Advertisement

Generalization of Linked Canonical Polyadic Tensor Decomposition for Group Analysis

  • Xiulin Wang
  • Chi Zhang
  • Tapani Ristaniemi
  • Fengyu CongEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11555)

Abstract

Real-world data are often linked with each other since they share some common characteristics. The mutual linking can be seen as a core driving force of group analysis. This study proposes a generalized linked canonical polyadic tensor decomposition (GLCPTD) model that is well suited to exploiting the linking nature in multi-block tensor analysis. To address GLCPTD model, an efficient algorithm based on hierarchical alternating least squa res (HALS) method is proposed, termed as GLCPTD-HALS algorithm. The proposed algorithm enables the simultaneous extraction of common components, individual components and core tensors from tensor blocks. Simulation experiments of synthetic EEG data analysis and image reconstruction and denoising were conducted to demonstrate the superior performance of the proposed generalized model and its realization.

Keywords

Linked tensor decomposition Hierarchical alternating least squares Canonical polyadic Simultaneous extraction 

Notes

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 81471742), the Fundamental Research Funds for the Central Universities [DUT16JJ(G)03] in Dalian University of Technology in China, and the scholarships from China scholarship Council (No. 201706060262).

References

  1. 1.
    Zhou, G.-X., Zhao, Q.-B., Zhang, Y., et al.: Linked component analysis from matrices to high-order tensors: applications to biomedical data. Proc. IEEE. 104(2), 310–331 (2016).  https://doi.org/10.1109/JPROC.2015.2474704Google Scholar
  2. 2.
    Sorensen, M., De Lathauwer, L.: Multidimensional harmonic retrieval via coupled canonical polyadic decomposition – part II: algorithm and multirate sampling. IEEE Trans. Signal Process. 65(2), 528–539 (2017).  https://doi.org/10.1109/TSP.2016.2614797Google Scholar
  3. 3.
    Gong, X.-F., Lin, Q.-H., Cong, F.-Y., De Lathauwer, L.: Double coupled canonical polyadic decomposition for joint blind source separation. IEEE Trans. Signal Process. 66(13), 3475–3490 (2016).  https://doi.org/10.1109/TSP.2018.2830317Google Scholar
  4. 4.
    Acar, E., Bro, R., Smilde, A.-K.: Data fusion in metabolomics using coupled matrix and tensor factorizations. Proc. IEEE. 103(9), 1602–1620 (2015).  https://doi.org/10.1109/JPROC.2015.2438719Google Scholar
  5. 5.
    Zhou, G.-X., Cichocki, A., Xie, S.-L.: Fast nonnegative matrix/tensor factorization based on low-rank approximation. IEEE Trans. Signal Process. 60(6), 2928–2940 (2012).  https://doi.org/10.1109/TSP.2012.2190410Google Scholar
  6. 6.
    Cong, F.-Y., Zhou, G.-X., Cichocki, A., et al.: Low-rank approximation based non-negative multi-way array decomposition on event-related potentials. Int. J. Neural Syst. 24(8), 1440005 (2014).  https://doi.org/10.1142/S012906571440005XGoogle Scholar
  7. 7.
    Cichocki, A., Zdunek, R., Amari, S.: Hierarchical ALS algorithms for nonnegative matrix and 3D tensor factorization. In: Davies, M.E., James, C.J., Abdallah, S.A., Plumbley, M.D. (eds.) ICA 2007. LNCS, vol. 4666, pp. 169–176. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-74494-8_22Google Scholar
  8. 8.
    Cong, F.-Y., Phan, A.-H., Zhao, Q.-B., et al.: Analysis of ongoing EEG elicited by natural music stimuli using nonnegative tensor factorization. In: 20th European Signal Processing Conference, pp. 494–498. Elsevier, Bucharest (2012)Google Scholar
  9. 9.
    Calhoun, V.-D., Liu, J., Adali, T.: A review of group ICA for fMRI data and ICA for joint inference of imaging, genetic, and ERP data. Neuroimage 45(1), 163–172 (2009).  https://doi.org/10.1016/j.neuroimage.2008.10.057Google Scholar
  10. 10.
    Gong, X.-F., Wang, X.-L., Lin, Q.-H.: Generalized non-orthogonal joint diagonalization with LU decomposition and successive rotations. IEEE Trans. Signal Process. 63(5), 1322–1334 (2015).  https://doi.org/10.1109/TSP.2015.2391074Google Scholar
  11. 11.
    Cichocki, A.: Tensor decompositions: a new concept in brain data analysis. arXiv Prepr. arXiv1305.0395 (2013)Google Scholar
  12. 12.
    Mørup, M.: Applications of tensor (multiway array) factorizations and decompositions in data mining. Wiley Interdisc. Rev.: Data Min. Knowl. Disc. 1(1), 24–40 (2011).  https://doi.org/10.1002/widm.1Google Scholar
  13. 13.
    Cong, F.-Y., Lin, Q.-H., Kuang, L.-D., et al.: Tensor decomposition of EEG signals: a brief review. J. Neurosci. Methods 248, 59–69 (2015).  https://doi.org/10.1016/j.jneumeth.2015.03.018Google Scholar
  14. 14.
    Yokota, T., Cichocki, A., Yamashita, Y.: Linked PARAFAC/CP tensor decomposition and its fast implementation for multi-block tensor analysis. In: Huang, T., Zeng, Z., Li, C., Leung, C.S. (eds.) ICONIP 2012. LNCS, vol. 7665, pp. 84–91. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-34487-9_11Google Scholar
  15. 15.
    Hitchcock, F.-L.: The expression of a tensor or a polyadic as a sum of products. J. Math. Phys. 6(1–4), 164–189 (1927).  https://doi.org/10.1002/sapm192761164Google Scholar
  16. 16.
    Harshman, R.-A.: Foundations of the PARAFAC procedure: models and conditions for an ‘explanatory’ multimodal factor analysis. UCLA Work. Pap. Phonetics. 16, 1–84 (1970)Google Scholar
  17. 17.
    Carroll, J.-D., Chang, J.-J.: Analysis of individual differences in multidimensional scaling via an n-way generalization of ‘Eckart-Young’ decomposition. Psychometrika 35(3), 283–319 (1970).  https://doi.org/10.1007/BF02310791Google Scholar
  18. 18.
    Kolda, T.-G., Bader, B.-W.: Tensor decompositions and applications. SIAM Rev. 51(3), 455–500 (2008).  https://doi.org/10.1137/07070111XGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Xiulin Wang
    • 1
    • 2
  • Chi Zhang
    • 1
  • Tapani Ristaniemi
    • 2
  • Fengyu Cong
    • 1
    • 2
    Email author
  1. 1.School of Biomedical Engineering, Faculty of Electronic Information and Electrical EngineeringDalian University of TechnologyDalianChina
  2. 2.Faculty of Information TechnologyUniversity of JyväskyläJyväskyläFinland

Personalised recommendations