Skip to main content

Advertisement

SpringerLink
Log in

Underdetermined mixing matrix estimation based on joint density-based clustering algorithms

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

In underdetermined blind source separation (UBSS), the estimation of the mixing matrix is crucial because it directly affects the performance of UBSS. To improve the estimation accuracy, this paper proposes a joint clustering analysis method based on density based spatial clustering of applications with noise (DBSCAN) and clustering by fast search and find of density peaks (CFSFDP). In the reprocessing, the observed signals in the time domain are transformed into sparse signals in the frequency domain through a short time Fourier transform (STFT), and single-source-point (SSP) detection is used to enhance the linear clustering characteristic of signals. In addition, to facilitate the use of density-based clustering analysis, mirroring mapping is used to transform the linear clustering into compact clustering on the positive half unit circle (or sphere). For the estimation of the underdetermined mixing matrix (UMM), the DBSCAN algorithm is first used to search for high-density data points, and automatically find the number of clusters and the cluster centers; then, the CFSFDP algorithm is used to search the density peaks of the data clusters, so as to further modify the cluster centers. Because each cluster center corresponds to a column vector of the mixing matrix, the proposed algorithm can estimate the UMM through cluster analysis. The simulation results show that the proposed algorithm can not only improve the estimation accuracy of the UMM, but also provide a more robust estimator. In addition, the joint clustering method also makes up for the shortcomings of the CFSFDP algorithm that requires human intervention.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Adalı T, Akhonda MABS, Calhoun VD (2019) ICA and IVA for data fusion: an overview and a new approach based on disjoint subspaces. IEEE Sensors Lett 3(1):7100404

    Google Scholar 

  2. Adalı T, Jutten C, Yeredor A, Cichocki A, Moreau E (2014) Source separation and applications. IEEE Signal Process Mag 31(3):16–17

    Google Scholar 

  3. Ambrois C, Dehman A, Neuvial P, Rigall G, Vialaneix N (2019) Adjacency-constrained hierarchical clustering of a band similarity matrix with application to genomics. Algorithms Mol Biol 14(22):1–14

    Google Scholar 

  4. Asaei A, Bourlard H, Taghizadeh MJ, Cevher V (2016) Computational methods for underdetermined convolutive speech localization and separation via model-based sparse component analysis. Speech Commun 76:201–217

    Google Scholar 

  5. Averbuch G, Assink JD, Smets PSM, Evers LG (2018) Extracting low signal-to-noise ratio events with the Hough transform from sparse array data. Geophysics 83(3):1–9

    Google Scholar 

  6. Bofill P, Zibulevsky M (2001) Underdetermined blind source separation using sparse representations. Signal Process 81:2353–2362

    MATH  Google Scholar 

  7. Chen Y, Li Y, Zhou J (2018) Mixing matrix estimation in underdetermined blind source separation based on single source points detection. 2018 18th IEEE International Conference on Communication Technology, Oct. 8-11, 2018, Chongqing China, pp. 1077–1081

  8. Chen Y, Tang S, Bouguila N, Wang C, Du J, Li H (2018) A fast clustering algorithm based on pruning unnecessary distance computations in DBSCAN for high-dimensional data. Pattern Recogn 83:375–387

    Google Scholar 

  9. Chowdhury K, Chaudhuri D, Pal AK, Samal A (2019) Seed selection algorithm through K-means on optimal number of clusters. Multimedia Tools Appl 78(13):18617–18651

    Google Scholar 

  10. Comon P, Jutten C (2010) Handbook of blind source separation: independent component analysis and applications. Academic Press, Burlington

  11. Duong TTH, Duong NQK, Nguyen PC, Nguyen CQ (2019) Gaussian modeling-based multichannel audio source separation exploiting generic source spectral model. IEEE Trans Audio Speech Lang Process 27(1):32–43

    Google Scholar 

  12. Ester M, Kriegel HP, Sander J, Xu X (1996) A density-based algorithm for discovering clusters in large spatial databases with noise. The Second International Conference on Knowledge Discovery and Data Mining, Aug. 2-4, 1996, Portland, USA, pp. 226–231

  13. Feng F, Kowalski K (2018) Revisiting sparse ICA from a synthesis point of view: blind source separation for over and underdetermined mixtures. Signal Process 152:165–177

