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The Power of Tensor-Based Approaches in Cardiac Applications

  • Sibasankar PadhyEmail author
  • Griet Goovaerts
  • Martijn Boussé
  • Lieven De Lathauwer
  • Sabine Van Huffel
Chapter
Part of the Series in BioEngineering book series (SERBIOENG)

Abstract

The electrocardiogram (ECG) is a biomedical signal that is widely used to monitor the heart and diagnose cardiac problems. Depending on the clinical need, the ECG is recorded with one or multiple leads (or channels) from different body locations. The signals from different ECG leads represent the cardiac activity in different spatial directions and are thus complementary to each other. In traditional methods, the ECG signal is represented as a vector or a matrix and processed to analyze temporal information. When multiple leads are present, most methods process each lead individually and combine decisions from all leads in a later stage. While this approach is popular, it fails to exploit the structural information captured by the different leads. Recently, there is a trend towards the use of tensor-based methods in biomedical signal processing. These methods represent the signals by tensors, which are higher-order generalizations of vectors and matrices that allow the analysis of multiple modes simultaneously. In the past years, tensor decomposition methods have been applied to ECG signals to solve different clinical challenges. This chapter discusses the power of different tensor decompositions with a focus on typical ECG problems that can be solved using tensors.

Notes

Acknowledgements

This research was supported by: imec funds 2017, Belgian Foreign Affairs Development Cooperation: VLIR-UOS programs (20132019), Fonds de la Recherche Scientifique—FNRS and Fonds Wetenschappelijk Onderzoek—Vlaanderen under EOS Project no 30468160 (SeLMA), Research Council KU Leuven: C1 project C16/15/059-nD, European Research Council: The research leading to these results has received funding from the European Research Council under the European Unions Seventh Framework Programme (FP7/2007–2013)/ERC Advanced Grant: BIOTENSORS (no. 339804). This paper reflects only the authors’ views and the Union is not liable for any use that may be made of the contained information. Griet Goovaerts is a SB Ph.D. fellow at Fonds voor Wetenschappelijk Onderzoek (FWO), Vlaanderen, supported by the Flemish government.

References

  1. 1.
    Abadi, B.M., Jarchi, D., Sanei, S.: Simultaneous localization and separation of biomedical signals by tensor factorization. In: 15th IEEE Workshop on Statistical Signal Processing, pp. 497–500. Cardiff, UK (2015)Google Scholar
  2. 2.
    Abenstein, J.P., Tompkins, W.J.: A new data-reduction algorithm for real-time ECG analysis. IEEE Trans. Biomed. Eng. BME 29(1), 43–48 (1982)CrossRefGoogle Scholar
  3. 3.
    Ansari, S., Farzaneh, N., Duda, M., Horan, K., Andersson, H.B., Goldberger, Z.D., Nallamothu, B.K., Najarian, K.: A review of automated methods for detection of myocardial ischemia and infarction using electrocardiogram and electronic health records. IEEE Rev. Biomed. Eng. 10, 264–298 (2017)CrossRefGoogle Scholar
  4. 4.
    Akhbari, M., Niknazar, M., Jutten, C., Shamsollahi, M., Rivet, B.: Fetal electrocardiogram R-peak detection using robust tensor decomposition and extended kalman filtering. In: Computing in Cardiology, Spain 2013, pp. 189–192 (2013)Google Scholar
  5. 5.
    Akbari, H., Shamsollahi, M.B., Phlypo, R.: Fetal ECG extraction using \(\pi \) tucker decomposition. In: 2015 International Conference on Systems, Signals and Image Processing (IWSSIP), Sept 2015, pp. 174–178 (2015)Google Scholar
  6. 6.
    Al-Fahoum, A.S.: Quality assessment of ECG compression techniques using a wavelet-based diagnostic measure. IEEE Trans. Inf. Technol. Biomed. 10(1), 182–191 (2006)CrossRefGoogle Scholar
  7. 7.
    Arif, M., Malagore, I., Afsar, F.: Detection and localization of myocardial infarction using k-nearest neighbor classifier. J. Med. Syst. 36(1), 279–289 (2012)CrossRefGoogle Scholar
  8. 8.
