# Multilinear EigenECGs and FisherECGs for Individual Identification from Information Obtained by an Electrocardiogram Sensor

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Multilinear Subspace Learning (MSL)

#### 2.1. Multilinear Principal Component Analysis (MPCA)

#### 2.2. Multilinear Linear Discriminant Analysis (MLDA)

#### 2.3. Comparison Multilinear Subspace Learning with Linear Subspace Learning

- Vectorization of LSL destroys the structural correlations of the original data, and that yields poor feature extraction.
- When a high dimensional tensor such as a video is rearranged into a one dimensional vector, the dimension of the one-dimensional tensor becomes very large. Analyzing a high dimensional vector results in a small sample size problem where the parameters to be estimated are larger than the number of data for training and results in high computing loads.

- The input form of the tensor is preserved as the original shape.
- It is possible to extract more compact and useful features than LSL. MSL is less severe than LSL in the problem that the dimension of the data is much larger than the number of data that is required for training.
- High dimensional tensors can be efficiently processed in a lower dimension than in the linear method.

## 3. ECG Biometrics Based on Multilinear Subspace Learning

#### 3.1. Preprocessing

#### 3.2. ECG Biometrics Based on Multilinear EigenECG (MEECG)

#### 3.3. ECG Biometrics Based on Multilinear Fisher ECG (MFECG)

#### 3.4. Similarity Measures

#### 3.5. Evaluation

#### 3.6. Comparison of Correlation by Reshaping

## 4. Experimental Results

#### 4.1. PTB-ECG Database

#### 4.2. CU-ECG Database

#### 4.3. Experimental Results

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Wang, H.; Hu, J.; Deng, W. Compressing fisher vector for robust face recognition. IEEE Access.
**2017**, 5, 23157–23165. [Google Scholar] [CrossRef] - Jain, A.K.; Arora, S.S.; Cao, K.; Best-Rowden, L.; Bhatnagar, A. Fingerprint recognition of young children. IEEE Trans. Inf. Forensics Secur.
**2017**, 12, 1505–1514. [Google Scholar] [CrossRef] - Nguyen, B.P.; Tay, W.L.; Chui, C.K. Robust biometric recognition from palm depth images for gloved hands. IEEE Trans. Hum.-Mach. Syst.
**2015**, 45, 799–804. [Google Scholar] [CrossRef] - Zhang, Y.; Juhola, M. On biometrics with eye movements. IEEE J. Biome Health Inform.
**2017**, 21, 1360–1366. [Google Scholar] [CrossRef] [PubMed] - Pokhriyal, N.; Tayal, K.; Nwogu, I.; Govindaraju, V. Cognitive-biometric recognition from language usage: A feasibility study. IEEE Trans. Inf. Forensics Secur.
**2017**, 12, 134–143. [Google Scholar] [CrossRef] - Boles, W.W. A security system based on human iris identification using wavelet transform. In Proceedings of the First International Conference on Conventional and Knowledge based Intelligent Electronics Systems, Adelaide, SA, Australia, 21–23 May 1997; pp. 533–541. [Google Scholar]
- Choi, G.H.; Moon, H.M.; Pan, S.B. Biometrics system technology trends based on biosignal. J. Digit. Convers.
**2017**, 15, 381–391. [Google Scholar] [CrossRef] - Gahi, Y.; Lamrani, M.; Zoglat, A.; Guennoun, M.; Kapralos, B.; El-Khatib, K. Biometric identification system based on electrocardiogram data. In Proceedings of the New Technologies, Mobility and Security, Tangier, Morocco, 5–7 November 2008; pp. 1–4. [Google Scholar]
- Kim, J.J.; Lee, S.M.; Ryu, G.S.; Lee, J.H.; Park, K.H. Hierarchical authentication algorithm using curvature based fiducial point extraction of ECG signals. J. Korea Multi Soc.
