In this paper, we address the problem of scalability to higher dimensional space in blind source separation (BSS), where the number of sources is greater than two. Herein, we propose two schemes of pairwise non-parametric independent component analysis (ICA) algorithms based on Convex Cauchy–Schwarz Divergence (CCS–DIV) for high dimensional problem in BSS. We extend the pairwise method to the scenario of more than two sources, two improved ICA algorithms are developed. Moreover, we employ adaptive sampling technique that samples the signal into small time blocks to evaluate the integration of the CCS–DIV and reduce the computational complexity. The two presented methods enable fast and efficient demixing of sources in real-world high dimensional source applications. Finally, we demonstrate with simulations including a wide variety of source distributions, showing that our presented methods outperform many of the presently known methods in terms of performance and computational complexity.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Albataineh, Z. (2018aa). Blind decoding of massive MIMO uplink systems based on the higher order cumulants. Wireless Personal Communications, 103, 1835–1847.
Albataineh, Z. (2018b). Robust blind channel estimation algorithm for linear STBC systems using fourth order cumulant matrices. Telecommunications and System, 68, 573–582.
Albataineh, Z., Hayajneh, K., Salameh, H., Dang, C., & Dagmseh, A. (2020). Robust massive MIMO channel estimation for 5G networks using compressive sensing technique. AEU—International Journal of Electronics and Communications, 120, 153197.
Albataineh, Z., & Salem, F. M. (2017). Adaptive blind CDMA receivers based on ICA filtered structures. Circuits Systems and Signal Processing, 36, 3320–3348.
Bataineh, Z., & Salem, F. (2018). A convex Cauchy-Schwarz divergence measure for blind source separation. International Journal of Circuits, Systems and Singal Processing, 12, 94–104.
Boscolo, R., Pan, H., & Roychowdhury, V. P. (2004). Independent component analysis based on nonparametric density estimation. IEEE Transactions on Neural Networks, 15(1), 55–65.
Cardoso, Jean-François. (1999). High-order contrasts for independent component analysis. Neural Computation, 11(1), 157–192.
Cardoso, J., & Souloumiac, A. (1993). Blind beamforming for non-Gaussian signals. IEE Proceedings F Radar and Signal Processing, 140(6), 362–370.
Chen, Y. (2005). Blind separation using convex function. IEEE Transactions on Signal Processing, 53(6), 2027–2035.
Chien, J.-T., & Chen, B.-C. (2006). A new independent component analysis for speech recognition and separation. IEEE Transactions on Audio, Speech, and Language Processing, 14(4), 1245–1254.
Cichocki, A., & Amari, S. (2002). Adaptive Blind Signal and Image Processing. Chichester, UK: Wiley.
Cichocki, A., Zdunek, R., & Amari, S. (2006). Csiszar’s divergences for non-negative matrix factorization: Family of new algorithms. In 6th International Conference on Independent Component Analysis and Blind Signal Separation, Charleston SC, USA, March 5–8, 2006 Springer LNCS 3889, pp. 32–39.
Comon, P. (1994). Independent component analysis, a new concept? Signal Processing (Special Issue on Higher-Order Statistics), 36(3), 287–314.
Comon, P., & Jutten, C. (Eds.). (2010). Handbook of blind source separation independent component analysis and applications. Oxford: Academic Press.
Duda, R. O., Hart, P. E., & Stork, D. G. (2001). Pattern classification, chapter 4 (pp. 2–18). New York: Wiley.
Golub, G. H., & Van Loan, C. F. (1996). Matrix computations (3rd ed.). Baltimore, MD: Johns Hopkins Univ. Press.
Hsieh, H.-L., & Chien, J.-T. (2010). A new nonnegative matrix factorization for independent component analysis. In Proceedings of the International Conference Acoustics, Speech, and Signal Processing (pp. 2026–2029).
Hyvarinen, A. (1999). Fast and robust fixed-point algorithm for independent component analysis. IEEE Transactions on Neural Network, 10(3), 626–634.
Jan, T., Wenwu, W., & DeLiang, W. (2009). A multistage approach for blind separation of convolutive speech mixtures. Acoustics, Speech and Signal Processing (ICASSP), 1713–1716.
