β-Divergence Two-Dimensional Nonnegative Matrix Factorization with Sparseness Constraints for Biomedical Signal Separation
Keywords:Nonnegative Matrix Factorization, Sparseness Constraints, ?-Divergence, Multiplicative Rules,
AbstractA novel of β-Divergence for nonnegative matrix factorization two-dimensional (NMF2D) with sparseness constraints is proposed in this paper. This research focuses on biomedical signal separation, which denotes a separation on the mixture of heart sound and lung sound. Initially, a mixture of heart sound and lung sound has been decomposed into an independent signal, which is an estimated heart sound signal and estimated lung sound signal. The spectrum of independent signal is modelled based on 2 dimensions, which are the temporal code and the spectral basis by using β-Divergence NMF2D algorithm with sparseness constraints. The algorithm has been updated multiplicative and iteratively via multiplicative update rules (MU rules). β-Divergence with sparseness constraints allows minimization on the vagueness of source model to be completed and oneness has been applied to it. Then, estimation of each separated audio has been analyzed via comparison with the original heart sound and lung sound signal in term of Signal-to-Distortion Ratio (SDR).
P. Paatero and U. Tapper. Positive matrix factorization: A nonnegative factor model with optimal utilization of error estimates of data values. Environmetrics, 5:111–126, 1994.
D. D. Lee and H. S. Seung. Learning the parts of objects by nonnegative matrix factorization. Nature, 401(6755):788–791, 1999.
D. FitzGerald, “Automatic drum transcription and source separation,” Ph.D. thesis, Dublin Institute of Technology, Dublin, Ireland, 2004.
S. Xie, Z. Yang, and Y. Fu, “Nonnegative matrix factorization applied to nonlinear speech and image cryptosystems,” IEEE Trans. on Circuits and Systems I, vol. 55, no. 8, pp. 2356-2367, Sep 2008.
I. Biciu, N. Nikolaidis, and I. Pitas, “Nonnegative matrix factorization in polynomial feature space”, IEEE Trans. On Neural Network, vol. 19, pp. 1090-1100, 2007.
C. S. Lin and E. Hasting, “Blind Source Separation of Heart and Lung Sounds Based on Nonnegative Matrix Factorization,” Intelligent Signal Processing and Communications Systems (ISPACS), 2013.
H. Pasterkamp, S. S. Kraman, and G. R. Wodicka, “Respiratory sounds: Advances beyond the stethoscope,” Amer. J. Respir. Crit. Care Med., vol. 156, pp. 974-987, 1997.
M. Morup and M. N. Schmidt, “Sparse nonnegative matrix factor 2-D deconvolution,” Techical Report, Technical University of Denmark, Copenhagen, Denmark, 2006.
D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” Journal of the Optical Society of America, 4:2379–2394, 1987.
M. Morup, M. N. Schmidt, “Sparse nonnegative matrix factor 2-D deconvolution, “ Technical Report, Technical University of Denmark, Copenhagen, Denmark, 2006.
S. K. Tjoa and K. J. Ray Liu, “Multiplicative Update Rules for Nonnegative Matrix Factorization with Co-Occurrence Constraints,” IEEE International Conference on Acoustics, Speech and Signal Processing, 2010.
L. Sui, X. Zhang, J. Huang, G. Zhao and Y. Yang, “Speech Enhancement Based on Sparse Nonnegative Matrix Factorization with Priors,” Systems and Informatics (ICSAI), 2012.
A.M. Darsono, N. Z. Haron, A. S. Jaafar and M. I. Ahmad, “β-Divergence Two-Dimensional Sparse Nonnegative Matrix Factorization for Audio Source Separation,” Wireless Sensor (ICWISE), 2013.
A. M. Darsono, N.Z. Haron, Shakir Saat, M.M. Ibrahim, and N.A. Manap, “Blind Audio Source Separation with Sparse Nonnegati Matrix Factorization”, Research Journal of Applied Sciences, Engineering and Tchnology, vol. 7 No 23, 2014.
A. Ozerov, and C. Févotte, “Multichannel Nonnegative Matrix Factorization in Convolutive Mixtures for Audio Source Separation,” IEEE Transactions On Audio, Speech, And Language Processing, Vol. 18, No. 3, March 2010.
S. R. Chintakindi, O. V. S. R. Varaprasad and D. V. S. S. Siva Sarma, “ Improved Hanning window based interpolated FFT for power harmonic analysis,” TENCON 2015, IEEE Region 10 Conference, 2015.
C. F´evotte, R. Gribonval and E. Vincent, “BSS EVAL Toolbox User Guide”, IRISA Technical Report 1706, Rennes, France, April 2005. http://www.irisa.fr/metiss/bss eval/.
How to Cite
TRANSFER OF COPYRIGHT AGREEMENT
The manuscript is herewith submitted for publication in the Journal of Telecommunication, Electronic and Computer Engineering (JTEC). It has not been published before, and it is not under consideration for publication in any other journals. It contains no material that is scandalous, obscene, libelous or otherwise contrary to law. When the manuscript is accepted for publication, I, as the author, hereby agree to transfer to JTEC, all rights including those pertaining to electronic forms and transmissions, under existing copyright laws, except for the following, which the author(s) specifically retain(s):
- All proprietary right other than copyright, such as patent rights
- The right to make further copies of all or part of the published article for my use in classroom teaching
- The right to reuse all or part of this manuscript in a compilation of my own works or in a textbook of which I am the author; and
- The right to make copies of the published work for internal distribution within the institution that employs me
I agree that copies made under these circumstances will continue to carry the copyright notice that appears in the original published work. I agree to inform my co-authors, if any, of the above terms. I certify that I have obtained written permission for the use of text, tables, and/or illustrations from any copyrighted source(s), and I agree to supply such written permission(s) to JTEC upon request.