    Bergqvist, G., Larsson, E.G.: The higher-order singular value decomposition: theory and an application. IEEE Signal Process. Mag. 27(3), 151–154 (2010)CrossRefGoogle Scholar
  9. 9.
    Bharath, H.N., Sauwen, N., Sima, D.M., Himmelreich, U., De Lathauwer, L., Van Huffel, S.: Canonical polyadic decomposition for tissue type differentiation using multi-parametric MRI in high-grade gliomas. In: 24th European Signal Processing Conference (EUSIPCO), Budapest, 2016, pp. 547–551 (2016)Google Scholar
  10. 10.
    Bharath, H.N., Sima, D.M., Sauwen, N., Himmelreich, U., De Lathauwer, L., Van Huffel, S.: Non-negative canonical polyadic decomposition for tissue type differentiation in gliomas. IEEE J. Biomed. Health Inform. 21(4), 1124–1132 (2017)CrossRefGoogle Scholar
  11. 11.
    Boussé, M., Goovaerts, G., Vervliet, N., Debals, O., Van Huffel, S., De Lathauwer, L.: Irregular heartbeat classification using Kronecker product equations. In: 39th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC 2017), July 2017, pp. 438–441 (2017)Google Scholar
  12. 12.
    Boussé, M., Vervliet, N., Domanov, I., Debals, O., De Lathauwer, L.: Linear systems with a canonical polyadic decomposition constrained solution: algorithms and applications. Numerical Linear Algebra with Applications 2018, p. e2190 (2018)Google Scholar
  13. 13.
    Boussé, M., De Lathauwer, L.: Nonlinear least squares algorithm for canonical polyadic decomposition using low-rank weights. In: 7th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, pp. 1–5. CAMSAP, Curaçao, Dutch Antilles (2017)Google Scholar
  14. 14.
    Boussé, M., Debals, O., De Lathauwer, L.: A tensor-based method for large-scale blind source separation using segmentation. IEEE Trans. Signal Process. 65(2), 346–358 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Bro, R., Andersson, C., Kiers, H.: PARAFAC2-Part II. Modeling chromatographic data with retention time shifts. J. Chemom. 309, 295–309 (1999)CrossRefGoogle Scholar
  16. 16.
    Bro, R., Kiers, H.A.L.: A new efficient method for determining the number of components in PARAFAC models. J. Chemom. 17, 274–286 (2003)CrossRefGoogle Scholar
  17. 17.
    Burattini, L., Man, S., Burattini, R., Swenne, C.A.: Comparison of standard versus orthogonal ecg leads for t-wave alternans identification. Ann. Noninvasive Electrocardiol. 17(2), 130–140 (2012)CrossRefGoogle Scholar
  18. 18.
    Cetin, A.E., Koymen, H., Aydin, M.C.: Multichannel ECG data compression by multirate signal processing and transform domain coding techniques. IEEE Trans. Biomed. Eng. 40(5), 495–499 (1993)CrossRefGoogle Scholar
  19. 19.
    Cichocki, A., Mandic, D.P., De Lathauwer, L., Zhou, G., Zhao, Q., Caiafa, C.F., Phan, A.H.: Tensor decompositions for signal processing applications: from two-way to multiway component analysis. IEEE Signal Process. Mag. 32(2), 145–163 (2015)CrossRefGoogle Scholar
  20. 20.
    Cong, F., Nandi, A.K., He, Z., Cichocki, A., Ristaniemi, T.: Fast and effective model order selection to determine the number of sources in a linear transformation model. In: Proceedings of the 20th European Signal Processing Conference (EUSIPCO), Bucharest, Romania, 2012, pp. 1870–1874 (2012)Google Scholar
  21. 21.
    Cox, J.R., Nolle, F.M., Fozzard, H.A., Oliver, G.C.: AZTEC: a preprocessing scheme for real-time ECG rhythm analysis. IEEE Trans. Biomed. Eng. BME 15, 128–129 (1968)CrossRefGoogle Scholar
  22. 22.
    Dauwels, J., Srinivasan, K., Reddy, M.R., Cichocki, A.: Near-lossless multichannel EEG compression based on matrix and tensor decompositions. IEEE J. of Biomed. Health Info. 17(3), 708–714 (2013)CrossRefGoogle Scholar
  23. 23.
