016/j.sigpro.2017.04.001
    [22]
    F. Roemer and M. Haardt, “A semialgebraic framework for approximate CP decompositions via simultaneous matrix diagonalizations”, Elsevier North-Holland, Inc., 2013.
    [23]
    K. Naskovska, M. Haardt, P. Tichavsky, et al., “Extension of the semi-algebraic framework for approximate CP decompositions via non-symmetric simultaneous matrix diagonalization”, IEEE International Conference on Acoustics, Speech and Signal Processing, pp.2971–2975, 2016.
    [24]
    A. Ziehe, P. Laskov, G. Nolte and K.R. Müller, “A fast algorithm for joint diagonalization with non-orthogonal transformations and its application to blind source separation”, Journal of Machine Learning Research, Vol.5, No.3, pp.777–800, 2004.
    [25]
    O. Macchi and E. Moreau, “Self-adaptive source separation by direct and recursive networks”, International Conference on Digital Signal Processing, pp.1154–1159, 1154.
    [26]
    A. Mesloub, K. Abed-Meraim and A. Belouchrani, “A new algorithm for complex nonorthogonal joint diagonalization based on Shear and Givens rotations”, IEEE Trans. Signal Processing, Vol.62, No.8, pp.1913–1925, 2014. doi: 10.1109/TSP.2014.2303947
    [27]
    N. Vervliet, O. Debals, L. Sorber, et al., “Tensorlab 3.0”, 2016.
    [28]
    M. Anderson, X.L. Li and T. Adali, “Complex-valued independent vector analysis: Application to multivariate Gaussian model”, Signal Processing, Vol.92, No.8, pp.1821–1831, 2012. doi: 10.1016/j.sigpro.2011.09.034
    [29]
    L. Zou, X. Chen and Z. J. Wang, “Underdetermined joint blind source separation for two datasets based on tensor decomposition”, IEEE Signal Process. Lett., Vol.23, No.5, pp.673–677, 2016. doi: 10.1109/LSP.2016.2546687
    [30]
    J. Benesty, J.D. Chen, Y.T. Huang, and I. Cohen, “Pearson correlation coefficient”, Springer Berlin Heidelberg, 2009.
    [31]
    A. L. Goldberger, L. A. N. Amaral, L. Glass, et al., “Physiobank, physiotoolkit, and physionet components of a new research resource for complex physiologic signals”, Circulation, Vol.101, No.23, Article No.215, 2000.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(12)  / Tables(2)

    Article Metrics

    Article views (159) PDF downloads(11) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return