Quaternion Valued Signal Processing, Neural Networks, and Machine Learning

Widely Linear Modeling, Quaternion LMS (QLMS), Quaternion widely linear LMS (WLQLMS), Adaptive Prediction, Wind Forecasting. You can also download the Matlab codes for most of quaternion-valued adaptive filters described in the articles below [MATLAB code]

Legend: MATLAB code, PDF files, Supplements and data.

  1. T. Nitta, M. Kobayashi, and D. P. Mandic "Hypercomplex widely linear estimation through the lens of underpinning geometry", IEEE Transactions on Signal Processing, vol. 67, no. 15, pp. 3985-3994, 2019. [pdf]
  2. A. Stott, B. Scalzo-Dees, I. Kisil, and D. P. Mandic, "A class of multidimensional NIPALS Algorithms for quaternion and tensor partial least squares regression", Signal Processing, vol. 160, pp. 316-327, 2019. [pdf]
  3. Y. Xia, M. Xiang, Z. Li, and D. P. Mandic, "Echo state networks for multidimensional data: Exploiting noncircularity and widely linear models", in D. Comminiello and J. Principe (editors), Adaptive Learning Methods for Nonlinear System Modelling, pp. 267-288, Elsevier, 2018. [pdf]
  4. M. Xiang, B. Scalzo-Dees, and D. P. Mandic, "Multiple model adaptive estimation for 3D and 4D signals: A widely linear quaternion approach", IEEE Transactions on Neural Networks and Learning Systems, vol. 30, no. 1, pp. 72-84, 2019. [pdf]
  5. Y. Xia, M. Xiang, Z. Li, and D. P. Mandic, "Echo state networks for multidimensional data: Exploiting noncircularity and widely linear models", in D. Comminiello and J. Principe (editors), Adaptive Learning Methods for Nonlinear System Modelling, pp. 267-288, Elsevier, 2018. [pdf]
  6. M. Xiang, S. Enshaeifar, A. E. Stott, C. Cheong Took, Y. Xia, S. Kanna, and D. P. Mandic, "Simultaneous diagonalisation of the covariance and complementary covariance matrices in quaternion widely linear signal processing", Signal Processing, vol. 148, pp. 193-204, 2018. [pdf]
  7. M. Xiang, S. Kanna, and D. P. Mandic, "Performance analysis of quaternion adaptive filters in nonstationary environments", IEEE Transactions on Signal Processing, vol. 66, no. 6, pp. 1566-1579, 2018. [pdf]
  8. S. Enshaeifar, C. Park, C. Cheong Took, and D. P. Mandic, "Quaternion common spatial patterns", IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 25, no. 8, pp. 1278-1286, 2017. [pdf]
  9. M. Xiang, S. Kanna, C. Cheong Took, and D. P. Mandic, "Cost-effective quaternion minimum mean square error estimation: From widely linear to four-channel processing", Signal Processing, vol. 136, pp. 81-91, 2017. [pdf]
  10. M. Xiang, S. C. Douglas, and D. P. Mandic "The quaternion least mean magnitude phase adaptive filtering algorithm", Proceedings of the 22nd International Conference on Digital Signal Processing (DSP'17), 2017. [pdf]
  11. D. Xu, H. Gao, and D. P. Mandic, "A new proof of the generalized HR calculus", Royal Society Open Science, in print, 2016. [pdf]
  12. M. Xiang, S. Kanna, S. C. Douglas, and D. P. Mandic, "Performance advantage of quaternion widely linear estimation: An approximate uncorrelating transform approach", Proceedings of ICASSP'16, pp. 4348-4352, 2016. [pdf]
  13. S. Enshaeifar, C. Cheong Took, S. Sanei, and D. P. Mandic, "Novel quaternion matrix factorisations", Proceedings of ICASSP'16, pp. 3946-3950, 2016. [pdf]
  14. S. P. Talebi, S. Kanna, and D. P. Mandic, "A distributed quaternion Kalman filter with applications to smart grid and target tracking", IEEE Transactions on Signal and Information Processing over Networks, vol. 2, no. 4, pp. 477-488, 2016. [pdf]
  15. D. Xu, Y. Xia, and D. P. Mandic, "Optimization in quaternion dynamic systems: Gradient, Hessian and learning algorithms", IEEE Transactions on Neural Networks and Learning Systems, vol. 27, no. 2, pp. 249-261, 2016. [pdf]