    Debals, O., De Lathauwer, L.: Stochastic and deterministic tensorization for blind signal separation. In: Latent Variable Analysis and Signal Separation, pp. 3–13 (2015)CrossRefGoogle Scholar
  24. 24.
    Debals, O., Van Barel, M., De Lathauwer, L.: Blind signal separation of rational functions using Löwner-based tensorization. In: International Conference on Acoustics, Speech, Signal Processing (ICASSP), Brisbane, Australia Apr 2015, pp. 4145–4149 (2015)Google Scholar
  25. 25.
    Debals, O., De Lathauwer, L.: The concept of tensorization. Technical Report 17-99, ESAT-STADIUS, KU Leuven, Leuven, Belgium (2017)Google Scholar
  26. 26.
    De Lathauwer, L., De Moor, B., Vandewalle, J.: A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl. 21(4), 1253–1278 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    De Lathauwer, L., Vandewalle, J.: Dimensionality reduction in higher-order signal processing and rank-(\(R_1\), \(R_2\), \(\ldots \), \(R_N\)) reduction in multilinear algebra. Linear Algebr. Its Appl. 391, 31–55 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    Domanov, I., De Lathauwer, L.: On the uniqueness of the canonical polyadic decomposition of third-order tensors—Part II: uniqueness of the overall decomposition. SIAM J. Matrix Anal. Appl. 34(3), 876–903 (2013)MathSciNetzbMATHCrossRefGoogle Scholar
  29. 29.
    Domanov, I., De Lathauwer, L.: Generic uniqueness conditions for the canonical polyadic decomposition and INDSCAL. SIAM J. Matrix Anal. Appl. 36(4), 1567–1589 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    Domanov, I., De Lathauwer, L.: Canonical polyadic decomposition of third-order tensors: relaxed uniqueness conditions and algebraic algorithm. Linear Algebr. Its Appl. 513, 342–375 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  31. 31.
    Geirnaert, S., Goovaerts, G., Padhy, S., Boussé, M., De Lathauwer, L., Van Huffel, S.: Tensor-based ECG signal processing applied to atrial fibrillation detection. In: Proceedings of the 52th IEEE Asilomar conference, Pacific Grove, CA, USA (2018)Google Scholar
  32. 32.
    Goldberger, A.L., et al.: Physiobank, physiotoolkit, and physionet: components of a new research resource for complex physiologic signals. Circulation 101(23), e215–e220 (2000)Google Scholar
  33. 33.
    Goovaerts, G., Varon, C., Vandenberk, B., Willems, R., Van Huffel, S.: Tensor-based detection of T wave alternans in multilead ECG signals. In: Computing in Cardiology Conference, pp. 185–188 (2014)Google Scholar
  34. 34.
    Goovaerts, G., De Wel, O., Vandenberk, B., Willems, R., Van Huffel, S.: Detection of irregular heartbeats using tensors. In: 42nd Annual Conference of Computing in Cardiology, Sept 2015 (2015)Google Scholar
  35. 35.
    Goovaerts, G., Vandenberk, B., Willems, R., Van Huffel, S.: Tensor-based detection of T wave alternans using ECG. In: Proceedings of the 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society of the IEEE (EMBC), Milan, Italy, Aug 2015, pp. 6991–6994 (2015)Google Scholar
  36. 36.
    Goovaerts, G., Vandenberk, B., Willems, R., Van Huffel, S.: Automatic detection of T wave alternans using tensor decompositions in multilead ECG signals. Physiol. Meas. 38(8), 1513–1528 (2017)CrossRefGoogle Scholar
  37. 37.
    Goovaerts, G., Van Huffel, S., Hu, X.: Tensor-based analysis of ECG changes prior to in-hospital cardiac arrest. In: Proceedings of the 44rd Annual Computing in Cardiology (CinC 2017). CinC, Rennes, France, Sept (2017)Google Scholar
  38. 38.
    Goovaerts, G., Willems, R., Van Huffel, S.: Tensor-based ECG analysis in sudden cardiac death. Ph.D. thesis, Department of Electrical Engineering, KU Leuven, Dec 2018 (2018)Google Scholar
  39. 39.
