Abstract
In this work, we propose an algebraic algorithm called coupled exact joint block decomposition (CE-JBD) for joint independent subspace analysis (JISA), an extension to joint blind source separation. In JISA, tensors admitting coupled rank-\((L_m,L_n,\cdot )\) Block Term Decomposition (BTD) can be constructed using second order statistics of non-stationary signals. And the loading matrices to be estimated will be computed from these tensors via coupled rank-\((L_m,L_n,\cdot )\) BTD based algorithms. However, most of the existing algorithms resort to iterative techniques. They heavily rely on a good starting point. Capable of providing such a point, our proposed CE-JBD, based on coupled rank-\((L_m,L_n,\cdot )\) BTD, achieves JISA only by employing generalized eigenvalue decomposition followed by a clustering step and singular value decomposition. To validate its efficacy, as well as its ability to serve its iterative counterparts, we present some experiment results in the end.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Kim, T., Attias, H.T., Lee, S.Y.: Blind source separation exploiting higher-order frequency dependencies. IEEE Trans. Audio Speech Lang. Proc. 15(1), 70–79 (2006)
Li, Y.O., Adali, T., Wang, W.: Joint blind source separation by multiset canonical correlation analysis. IEEE Trans. Signal Proc. 57(10), 3918–3929 (2009)
Correa, N.M., Eichele, T., Adali, T.: Multi-set canonical correlation analysis for the fusion of concurrent single trial ERP and functional MRI. Neuroimage 50(4), 1438–1445 (2010)
Correa, N.M., Adali, T., Li, Y.O.: Canonical correlation analysis for data fusion and group inferences. Signal Proc. Mag. IEEE 27(4), 39–50 (2010)
Chatel-Goldman, J., Congedo, M., Phlypo, R.: Joint BSS as a natural analysis framework for EEG-hyperscanning. In: IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 1212–1216. IEEE Press, Vancouver (2013)
Gong, X.F., Wang, X.L., Lin, Q.H.: Generalized non-orthgonal joint diagonalization with LU decomposition and successive rotation. IEEE Trans. Signal Proc. 63(5), 1322–1334 (2015)
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 Proc. 66(13), 3475–3490 (2018)
Lahat, D., Jutten, C.: Joint independent subspace analysis using second-order statistics. IEEE Trans. Signal Proc. 64(18), 4891–4904 (2016)
Lahat, D., Jutten, C.: Joint blind source separation of multidimensional components: model and algorithm. In: European Signal Processing Conference, pp. 1417–1421. IEEE Press, Lisbonne (2014)
Lahat, D., Jutten, C.: Joint independent subspace analysis: a quasi-Newton algorithm. In: Vincent, E., Yeredor, A., Koldovský, Z., Tichavský, P. (eds.) LVA/ICA 2015. LNCS, vol. 9237, pp. 111–118. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-22482-4_13
Sorber, L., Barel, M.V., De Lathauwer, L.: Structured data fusion. IEEE J. Sel. Top. Signal Proc. 9(4), 586–600 (2015)
Gong, X.F., Lin, Q.H., et al.: Coupled rank-\((Lm, Ln, \cdot )\) block term decomposition by coupled block simultaneous generalized schur decomposition. In: International Conference on Acoustics, Speech and Signal Processing, pp. 2554–2558. IEEE Press, Shanghai (2016)
Lahat, D., Jutten, C.: Joint independent subspace analysis: uniqueness and identifiability. IEEE Trans. Signal Proc. 67(3), 684–699 (2019)
De Lathauwer, L.: Decompositions of a higher-order tensor in block terms-part I: lemmas for partitioned matrices. SIAM J. Matrix Anal. Appl. 30(3), 1022–1032 (2008)
Nion, D.: A tensor framework for nonunitary joint block diagonalization. IEEE Trans. Signal Proc. 59(10), 4585–4594 (2011)
Anderson, T.W.: An Introduction to Multivariate Statistical Analysis, New York (2003)
Tensorlab 3.0 - numerical optimization strategies for large-scale constrained and coupled matrix/tensor factorization. https://www.tensorlab.net
Acknowledgments
This research is funded by national natural science foundation of China (Grant nos. 61331019 and 61379012).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Yang, JX., Gong, XF., Yu, GC. (2019). An Algebraic Algorithm for Joint Independent Subspace Analysis. In: Lu, H., Tang, H., Wang, Z. (eds) Advances in Neural Networks – ISNN 2019. ISNN 2019. Lecture Notes in Computer Science(), vol 11554. Springer, Cham. https://doi.org/10.1007/978-3-030-22796-8_42
Download citation
DOI: https://doi.org/10.1007/978-3-030-22796-8_42
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-22795-1
Online ISBN: 978-3-030-22796-8
eBook Packages: Computer ScienceComputer Science (R0)