  16. D. Xu, C. Jahanchahi, C. Cheong Took, and D. P. Mandic, "Enabling quaternion derivatives: The GHR calculus", Royal Society Open Science, vol. 2, no. 8, pp. 1-24, 2015. [pdf]
  17. S. P. Talebi and D. P. Mandic, "A quaternion frequency estimator for three-phase power systems", Proceedings of ICASSP'15, 3956--3960, 2015. [pdf]
  18. S. P. Talebi, S. Kanna, and D. P. Mandic, "Real-time estimation of quaternion impropriety", Proceedings of the IEEE International Conference on Digital Signal Processing (DSP'15), pp. 557-561, 2015. [pdf]
  19. T. Thanthawaritthisai, F. Tobar, A. G. Constantinides, and D. P. Mandic, "The widely linear quaternion recursive total least squares", Proceedings of ICASSP'15, pp. 3357-3361, 2015. [pdf]
  20. Y. Xia, C. Jahanchahi, T. Nitta, and D. P. Mandic, "Performance bounds of quaternion estimators", IEEE Transactions on Neural Networks and Learning Systems, vol. 26, no. 12, pp. 3287-3292, 2015. [pdf]
  21. Y. Xia, C. Jahanchahi, and D. P. Mandic, "Quaternion-valued echo state networks", IEEE Transactions on Neural Networks and Learning Systems, vol. 26, no. 4, pp. 663-673, 2015. [pdf]
  22. D. Xu and D. P. Mandic, "The theory of quaternion matrix derivatives", IEEE Transactions on Signal Processing, vol. 63, no. 6, pp. 1543-1556, 2015. [pdf]
  23. F. Tobar and D. P. Mandic, "Quaternion reproducing kernel Hilbert spaces: Existence and uniqueness conditions", IEEE Transactions on Information Theory, vol. 60, no. 9, pp. 5736-5748, 2014. [pdf]
  24. Y. Xia, C. Jahanchahi, D. Xu, and D. P. Mandic, "The HC calculus, quaternion derivatives and Cayley-Dickson form of quaternion adaptive filters and learning systems", Proceedings of the IEEE International Joint Conference on Neural Networks, IJCNN'14, pp. 3395-3401, 2014. [pdf]
  25. C. Jahanchahi, S. Kanna, and D. P. Mandic, "A theoretical bound on the performance advantage of in quaternion widely linear estimation", Proceedings of the 19th International DSP Conference, DSP'14, pp. 254-258, 2014. [pdf]
  26. P. Talebi, D. Xu, A. Kuh, and D. P. Mandic, "A quaternion least mean phase adaptive estimator", Proceedings of ICASSP 2014, pp. 6419-6423, 2014. [pdf]
  27. C. Jahanchahi and D. P. Mandic, "A class of quaternion Kalman filters", IEEE Transactions on Neural Networks and Learning Systems, vol. 52, no. 3, pp. 533-544, 2014. [pdf]
  28. C. Ujang Bukhari, C. Jahanchahi, C. Cheong-Took, and D. P. Mandic, "An adaptive convex combination approach for the identification of improper quaternion processes", IEEE Transactions on Neural Networks and Learning Systems, vol. 25, no. 1, pp. 172–182, 2014. 10.pdf" title="download in PDF form">[pdf] [MATLAB code]
  29. J. Navarro-Moreno, J. Fernandez Alcala, C. Cheong Took, and D. P. Mandic, "Prediction of wide-sense stationary quaternion random signals", Signal Processing, vol. 93, no. 9, pp. 2573-2580, 2013. 10.pdf" title="download in PDF form">[pdf] [MATLAB code]
  30. C. Jahanchahi and D. P. Mandic, "An adaptive diffusion quaternion LMS algorithm for distributed networks of 3D and 4D vector sensors", in Proceedings of EUSIPCO’13, pp. 2013. 10.pdf" title="download in PDF form">[pdf] [MATLAB code]
  31. F. Tobar and D. P. Mandic,"Quaternion kernel least squares" in Proceedings of ICASSP’13, pp. 6128–6132, 2013. 10.pdf" title="download in PDF form">[pdf]
  32. C. Jahanchahi, C. Cheong Took, and D. P. Mandic, "A class of quaternion valued affine projection algorithms," Signal Processing, vol. 93, no. 9, pp. 1712–1723, 2013. 10.pdf" title="download in PDF form">[pdf] [MATLAB code]
  33. D. Dini, C. Jahanchahi, and D. P. Mandic, "Widely linear complex and quaternion valued bearings only tracking," IET Signal Processing (invited), vol. 6, no. 5, pp. 435–445, 2012. 10.pdf" title="download in PDF form">[pdf]
  34. C. Jahanchahi, C. Cheong Took, and D. P. Mandic, "On gradient calculation in quaternion adaptive filtering", in Proceedings of ICASSP’12, 3773–3776, 2012. [pdf]