    Goovaerts, G., Boussé, M., Do, D., De Lathauwer, L., Van Huffel, S., Hu, X.: Analysis of changes in ECG morphology prior to in-hospital cardiac arrest using weighted tensor decompositions. Submitted for publicationGoogle Scholar
  40. 40.
    Håstad, J.: Tensor rank is NP-complete. J. Algorithms 11(4), 644–654 (1990)MathSciNetzbMATHCrossRefGoogle Scholar
  41. 41.
    Hayn, D., Kollmann, A., Schreier, G.: Automated QT interval measurement from multilead ECG signals. In: Computing in Cardiology, Valencia, Spain, 2006, pp. 381–384 (2006)Google Scholar
  42. 42.
    He, H., Tan, Y., Xing, J.: Unsupervised classification of 12-lead ECG signals using wavelet tensor decomposition and two-dimensional Gaussian spectral clustering. Knowl.-Based Syst. 163, 392–403 (2019)CrossRefGoogle Scholar
  43. 43.
    He, J., Liu, Q., Christodoulou, A.G., Ma, C., Lam, F., Liang, Z.: Accelerated high-dimensional MR imaging with sparse sampling using low-rank tensors. IEEE Trans. Med. Imaging 35(9), 2119–2129 (2016)CrossRefGoogle Scholar
  44. 44.
    Hearing, B.D., Stone, P.H., Verrier, R.L.: Frequency response characteristics required for detection of T-wave alternans during ambulatory ECG monitoring. Ann. Noninvasive Electrocardiol. 1(2), 103–112 (1996)CrossRefGoogle Scholar
  45. 45.
    Hillar, C.J., Lim, L.H.: Most tensor problems are NP-hard. Technical Report, Eprint arXiv:0911.1393v4 (2009)
  46. 46.
    Huang, K., Zhang, L.: Cardiology knowledge free ECG feature extraction using generalized tensor rank one discriminant analysis. EURASIP J. Adv. Signal Process. (1) (2014)Google Scholar
  47. 47.
    Ikeda, T., Saito, H., Tanno, K., Shimizu, H., Watanabe, J., Ohnishi, Y., Kasamaki, Y., Ozawa, Y.: T-wave alternans as a predictor for sudden cardiac after myocardial infarction. Am. J. Cardiol. 89(1), 79–82 (2002)CrossRefGoogle Scholar
  48. 48.
    Ishteva, M., Absil, P.A., Van Huffel, S., De Lathauwer, L.: Best low multilinear rank approximation of higher-order tensors, based on the riemannian trust-region scheme. SIAM J. Matrix Anal. Appl. 32(1), 115–135 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  49. 49.
    Jalaleddine, S., Hutchens, C., Stratran, R., Coberly, W.: ECG data compression techniques—a unified approach. IEEE Trans. Biomed. Eng. 37(4), 329–343 (1990)CrossRefGoogle Scholar
  50. 50.
    Jayachandran, E., Joseph, K.P., Acharya, U.R.: Analysis of myocardial infarction using discrete wavelet transform. J. Med. Syst. 34(6), 985–992 (2010)CrossRefGoogle Scholar
  51. 51.
    Kargas, N., Weingartner, S., Sidiropoulos, N.D., Akcakaya, M.: Low-rank tensor regularization for improved dynamic quantitative magnetic resonance imaging. In: SPARS 2017, Lisbon, Portugal, pp. 1–2 (2017)Google Scholar
  52. 52.
    Kolda, T.G., Bader, B.W.: Tensor decompositions and applications. SIAM Rev. 51(3), 455–500 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  53. 53.
    Kuang, L., Hao, F., Yang, L., Lin, M., Luo, C., Min, G.: A tensor-based approach for big data representation and dimensionality reduction. IEEE Trans. Emerg. Top. Comput. 2(3), 280–291 (2014)CrossRefGoogle Scholar
  54. 54.
    Kuzilek, J., Kremen, V., Lhotska, L.: Comparison of JADE and canonical correlation analysis for ECG de-noising. In: Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Chicago, USA, pp. 3857–3860 (2014)Google Scholar
  55. 55.
    Laguna, P., Jane, R., Caminal, P.: Automatic detection of wave boundaries in multilead ECG signals: validation with the CSE database. Comput. Biomed. Res. 27, 45–60 (1994)CrossRefGoogle Scholar
  56. 56.
