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.
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References
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.2015.2474704
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.2016.2614797
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.2018.2830317
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.2015.2438719
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.2012.2190410
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/S012906571440005X
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_22
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)
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.2008.10.057
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.2015.2391074
Cichocki, A.: Tensor decompositions: a new concept in brain data analysis. arXiv Prepr. arXiv1305.0395 (2013)
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.1
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.2015.03.018
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_11
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/sapm192761164
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)
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/BF02310791
Kolda, T.-G., Bader, B.-W.: Tensor decompositions and applications. SIAM Rev. 51(3), 455–500 (2008). https://doi.org/10.1137/07070111X
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).
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Wang, X., Zhang, C., Ristaniemi, T., Cong, F. (2019). Generalization of Linked Canonical Polyadic Tensor Decomposition for Group Analysis. In: Lu, H., Tang, H., Wang, Z. (eds) Advances in Neural Networks – ISNN 2019. ISNN 2019. Lecture Notes in Computer Science(), vol 11555. Springer, Cham. https://doi.org/10.1007/978-3-030-22808-8_19
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