  35. C. U. Bukhari, C. Cheong Took, and D. P. Mandic, "On quaternion analyticity: Enabling quaternion valued nonlinear adaptive filtering", in Proceedings of ICASSP’12, pp. 2117–2120, 2012. [pdf] [MATLAB code]
  36. M. Wang, C. Cheong Took and D. P. Mandic,"A class of fast quaternion valued variable stepsize stochastic gradient learning algorithms for vector sensor processes",in Proceedings of IJCNN’11, pp. 1700 - 1705, 2011. 10.pdf" title="download in PDF form">[pdf]
  37. S. Javidi, C. Cheong-Took, and D. P. Mandic, "A Fast Independent Component Analysis Algorithm for Quaternion Signals," IEEE Transactions on Neural Networks, vol. 22. no. 12, pp. 1967-1978, 2011. 10.pdf" title="download in PDF form">[pdf]
  38. C. Cheong-Took and D. P. Mandic, "Augmented Second-order Statistics of Quaternion Random Signals ," Signal Processing, vol. 91, pp. 214-224, 2011. 10.pdf" title="download in PDF form">[pdf] [MATLAB code]
    Addendum to the paper and some clarifications
  39. C. Cheong Took, C. Jahanchahi, and D. P. Mandic, "A unifying framework for the analysis of quaternion-valued adaptive filters," in Proceedings of the Asilomar Conference on Signals, Systems, and Computers, pp. 1771–1774, 2011. 10.pdf" title="download in PDF form">[pdf] [MATLAB code]
  40. C. U. Bukhari, C. Cheong-Took, and D. P. Mandic, "Quaternion Valued Nonlinear Adaptive Filtering," IEEE Transactions on Neural Networks, vol. 22, no. 8, pp. 1193- 1206, 2011. 10.pdf" title="download in PDF form">[pdf] [MATLAB code]
  41. D. P. Mandic, C. Jahanchahi, and C. Cheong-Took, "A quaternion gradient operator and its applications", IEEE Signal Processing Letters, vol. 18, no. 1, pp. 1–5, 2011. [pdf] [MATLAB code]
  42. C. Cheong-Took, D. P. Mandic, and F. Zhang, "On Unitary Diagonalisation of a Special Class of Quaternion Matrices ," Applied Mathematics Letters, vol. 24, pp. 1806-1809, 2011. [pdf]
  43. S. Javidi, C. Cheong Took, C. Jahancahi, N. Le Bihan, and D. P. Mandic, "Blind Extraction of Improper Quaternion Sources ," in Proceedings of ICASSP'11, pp. 3708-3711, 2011. [pdf]
  44. C. Cheong-Took, G. Strbac, K. Aihara, and D. P. Mandic, "Quaternion-valued short term forecasting of three-dimensional wind and atmpospheric parameters," Renewable Energy, vol. 36, pp. 1754-1760,2011. [pdf] [MATLAB code]
  45. C. Jahanchahi, C. Cheong-Took and D. P. Mandic, "A Widely Linear Quaternion Recursive Least Squares Filter," in Proceedings of the Cognitive Information Processing Conference, pp. 87-92, 2010. [pdf] [MATLAB code]
  46. C. Cheong-Took, D. P. Mandic, and J. Benesty, "Study of the quaternion LMS and four-channel LMS algorithms," in Proceedings of ICASSP’09, pp. 3109–3112, 2009. [pdf] [MATLAB code]
  47. C. C. Cheong-Took and D. P. Mandic, "A Quaternion Widely Linear Adaptive Filter," IEEE Transactions on Signal Processing, vol. 58, no. 8, pp. 4427-4431, 2010. [pdf] [MATLAB code]
  48. C. Cheong-Took, D. P. Mandic, and K. Aihara, "Quaternion-valued short term forecasting of wind profile," in Proceedings of IJCNN, pp. 3412-3417,2010. [pdf] [MATLAB code]
  49. C. Cheong-Took and D. P. Mandic, "The Quaternion LMS Algorithm for Adaptive Filtering of Hypercomplex Processes," IEEE Transactions on Signal Processing, vol. 57, no. 4, pp. 1316-1327, 2009. [pdf] [MATLAB code]
  50. C. Cheong-Took and D. P. Mandic, "Quaternion-Valued Stochastic Gradient-Based Adaptive IIR Filtering," IEEE Transactions on Signal Processing, vol. 58, no. 7, pp. 3895-3901, 2010. [pdf]
  51. B. C. Ujang, C. Cheong-Took and D. P. Mandic, "Split quaternion nonlinear adaptive filtering," Neural Networks, vol. 23, no. 3, pp. 426-434, 2010. [pdf]
  52. C. Cheong-Took and D. P. Mandic, "Fusion of Heterogeneous Data Sources: A Quaternionic Approach," Proceedings of MSLP'09, pp. 456-461, 2008. [pdf] [MATLAB code]