**2017**, 20, 465–473. [Google Scholar] [CrossRef] - Kim, J.K.; Lee, K.B.; Hong, S.G. ECG-based biometric authentication using random forest. J. Inst. Electron. Inf. Eng.
**2017**, 54, 100–105. [Google Scholar] - Lim, C.S. A study on the analysis of technology and service issues for wearable devices and future development direction. J. Korea Inst. Next Gener. Comput.
**2017**, 13, 81–89. [Google Scholar] - Lathauwer, L.D.; Moor, B.D.; Vandewalle, J. A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl.
**2000**, 21, 1253–1278. [Google Scholar] [CrossRef] - Greub, W. Multilinear Algebra, 2nd ed.; Springer-Verlag: New York, NY, USA, 1978; pp. 1–296. ISBN 9780387902845. [Google Scholar]
- Kolda, T.G.; Bader, B.W. Tensor decompositions and applications. Siam Rev.
**2009**, 51, 455–500. [Google Scholar] [CrossRef] - Howe, D.; Costanzo, M.; Fey, P.; Gojobori, T.; Hannick, L.; Hide, W.; Hill, D.P.; Kania, R.; Schaeffer, M.; Pierre, S.S.; et al. Big data: The future of biocuration. Nature
**2008**, 455, 47–50. [Google Scholar] [CrossRef] [PubMed] - Armbrust, M.; Fox, A.; Griffith, R.; Joseph, A.D.; Katz, R.; Konwinski, A.; Lee, G.H.; Patterson, D.; Babkin, A.; Stoica, I.; et al. A view of cloud computing. Commun. ACM
**2010**, 53, 50–58. [Google Scholar] [CrossRef] - Dean, J.; Ghemawat, S. MapReduce: Simplified data processing on large clusters. Commun. ACM
**2008**, 51, 107–113. [Google Scholar] [CrossRef] - Shakhnarovich, G.; Moghaddam, B. Face recognition in subspaces. In Handbook of Face Recognition; Li, S.Z., Jain, A.K., Eds.; Springer-Verlag: New York, NY, USA, 2004; pp. 141–168. ISBN 038740595X. [Google Scholar]
- Zhang, J.; Li, S.Z.; Wang, J. Manifold learning and applications in recognition. In Intelligent Multimedia Processing with Soft Computing; Tan, Y.P., Yap, K.H., Wang, L., Eds.; Springer-Verlag: Berlin, Germany, 2004; Volume 168, pp. 281–300. ISBN 354023053X. [Google Scholar]
- Burges, C.J.C. Dimension reduction: A guided tour. Found. Trends Mach. Learn.
**2010**, 2, 275–365. [Google Scholar] [CrossRef] - Law, M.H.C.; Jain, A.K. Incremental nonlinear dimensionality reduction by manifold learning. IEEE Trans. Pattern Anal. Mach. Int.
**2006**, 28, 377–391. [Google Scholar] [CrossRef] [PubMed] - Jolliffe, I.T. Principal Component Analysis, 2nd ed.; Springer-Verlag: New York, NY, USA, 2002; pp. 1–488. ISBN 9780387954424. [Google Scholar]
- Yang, J.; Zhang, D.; Frangi, A.F.; Yang, J. Two-dimensional PCA: A new approach to appearance-based face representation and recognition. IEEE Trans. Pattern Anal. Mach. Int.
**2004**, 26, 131–137. [Google Scholar] [CrossRef] - Ye, J.; Janardan, R.; Li, Q. GPCA: An efficient dimension reduction scheme for image compression and retrieval. In Proceedings of the Tenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Seattle, WA, USA, 22–25 August 2004; pp. 354–363. [Google Scholar]
- Ye, J. Generalized low rank approximations of matrices. Mach. Learn.
**2005**, 61, 167–191. [Google Scholar] [CrossRef] - He, X.; Cai, D.; Niyogi, P. Tensor subspace analysis. Advances in Neural Information Processing Systems 18 (NIPS), Vancouver, BC, Canada, 5–8 December 2005; pp. 1–8. [Google Scholar]
- Lu, H.; Plataniotis, K.N.; Venetsanopoulos, A.N. MPCA: Multilinear principal component analysis of tensor objects. IEEE Trans. Neural Netw.
**2008**, 19, 18–39. [Google Scholar] [PubMed] - Lu, H.; Plataniotis, K.N.; Venetsanopoulos, A.N. Multilinear Subspace Learning: Dimensionality Reduction of Multidimensional Data, 1st ed.; CRC Press: London, UK, 2013; pp. 1–296. ISBN 9781439857243. [Google Scholar]
- Sahambi, H.S.; Khorasani, K. A neural-network appearance-based 3-D object recognition using independent component analysis. IEEE Trans. Neural Netw.
**2003**, 14, 138–149. [Google Scholar] [CrossRef] [PubMed] - Li, N.; Liu, C.; Pfeifer, N.; Yin, J.F.; Liao, Z.Y.; Zhou, Y. Tensor modeling based for airborne LiDAR data classification. In Proceedings of the Congress of 23rd ISPRS, Prague, Czech Republic, 12–19 July 2016; pp. 283–287. [Google Scholar]
- Chen, J. Gait correlation analysis based human identification. Sci. World J.