    Laguna, P., Martinez Cortes, J.P., Pueyo, E.: Techniques for ventricular repolarization instability assessment from the ECG. Proc. IEEE 104(2), 392–415 (2016)CrossRefGoogle Scholar
  57. 57.
    Lee, H., Buckley, K.M.: ECG data compression using cut and align beats approach and 2-D transforms. IEEE Trans. Biomed. Eng. 46(5), 556–564 (1999)CrossRefGoogle Scholar
  58. 58.
    Li, J., Zhang, L., Tao, D., Sun, H., Zhao, Q.: Aprior neurophysiologic knowledge free tensor-based scheme for single trial EEG classification. IEEE Trans. Neural Syst. Rehabil. Eng. 17(2), 107–115 (2009)CrossRefGoogle Scholar
  59. 59.
    Li, D., Huang, K., Zhang, H., Zhang, L.: UMPCA based feature extraction for ECG. ISNN2013 Advances in Neural Networks, pp. 383–390. Springer, Berlin, Heidelberg (2013)Google Scholar
  60. 60.
    Li, X., Zhou, H., Li, L.: Tucker tensor regression and neuroimaging analysis. arXiv:1304.5637 pp. 1–28 (2013)
  61. 61.
    Llamedo, M., Khawaja, A., Martínez, J.: Analysis of 12-lead classification models for ECG classification. In: Computing in Cardiology, Sept 2010, pp. 673–676 (2010)Google Scholar
  62. 62.
    Lu, H.L., Ong, K., Chia, P.: An automated ECG classification system based on a neuro-fuzzy system. Comput. Cardiol. 387–390 (2000)Google Scholar
  63. 63.
    Lu, H., Plataniotis, K.N., Venetsanopoulos, A.N.: MPCA: multilinear principal component analysis of tensor objects. IEEE Trans. Neural Netw. 19(1), 18–39 (2008)CrossRefGoogle Scholar
  64. 64.
    Lu, H., Plataniotis, K.N., Venetsanopoulos, A.N.: Uncorrelated multilinear principal component analysis for unsupervised multilinear subspace learning. IEEE Trans. Neural Netw. 20(11), 1820–1836 (2009)CrossRefGoogle Scholar
  65. 65.
    Martinez, J., Olmos, S.: Methodological principles of T wave alternans analysis: a unified framework. IEEE Trans. Biomed. Eng. 52(4), 599–613 (2005)CrossRefGoogle Scholar
  66. 66.
    Manikandan, M.S., Dandapat, S.: Wavelet energy based diagnostic distortion measure for ECG. Biomed. Signal Process. Control., Elsevier 2, 80–96 (2007)CrossRefGoogle Scholar
  67. 67.
    Manikandan, M.S., Dandapat, S.: Wavelet threshold based TDL and TDR algorithms for real-time ECG signal compression. Biomed. Signal Process. Control., Elsevier 3, 44–66 (2008)CrossRefGoogle Scholar
  68. 68.
    Monasterio, V., Laguna, P., Martinez, J.: Multilead analysis of T-wave alternans in the ECG using principal component analysis. IEEE Trans. Biomed. Eng. 56(7), 1880–1890 (2009)CrossRefGoogle Scholar
  69. 69.
    Mueller, W.: Arrhythmia detection program for an ambulatory ECG monitor. Biomed. Sci. Instrum. 14, 81–85 (1978)Google Scholar
  70. 70.
    Narayan, S.M., Smith, J.M.: Spectral analysis of periodic fluctuations in electrocardiographic repolarization. IEEE Trans. Biomed. Eng. 46(2), 203–212 (1999)CrossRefGoogle Scholar
  71. 71.
    Nearing, B.D., Verrier, R.L.: Modified moving average analysis of T-wave alternans to predict ventricular fibrillation with high accuracy. J. Appl. Physiol. 92(2), 541–549 (2002) (Bethesda, Md.: 1985)CrossRefGoogle Scholar
  72. 72.
    Niknazar, M., Rivet, B., Jutten, C.: Fetal QRS complex detection based on three-way tensor decomposition. Comput. Cardiol., Spain, 185–188 (2013)Google Scholar
  73. 73.