Jenssen, R., Erdogmus, D., Hild, K., Principe, J., & Eltoft, T. (2005). Optimizing the Cauchy-Schwarz PDF distance for information theoretic, nonparametric clustering. In Energy Minimization Methods in Computer Vision and Pattern Recognition (pp. 34–45). Springer.
Jen-TzungChien, H.-L. H. (2012). Convex divergence ICA for blind source separation. IEEE Transactions on Audio, Speech, and Language Processing, 20(1), 302–313.
Kampa, K., Hasanbelliu, E., & Principe, J. C. (2011). Closed-form Cauchy-Schwarz pdf divergence for mixture of Gaussians. In International Joint Conference on Neural Networks (IJCNN) (pp. 2578–2585).
Lin, J. (1991). Divergence measures based on the Shannon entropy. IEEE Transactions on Information Theory, 37(1), 145–151.
Matsuyama, Y., Katsumata, N., Suzuki, Y., & Imahara, S. (2000). The \(\alpha\)-ICA algorithm. In Proceedings of the International Workshop on Independent Component Analysis and Blind Signal Separation (pp. 297–302).
Na, Y., & Yu, J. (2012). Kernel and spectral methods for solving the permutation problem in frequency domain BSS. Neural Networks (IJCNN), 1–8.
Rutishauser, H. (1966). The Jacobi method for real symmetric matrices. Numerical Mathematics, 9, 1–10.
Schobben, D., Torkkola, K., & Smaragdis, P. (1999). Evaluation of blind signal separation methods. In Proceedings International Workshop on Independent Component Analysis and Blind Signal Separation (pp. 261–266).
Seth, S., Rao, M., Park, I., & Principe, J. C. (2011). A unified framework for quadratic measures of independence. IEEE Transactions on Signal Processing, 59(8), 3624–3635.
Takeda, R., Nakadai, K., Takahashi, T., Komatani, K., Ogata, T., & Okuno, H. G. (2009). Step-size parameter adaptation of multi-channel semi-blind ICA with piecewise linear model for barge-in-able robot audition. Intelligent Robots and Systems (pp. 2277–2282).
Takeda, R., Nakadai, K., Takahashi, T., Komatani, K., Ogata, T., & Okuno, H. G. (2010). Upper-limit evaluation of robot audition based on ICA-BSS in multi-source, barge-in and highly reverberant conditions. In IEEE International Conference on Robotics and Automation (ICRA) (pp. 4366–4371).
Xu, D., Principe, J. C., Fisher, J, I. I. I., & Wu, H.-C. (1998). A novel measure for independent component analysis (ICA). Proceedings of the International Conference on Acoustics, Speech and Signal Processing, 2, 1161–1164.
Yokote, R., & Matsuyama, Y. (2012). Rapid algorithm for independent component analysis. Journal of Signal and Information Processing, 3, 275–285.
Yoshioka, T. N., Tomohiro, M., Masato, O., & Hiroshi, G. (2011). Blind separation and dereverberation of speech mixtures by joint optimization. IEEE Transactions on Audio Speech and Language Processing, 19(1), 69.
Zarzoso, V., & Comon, P. (2010). Robust independent component analysis by iterative maximization of the Kurtosis contrast with algebraic optimal step size. IEEE Transactions on Neural Networks, 21(2), 248–261.
Zarzoso, V., Murillo-Fuentes, J. J., Boloix-Tortosa, R., & Nandi, A. K. (2006). Optimal pairwise fourth-order independent component analysis. IEEE Transactions on Signal Processing, 54(8), 3049–3063.
Zhang, J. (2004). Divergence function, duality, and convex analysis. Neural Computing, 16, 159–195.
Conflict of interest
The authors declare that they have no conflict of interest.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations
About this article
Cite this article
Albataineh, Z., Salem, F. Two pairwise iterative schemes for high dimensional blind source separation. Int J Speech Technol (2020). https://doi.org/10.1007/s10772-020-09729-4
- Blind source separation (BSS)
- Cauchy–Schwarz inequality
- Non-parametric independent component analysis (ICA)