**2014**, 2014, 1–8. [Google Scholar] [CrossRef] [PubMed] - Bowyer, K.W.; Chang, K.; Flynn, P. A survey of approaches and challenges in 3D and multi-modal 3D + 2D face recognition. Comput. Vis. Image Underst.
**2006**, 101, 1–15. [Google Scholar] [CrossRef] - Li, S.Z.; Zhao, C.; Zhu, X.; Lei, Z. Learning to fuse 3D+2D based face recognition at both feature and decision levels. In Proceedings of the IEEE International Workshop on Analysis and Modeling of Faces and Gestures, Beijing, China, 16 October 2005; pp. 44–45. [Google Scholar]
- Colombo, A.; Cusano, C.; Schettini, R. 3D face detection using curvature analysis. Pattern Recognit.
**2006**, 39, 444–455. [Google Scholar] [CrossRef] - Goldberger, A.L.; Amaral, L.N.; Glass, L.; Hausdorff, J.M.; Ivanov, P.C.; Mark, R.G.; Mietus, J.E.; Moody, G.B.; Peng, C.K.; Stanley, H.E. PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals. Circulation
**2000**, 101, e215–e220. [Google Scholar] [CrossRef] [PubMed] - Wang, S.; Yang, X.; Zhang, Y.; Phillips, P.; Yang, J.; Yuan, T.F. Identification of green, oolong and black teas in China via wavelet packet entropy and fuzzy support vector machine. Entropy
**2015**, 17, 6663–6682. [Google Scholar] [CrossRef] - Belhumeur, P.; Hespanha, J.; Kriegman, D. Eigenfaces vs. Fisher faces: Recognition using class specific linear projection. IEEE Trans. Pattern Anal. Mach. Int.
**1997**, 19, 711–720. [Google Scholar] [CrossRef] - Lin, C.; Wang, B.; Fan, X.; Ma, Y.; Liu, H. Orthogonal enhanced linear discriminant analysis for face recognition. IET Biom.
**2016**, 5, 100–110. [Google Scholar] [CrossRef] - Hu, H.; Zhang, P.; Torre, F.D. Face recognition using enhanced linear discriminant analysis. IET Comput. Vis.
**2009**, 4, 195–208. [Google Scholar] [CrossRef] - Lu, H.; Plataniotis, K.N.; Venetsanopoulos, A.N. A survey of multilinear subspace learning for tensor data. Pattern Recognit.
**2011**, 44, 1540–1551. [Google Scholar] [CrossRef] - Israel, S.A.; Irvine, J.M.; Cheng, A.; Wiederhold, M.D.; Wiederhold, B.K. ECG to identify individuals. Pattern Recognit.
**2005**, 38, 133–142. [Google Scholar] [CrossRef] - Wang, Y.; Agrafioti, F.; Hatzinakos, D.; Plataniotis, K.N. Analysis of human electrocardiogram for biometric recognition. EURASIP J. Adv. Signal Process.
**2007**, 2008, 1–11. [Google Scholar] [CrossRef] - Greche, L.; Jazouli, M.; Es-Sbai, N.; Majda, A.; Zarghili, A. Comparison between Euclidean and Manhattan distance measure for facial expressions classification. In Proceedings of the Wireless Technologies, Embedded and Intelligent Systems, Fez, Morocco, 19–20 April 2017; pp. 1–4. [Google Scholar]
- Ambardekar, P.; Jamthe, A.; Chincholkar, M. Predicting defect resolution time using cosine similarity. In Proceedings of the Data and Software Engineering, Palembang, Indonesia, 1–2 November 2017; pp. 1–6. [Google Scholar]
- Najat, N.; Abdulazeez, A.M. Gene clustering with partition around mediods algorithm based on weighted and normalized Mahalanobis distance. In Proceedings of the Intelligent Informatics and Biomedical Sciences, Okinawa, Japan, 24–26 November 2017; pp. 140–145. [Google Scholar]
- Choi, H.S.; Lee, B.H.; Yoon, S.R. Biometric authentication using noisy electrocardiograms acquired by mobile sensors. IEEE Access.
**2016**, 4, 1266–1273. [Google Scholar] [CrossRef] - Wang, S.H.; Du, S.; Zhang, Y.; Phillips, P.; Wu, L.N.; Chen, X.Q.; Zhang, Y.D. Alzheimer’s Disease detection by pseudo Zernike moment and linear regression classification. CNC Neuro. Disor. Drug Target
**2016**, 16, 11–15. [Google Scholar] [CrossRef] [PubMed] - Wubbeler, G.; Stavridis, M.; Kreiseler, D.; Bousseljot, R.D.; Elster, C. Verification of humans using the electrocardiogram. Pattern Recognit. Lett.
**2007**, 28, 1172–1175. [Google Scholar] [CrossRef]