    Oliveira, P.M.R., de, Zarzoso, V.: Source analysis and selection using block term decomposition in Atrial fibrillation. In: Latent Variable Analysis and Signal Separation, pp. 46–56. Springer (2018)Google Scholar
  74. 74.
    Paatero, P.: A weighted non-negative least squares algorithm for three-way ‘PARAFAC’ factor analysis. Chemom. Intell. Lab. Syst. 38(2), 223–242 (1997)CrossRefGoogle Scholar
  75. 75.
    Padhy, S., Dandapat, S.: Exploiting multi-lead electrocardiogram correlations using robust third-order tensor decomposition. Healthc. Technol. Lett. 2(5), 112–117 (2015)CrossRefGoogle Scholar
  76. 76.
    Padhy, S., Sharma, L., Dandapat, S.: Multilead ECG data compression using SVD in multiresolution domain. Biomed. Signal Process. Control., Elsevier 23, 10–18 (2016)CrossRefGoogle Scholar
  77. 77.
    Padhy, S., Dandapat, S.: Third-order tensor based analysis of multilead ECG for classification of myocardial infarction. Biomed. Signal Process. Control., Elsevier 31, 71–78 (2017)CrossRefGoogle Scholar
  78. 78.
    Padhy, S., Multilead, E.C.G.: Data analysis using SVD and higher-order SVD. Ph.D. thesis, Indian Institute of Technology Guwahati, India, March 2017. http://gyan.iitg.ernet.in/handle/123456789/1006 (2017)
  79. 79.
    Padhy, S., Dandapat, S.: Validation of \(\mu \)-volt T-wave alternans analysis using multiscale analysis-by-synthesis and higher-order SVD. Biomed. Signal Process. Control., Elsevier 40, 171–179 (2018)CrossRefGoogle Scholar
  80. 80.
    Reddy, M.R.S., Edenbrandt, L., Svensson, J., Haisty, W.K., Pahlm, O.: Neural network versus electrocardiographer and conventional computer criteria in diagnosing anterior infarct from the ECG. In: Computers in Cardiology, Oct 1992, pp. 667–670 (1992)Google Scholar
  81. 81.
    Ribeiro, L.N., Hidalgo-Muñoz, A.R., Favier, G., Mota, J.C.M., De Almeida, A.L.F., Zarzoso, V.: A tensor decomposition approach to noninvasive atrial activity extraction in atrial fibrillation ecg. In: 23rd European Signal Processing Conference (EUSIPCO-2015), Aug 2015, pp. 2576–2580 (2015)Google Scholar
  82. 82.
    Sharma, L.N., Dandapat, S., Mahanta, A.: Multichannel ECG data compression based on multiscale principal component analysis. IEEE Trans. Inf. Technol. Biomed. 16(4), 730–736 (2012)CrossRefGoogle Scholar
  83. 83.
    Sharma, L.N., Tripathy, R., Dandapat, S.: Multiscale energy and eigenspace approach to detection and localization of myocardial infarction. IEEE Trans. Biomed. Eng. 62(7), 1827–1837 (2015)CrossRefGoogle Scholar
  84. 84.
    Sidiropoulos, N., De Lathauwer, L., Fu, X., Huang, K., Papalexakis, E., Faloutsos, C.: Tensor decomposition for signal processing and machine learning. IEEE Trans. Signal Process. 65(13), 3551–3582 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  85. 85.
    Smith, J.M., Clancy, E.A., Valeri, C.R., Ruskin, J.N., Cohen, R.J.: Electrical alternans and cardiac electrical instability. Circulation 77(1), 110–121 (1988)CrossRefGoogle Scholar
  86. 86.
    Srinivasan, K., Dauwels, J., Reddy, M.R.: Multichannel EEG compression: Wavelet-based image and volumetric coding approach. IEEE J. Biomed. Health Inform. 17(1), 113–120 (2013)CrossRefGoogle Scholar
  87. 87.
    Sun, L., Lu, Y., Yang, K., Li, S.: ECG analysis using multiple instance learning for myocardial infarction detection. IEEE Trans. Biomed. Eng. 59(12), 3348–3356 (2012)CrossRefGoogle Scholar
  88. 88.