    Google Scholar 

  14. Feng F, Kowalski M (2019) Underdetermined reverberant blind source separation: sparse approaches for multiplicative and convolutive narrowband approximation. IEEE/ACM Trans Audio Speech Lang Process 27(2):442–456

    Google Scholar 

  15. Fevotte C, Godsill SJ (2006) A Bayesian approach for blind source separation of sparse sources. IEEE Trans Audio Speech Lang Process 14(6):2174–2188

    MATH  Google Scholar 

  16. Frey B, Dueck D (2007) Clustering by passing messages between data points. Science 315:972–976

    MathSciNet  MATH  Google Scholar 

  17. Fu N, Peng X (2008) K-Hough underdetermined blind mixing model recovery algorithm. J Electron Meas Instrum 22(5):63–67

    Google Scholar 

  18. Georgiev P, Theis F, Cichocki A (2005) Sparse component analysis and blind source separation of underdetermined mixtures. IEEE Trans Neural Netw 16(4):992–996

    Google Scholar 

  19. Hajji Z, Aissa-El-bey A, Amis K (2018) Simplicity-based recovery of finite-alphabet signals for large-scale MIMO systems. Digit Signal Process 80:70–82

    Google Scholar 

  20. He X, He F (2020) Underdetermined mixing matrix estimation based on artificial bee colony optimization and single-source-point detection. Multimed Tools Appl 79:13061–13087

    Google Scholar 

  21. He X, He F, Cai W (2016) Underdetermined BSS based on K-means and AP clustering. Circuits Syst Signal Process 35(8):2881–2913

    Google Scholar 

  22. He X, Wang F, Cai W, Wu L (2013) Ant colony clustering algorithm for underdetermined BSS. Chinese J Electron 22(2):319–324

    Google Scholar 

  23. He Z, Xie S, Ding S, Cichocki A (2007) Convolutive blind source separation in frequency domain based on sparse representation. IEEE Trans Audio Speech Lang Process 15(5):1551–1563

    Google Scholar 

  24. Hyvarinen A, Karhunen J, Oja E (2001) Independent component analysis. John Wiley & Sons, New York

  25. Jia M, Sun J, Bao C, Ritz C (2018) Separation of multiple speech sources by recovering sparse and non-sparse components from B-format microphone recordings. Speech Commun 96:184–196

    Google Scholar 

  26. Koldovsky Z, Tichavsky P (2019) Gradient algorithms for complex non-Gaussian independent component/vector extraction, question of convergence. IEEE Trans Signal Process 67(4):1050–1064

    MathSciNet  MATH  Google Scholar 

  27. Li Y, Amari SI, Cichocki A, Guan C (2006) Probability estimation for recoverability analysis of blind source separation based on sparse representation. IEEE Trans Inf Theory 52(7):3139–3152

    MathSciNet  MATH  Google Scholar 

  28. Li Y, Amari SI, Cichocki A, Ho DWC, Xie S (2006) Underdetermined blind source separation based on sparse representation. IEEE Trans Signal Process 54(2):423–437

    MATH  Google Scholar 

  29. Li Y, Yu Z, Bi N, Xu Y, Gu Z, Amari SI (2014) Sparse representation for brain signal processing. IEEE Signal Process Mag 31(3):96–106

    Google Scholar 

  30. Mirzaei S, Hamme HV, Norouzi Y (2016) Underdetermined reverberant audio source separation using Bayesian non-negative matrix factorization. Speech Commun 81:129–137

    Google Scholar 

  31. Mohimani H, Babaie-Zadeh M, Jutten C (2009) A fast approach for overcomplete sparse decomposition based on smoothed l0 norm. IEEE Trans Signal Process 57(1):289–301

    MathSciNet  MATH  Google Scholar 

  32. Qin Z, Fan J, Liu Y, Gao Y, Li GY (2018) Sparse representation for wireless communications. IEEE Signal Process Mag 35(1):40–58

    Google Scholar 

  33. Reju VG, Koh SN, Soon IY (2009) An algorithm for mixing matrix estimation in instantaneous blind source separation. Signal Process 89:1762–1773

