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Matrix Completion Using Graph Total Variation Based on Directed Laplacian Matrix

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Abstract

We propose two graph matrix completion algorithms called GMCM-DL and GMCR-DL, by employing a new definition of Graph Total Variation for matrices based on the directed Laplacian Matrix. We show that these algorithms outperform their peers in terms of RMSEs for both cases of uniform and row observations.

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Data Availability

The datasets analyzed during the current study are available in the repository of the National Centers for Environmental Information, ftp://ftp.ncdc.noaa.gov/pub/data/gsod.

References

  1. S. Aliaksei, J. Moura, Big data analysis with signal processing on graphs: Representation and processing of massive data sets with irregular structure. IEEE Signal Process. Mag. 31(5), 80–90 (2014)

    Article  Google Scholar 

  2. J. Cai, Jian-Feng, E. Candès, Z. Shen. A singular value thresholding algorithm for matrix completion. SIAM Journal on Optimization, 20(4), 1956–1982, (2010).

  3. S. Chen, A. Sandryhaila, J. Moura, J. Kovacevic, Signal recovery on graphs: Variation minimization. IEEE Trans. Signal Process. 63(17), 4609–4624 (2015)

    Article  MathSciNet  Google Scholar 

  4. M. Davenport, J. Romberg, An overview of low-rank matrix recovery from incomplete observations. IEEE Journal of Selected Topics in Signal Processing 10(4), 608–622 (2016)

    Article  Google Scholar 

  5. Y. Fang, H. Wang, S. Zhu, S. Li, Reconstructing DOA Estimation in the Second-Order Statistic Domain by Exploiting Matrix Completion. Circuits, Systems, and Signal Processing 38(10), 4855–4873 (2019)

    Article  Google Scholar 

  6. C. Guestrin, P. Bodik, R. Thibaux, M. Paskin, and S. Madden. Distributed regression: an efficient framework for modeling sensor network data. in Proc. of the International Conference on Information Processing in Sensor Networks (IPSN), pp.1–10, (2004).

  7. D. Hammond, P. Vandergheynst, R. Gribonval, Wavelets on graphs via spectral graph theory. Applied and Computational Harmonic Analysis 30(2), 129–150 (2011)

    Article  MathSciNet  Google Scholar 

  8. R. Hu, J. Tong, J. Xi, Q. Guo, Y. Yu, Matrix completion-based channel estimation for mmWave communication systems with array-inherent impairments. IEEE Access. 6, 62915–62931 (2018)

    Article  Google Scholar 

  9. S. Majidian, M.H. Kahaei, NGS based haplotype assembly using matrix completion. PLoS ONE 14(3), e0214455 (2019)

    Article  Google Scholar 

  10. S. Mavaddati. A novel singing voice separation method based on sparse non-negative matrix factorization and low-rank modeling. Iranian Journal of Electrical and Electronic Engineering. 15(2), 161–171, (2019). https://doi.org/10.22068/IJEEE.15.2.161.

  11. P. Milanfar, A tour of modern image filtering: new insights and methods, both practical and theoretical. IEEE Signal Process. Mag. 30(1), 106–128 (2013)

    Article  Google Scholar 

  12. A. Ortega, P. Frossard, J. Kovačević, J. Moura, P. Vandergheynst, Graph signal processing: overview, challenges, and applications. Proc. IEEE 106(5), 808–828 (2018)

    Article  Google Scholar 

  13. N. Parikh, S. Boyd, Proximal algorithms. Foundations and Trends in Optimization 1(3), 127–239 (2014)

    Article  Google Scholar 

  14. S. Razavikia, A. Amini, S. Daei, Reconstruction of binary shapes from blurred images via Hankel-structured low-rank matrix recovery. IEEE Trans. Image Process. 29, 2452–2462 (2019)

    Article  MathSciNet  Google Scholar 

  15. B. Recht, M. Fazel, P. Parrilo, Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM review. 52(3), 471–501 (2010)

    Article  MathSciNet  Google Scholar 

  16. J. Shi, J. Malik, Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22(8), 888–905 (2000)

    Article  Google Scholar 

  17. D. Shuman, S. Narang, P. Frossard, A. Ortega, P. Vandergheynst, The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains. IEEE Signal Process. Mag. 30(3), 83–98 (2013)

    Article  Google Scholar 

  18. R. Singh, C. Abhishek, B. Manoj. Graph Fourier transform based on directed Laplacian. International Conference on Signal Processing and Communications (SPCOM) IEEE, (2016).

  19. D. Tian, H. Mansour, A. Knyazev, A. Vetro. Chebyshev and conjugate gradient filters for graph image denoising, IEEE International Conference on Multimedia and Expo Workshops (ICMEW), 1–6, (2014).

  20. F. Wen, J. Shi, Z. Zhang, Direction finding for bistatic MIMO radar with unknown spatially colored noise. Circuits, Systems, and Signal Processing 39(5), 2412–2424 (2020)

    Article  Google Scholar 

  21. Z. Wu, R. Leahy, An optimal graph theoretic approach to data clustering: Theory and its application to image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 15(11), 1101–1113 (1993)

    Article  Google Scholar 

  22. N. Zarmehi, A. Amini, F. Marvasti, Low Rank and Sparse Decomposition for Image and Video Applications. IEEE Trans. Circuits Syst. Video Technol. 30(7), 2046–2056 (2019)

    Article  Google Scholar 

  23. X. Zhu and M. Rabbat. Approximating signals supported on graphs, in Proc. of the international Conference on Acoustics, Speech, and Signal Processing (ICASSP), 3921–3924, (2012).

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Authors and Affiliations

  1. School of Electrical Engineering, Iran University of Science & Technology, 16846-13114, Tehran, Iran

    Alireza Ahmadi, Sina Majidian & Mohammad Hossein Kahaei

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  1. Alireza Ahmadi
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  2. Sina Majidian
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  3. Mohammad Hossein Kahaei
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Correspondence to Mohammad Hossein Kahaei.

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Ahmadi, A., Majidian, S. & Kahaei, M.H. Matrix Completion Using Graph Total Variation Based on Directed Laplacian Matrix. Circuits Syst Signal Process 40, 3099–3106 (2021). https://doi.org/10.1007/s00034-020-01613-5

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  • DOI: https://doi.org/10.1007/s00034-020-01613-5

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