**Figure 4.**Comparison of multilinear subspace learning (MSL) with unsupervised linear subspace learning (LSL): (

**a**) LSL; (

**b**) MSL.

**Figure 5.**Course of preprocessing: (

**a**) Original signal; (

**b**) regularized signal; (

**c**) spike-removed signal; (

**d**) detected peaks.

**Figure 8.**Course of MFECG feature extraction: (

**a**) Parameters calculation of MFECG using training data; (

**b**) Projection of the training and test data.

**Figure 9.**Comparison of correlation by reshaping: (

**a**) Correlation of a 1D vector; (

**b**) correlation of a 3D tensor reshaped from a low dimension to a high dimension; (

**c**) correlation of a 3D tensor; (

**d**) correlation of a 1D vector reshaped from a high dimension to a low dimension.

PCA Dimension | L1 (%) | L2 (%) | Angle distance (AD) (%) |
---|---|---|---|

10 | 98.70 | 98.71 | 98.51 |

20 | 98.74 | 98.76 | 98.69 |

30 | 98.82 | 98.74 | 98.68 |

40 | 98.73 | 98.72 | 98.68 |

50 | 98.72 | 98.72 | 98.66 |

60 | 98.68 | 98.72 | 98.67 |

70 | 98.68 | 98.72 | 98.67 |

80 | 98.68 | 98.72 | 98.67 |

90 | 98.68 | 98.72 | 98.67 |

100 | 98.67 | 98.72 | 98.67 |

LDA Dimension | PCA Dimension | L1 (%) | L2 (%) | AD (%) |
---|---|---|---|---|

21 | 11 | 98.70 | 98.70 | 98.64 |

12 | 98.72 | 98.77 | 98.66 | |

13 | 98.73 | 98.72 | 98.64 | |

14 | 98.72 | 98.71 | 98.67 | |

15 | 98.71 | 98.74 | 98.69 | |

16 | 98.70 | 98.76 | 98.70 | |

17 | 98.74 | 98.74 | 98.71 | |

18 | 98.72 | 98.78 | 98.77 | |

19 | 98.70 | 98.76 | 98.71 | |

20 | 98.63 | 98.77 | 98.74 |

MEECG Dimension | L1 (%) | L2 (%) | AD (%) |
---|---|---|---|

10 | 98.91 | 98.65 | 98.25 |

20 | 99.10 | 99.03 | 98.82 |

30 | 99.15 | 99.10 | 99.15 |

40 | 99.05 | 98.98 | 99.08 |

50 | 99.05 | 98.98 | 99.12 |

60 | 98.96 | 98.86 | 98.98 |

70 | 98.96 | 98.74 | 98.82 |

80 | 98.96 | 98.72 | 98.79 |

90 | 98.96 | 98.72 | 98.74 |

100 | 98.74 | 98.65 | 98.67 |

MFECG Dimension | L1 (%) | L2 (%) | AD (%) |
---|---|---|---|

10 | 98.72 | 98.89 | 98.77 |

20 | 98.89 | 98.93 | 98.98 |

30 | 98.86 | 98.93 | 99.00 |

40 | 98.82 | 98.91 | 99.03 |

50 | 98.82 | 98.89 | 99.00 |

60 | 98.82 | 98.86 | 99.03 |

70 | 98.84 | 98.84 | 99.03 |

80 | 98.70 | 98.82 | 98.91 |