    Tao, D., Li, X., Wu, X., Maybank, S.J.: General tensor discriminant analysis and Gabor features for gait recognition. IEEE Trans. Pattern Anal. Mach. Intell. 29(10), 1700–1715 (2007)CrossRefGoogle Scholar
  89. 89.
    Vervliet, N., Debals, O., De Lathauwer, L.: Tensorlab 3.0—Numerical optimization strategies for large-scale constrained and coupled matrix/tensor factorization. In: 50th Asilomar Conference on Signals, Systems and Computers, pp. 1733–1738. IEEE (2016)Google Scholar
  90. 90.
    Thygesen, K., Alpert, J.S., Jaffe, A.S., Simoons, M.L., Chaitman, B.R., White, H.D.: Third universal definition of myocardial infarction. Circulation 126(16), 2020–2035 (2012)CrossRefGoogle Scholar
  91. 91.
    Vandecappelle, M., Boussé, M., Vervliet, N., De Lathauwer, L.: CPD updating using low-rank weights. In: 25th European Signal Processing Conference (EUSIPCO), pp. 557–663. Kos, Greece (2017)Google Scholar
  92. 92.
    Van Eyndhoven, S., Boussé, M., Hunyadi, B., De Lathauwer, L., Van Huffel, S.: Single-channel EEG classification by multi-channel tensor subspace learning and regression. In: Proceedings of the 28th IEEE International Workshop on Machine Learning for Signal Processing (MLSP 2018), Sept (2018)Google Scholar
  93. 93.
    Vasilescu, M., Terzopoulos, D.: Multilinear (tensor) image synthesis, analysis, and recognition [exploratory dsp]. IEEE Signal Process. Mag. 24(6), 118–123 (2007)CrossRefGoogle Scholar
  94. 94.
    Vervliet, N., Debals, O., Sorber, L., De Lathauwer, L.: Breaking the curse of dimensionality using decompositions of incomplete tensors: tensor-based scientific computing in big data analysis. IEEE Signal Process. Mag. 31(5), 71–79 (2014)CrossRefGoogle Scholar
  95. 95.
    Vítek, M., Hrubeš, J., Kozumplík, J.: A wavelet-based ECG delineation in multilead ECG signals: evaluation on the CSE database. In: World Congress on Medical Physics and Biomedical Engineering, pp. 177–180. Springer, Berlin, Heidelberg (2009)Google Scholar
  96. 96.
    Wei, J., Chang, C., Chou, N., Jan, G.: ECG data compression using truncated singular value decomposition. IEEE Trans. Inf. Technol. Biomed. 5(4), 290–299 (2001)CrossRefGoogle Scholar
  97. 97.
    Yaman, B., Weingärtner, S., Kargas, N., Sidiropoulos, N.D., Akcakaya, M.: Locally low-rank tensor regularization for high-resolution quantitative dynamic MRI. In: 7th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, pp. 1–5. CAMSAP, Curaçao, Dutch Antilles (2017)Google Scholar
  98. 98.
    Zarzoso, V.: Parameter estimation in block term decomposition for noninvasive atrial fibrillation analysis. In: 7th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, pp. 1–5. CAMSAP, Curaçao, Dutch Antilles (2017)Google Scholar
  99. 99.
    Zhou, H., Li, L., Zhu, H.: Tensor regression with applications in neuroimaging data analysis. J. Am. Stat. Assoc. 108(502), 540–552 (2013)MathSciNetzbMATHCrossRefGoogle Scholar

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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Sibasankar Padhy
    • 1
    • 2
    • 3
    Email author
  • Griet Goovaerts
    • 1
    • 2
  • Martijn Boussé
    • 1
  • Lieven De Lathauwer
    • 1
    • 4
  • Sabine Van Huffel
    • 1
    • 2
  1. 1.Department of Electrical Engineering (ESAT)STADIUS Center for Dynamical Systems, Signal Processing and Data Analytics, KU LeuvenLeuvenBelgium
  2. 2.imecLeuvenBelgium
  3. 3.School of Electronics (SENSE)Vellore Institute of TechnologyVelloreIndia
  4. 4.Group Science, Engineering and TechnologyKU Leuven KulakKortrijkBelgium

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