    MATH  Google Scholar 

  34. Rodriguez A, Laio A (2014) Clustering by fast search and find of density peaks. Science 344(6191):1492–1496

    Google Scholar 

  35. Su Q, Shen Y, Wei Y, Deng C (2017) Underdetermined blind source separation by a novel time-frequency method. Int J Electron Commun 77:43–49

    Google Scholar 

  36. Sugden P, Canagarajah N (2003) Underdetermined blind separation using learned basis function sets. Electron Lett 39(1):158–160

    Google Scholar 

  37. Sun J, Li Y, Wen J, Yan S (2016) Novel mixing matrix estimation approach in underdetermined blind source separation. Neurocomputing 173:623–632

    Google Scholar 

  38. Taseska M, Habets EAP (2018) Blind source separation of moving sources using sparsity-based source detection and tracking. IEEE Trans Audio Speech Lang Process 26(3):657–670

    Google Scholar 

  39. Theis FJ, Puntonet CG, Lang EW (2006) Median-based clustering for underdetermined blind signal processing. IEEE Signal Process Lett 13(2):96–99

    Google Scholar 

  40. Took CC, Sanei S, Chambers J, Dunne S (2006) Underdetermined blind source separation of temporomandibular joint sources. IEEE Trans Biomedical Eng 53(10):2123–2126

    Google Scholar 

  41. Vaerenbergh SV, Santamaria I (2006) A spectral clustering approach to underdetermined postnonlinear blind source separation of sparse sources. IEEE Trans Neural Netw 17(3):811–814

    Google Scholar 

  42. Xu R, Wunsch II DC (2009) Clustering. John Wiley & Sons, IEEE Press. Hoboken, New Jersey

  43. Yang J, Guo Y, Yang Z, Xie S (2019) Under-determined convolutive blind source separation combining density-based clustering and sparse reconstruction in time-frequency domain. IEEE Trans Circuits Syst I Reg Papers 66(8):3015–3027

    MathSciNet  Google Scholar 

  44. Zayyani H, Babaie-Zadeh M, Jutten C (2009) An iterative Bayesian algorithm for sparse component analysis in presence of noise. IEEE Trans Signal Process 57(11):4378–4390

    MathSciNet  MATH  Google Scholar 

  45. Zhang H, Hua G, Yu L, Cai Y, Bi G (2017) Underdetermined blind separation of overlapped speech mixtures in time-frequency domain with estimated number of sources. Speech Commun 89:1–16

    Google Scholar 

  46. Zhang W, Lv J, Li X, Zhu D, Jiang X, Zhang S, Zhao Y, Guo L, Ye J, Hu D, Liu T (2019) Experimental comparisons of sparse dictionary learning and independent component analysis for brain network inference from fMRI data. IEEE Trans Biomed Eng 66(1):289–299

    Google Scholar 

  47. Zhen L, Peng D, Yi Z, Xiang Y, Chen P (2017) Underdetermined blind source separation using sparse coding. IEEE Trans Neural Netw Learn Sys 28(12):3102–3108

    MathSciNet  Google Scholar 

  48. Zhong Y, Wang X, Zhao L, Feng R, Zhang L, Xu Y (2016) Blind spectral unmixing based on sparse component analysis for hyperspectral remote sensing imagery. ISPRS J Photogramm Remote Sens 119:49–63

    Google Scholar 

Download references

Acknowledgments

This project supported by National Natural Science Foundation of China (No. 60572183).

Author information

Authors and Affiliations

  1. School of Information Technology & Engineering, Guangzhou College of Commerce, Guangzhou, 511363, China

    Xuan-sen He & Li Xu

  2. College of Information Science and Engineering, Hunan University, Changsha, 410082, China

    Xuan-sen He

  3. School of Management and Economics, Beijing Institute of Technology, Beijing, 100081, China

    Fan He

Authors
  1. Xuan-sen He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fan He
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Li Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xuan-sen He.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

He, Xs., He, F. & Xu, L. Underdetermined mixing matrix estimation based on joint density-based clustering algorithms. Multimed Tools Appl 80, 8281–8308 (2021). https://doi.org/10.1007/s11042-020-10102-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-020-10102-5

Keywords

Search

Navigation