PCA Dimension | L1 (%) | L2 (%) | AD (%) |
---|---|---|---|

10 | 91.52 | 91.58 | 89.67 |

20 | 93.41 | 93.21 | 92.51 |

30 | 93.64 | 93.30 | 92.66 |

40 | 93.63 | 93.33 | 92.65 |

50 | 93.42 | 93.29 | 92.42 |

60 | 93.25 | 93.22 | 92.34 |

70 | 93.11 | 93.21 | 92.27 |

80 | 93.07 | 93.22 | 92.27 |

90 | 93.03 | 93.22 | 92.24 |

100 | 92.98 | 93.22 | 92.19 |

LDA Dimension | PCA Dimension | L1 (%) | L2 (%) | AD (%) |
---|---|---|---|---|

19 | 9 | 91.86 | 91.89 | 90.70 |

10 | 92.84 | 92.84 | 91.98 | |

11 | 93.16 | 93.18 | 92.65 | |

12 | 93.08 | 93.21 | 92.95 | |

13 | 93.23 | 93.30 | 93.02 | |

14 | 93.16 | 93.12 | 92.97 | |

15 | 93.19 | 93.14 | 92.96 | |

16 | 93.28 | 93.17 | 92.92 | |

17 | 93.14 | 93.16 | 92.88 | |

18 | 93.00 | 93.17 | 92.86 |

MEECG Dimension | L1 (%) | L2 (%) | AD (%) |
---|---|---|---|

10 | 93.84 | 93.45 | 91.43 |

20 | 95.92 | 95.68 | 94.65 |

30 | 95.62 | 95.07 | 94.14 |

40 | 94.73 | 94.34 | 93.45 |

50 | 94.26 | 94.02 | 93.07 |

60 | 94.20 | 93.90 | 92.89 |

70 | 94.10 | 93.96 | 92.87 |

80 | 94.00 | 93.96 | 92.69 |

MFECG Dimension | L1 (%) | L2 (%) | AD (%) |
---|---|---|---|

10 | 95.94 | 95.70 | 94.99 |

20 | 95.90 | 95.76 | 95.72 |

30 | 95.72 | 95.72 | 95.45 |

40 | 95.41 | 95.43 | 95.33 |

50 | 94.99 | 95.13 | 95.13 |

60 | 94.59 | 95.01 | 94.95 |

70 | 94.30 | 94.93 | 94.85 |

80 | 93.66 | 94.77 | 94.79 |

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**MDPI and ACS Style**

Byeon, Y.-H.; Lee, J.-N.; Pan, S.-B.; Kwak, K.-C.
Multilinear EigenECGs and FisherECGs for Individual Identification from Information Obtained by an Electrocardiogram Sensor. *Symmetry* **2018**, *10*, 487.
https://doi.org/10.3390/sym10100487

**AMA Style**

Byeon Y-H, Lee J-N, Pan S-B, Kwak K-C.
Multilinear EigenECGs and FisherECGs for Individual Identification from Information Obtained by an Electrocardiogram Sensor. *Symmetry*. 2018; 10(10):487.
https://doi.org/10.3390/sym10100487

**Chicago/Turabian Style**

Byeon, Yeong-Hyeon, Jae-Neung Lee, Sung-Bum Pan, and Keun-Chang Kwak.
2018. "Multilinear EigenECGs and FisherECGs for Individual Identification from Information Obtained by an Electrocardiogram Sensor" *Symmetry* 10, no. 10: 487.
https://doi.org/10.3390/sym10100487