# Continuous m-Health Data Authentication Using Wavelet Decomposition for Feature Extraction

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## Abstract

**:**

## 1. Introduction

## 2. State of the Art

#### 2.1. Biorthogonal Wavelets

#### 2.2. Heart Rate Variability

## 3. Methodology

#### 3.1. Transparent Data Extraction

#### 3.2. Data Segmentation for Continuous Authentication

#### 3.3. Biorthogonal Wavelet Decomposition

- Low-pass decomposition filter = Lo_D
- High-pass decomposition filter = Hi_D
- Low-pass reconstruction filter = Lo_R
- High-pass reconstruction filter = Hi_R

#### 3.4. Feature Extraction

- Variance: This is the sum of square distance of the bioelectrical signal.$$Variance=\text{}\frac{{\displaystyle \sum}{(X-\mu )}^{2}}{N}$$
- Mean of the energy: The signal mean of the energy is the energy average value of the bioelectrical signal.$$Mean\text{}of\text{}the\text{}Energy=\frac{{{\displaystyle \sum}}_{r}\mathrm{exp}\left(-\beta {E}_{r}\right){E}_{r}}{{{\displaystyle \sum}}_{r}\mathrm{exp}\left(-\beta {E}_{r}\right)}$$
- Minimum energy: This is the lowest energy value of the bioelectrical signal$$Minimum\text{}Energy=Minimum\text{}Signal\text{}Energy$$
- Maximum energy: This is the highest energy value of the bioelectrical signal.$$Maximum\text{}Energy=Maximum\text{}Signal\text{}Energy$$
- Mean: These are the values diversity of the data around the median.$$Mean=\text{}\frac{1}{n}{\displaystyle \sum}_{i=1}^{n}{x}_{i}$$
- Minimum amplitude: This is the lowest point from the equilibrium point of the bioelectrical signal.$$Min.\text{}Amplitude=Minimum\text{}displacement$$
- Standard deviation (STD): This is the square root of the variance of a random variation.$$STD=\sqrt{\frac{1}{n}{\displaystyle \sum}_{i=1}^{n}\text{}{\left({x}_{i}-\mu \right)}^{2}}$$
- Maximum amplitude: This is the highest point from the equilibrium point of the bioelectrical signal.$$Max.\text{}Amp.=Maximum\text{}displacement$$
- Range: This is the difference between the highest signal value and the lowest signal value.$$Range=Maximum\text{}signal-minimum\text{}signal$$
- Peak2peak: This is the difference between the maximum and minimum values of the bioelectrical signal.$$P2P=Signal\text{}Maxi\text{}to\text{}Min\text{}diff.\text{}displacement$$
- Root mean square (RMS): The RMS is the measurement of the magnitude of a set values within the signal.$$Root\text{}Mean\text{}Square\text{}=\sqrt{\frac{1}{n}{\displaystyle {\sum}_{i=1}^{N}}{X}_{I}^{2}}$$
- Peak magnitude to RMS ratio: This is the ratio of the largest absolute value of a signal to the root mean square (RMS) value of that signal.$$Peak\text{}Magnitude\text{}to\text{}RMS=\sqrt{\frac{{X}_{\infty}}{\frac{1}{N}{{\displaystyle \sum}}_{n=1}^{N}{X}_{n}^{2}}}$$
- Average frequency: this the arithmetic mean of the signal frequency.$$Average\text{}Frequency=\text{}\frac{{X}_{1}+{X}_{2}\text{}+\text{}{X}_{3}\dots {X}_{n}}{N}$$

#### 3.5. Classification

#### 3.6. Experimentation

- Experiment 1: the experimentation to select the most suitable features for use in the other experiments. The experiment used 12 subjects’ data for the 13 statistical features extraction experimentation.
- Experiment 2: the second experimentation is the classification of the sub-bands after extracting features. The 30 subjects’ data are used with 12 selected features for each sub-band for both the approximation of coefficient and detail coefficient for fifteen biorthogonal wavelet family.
- Experiment 3: this experiment is done on the fusion of the sub-bands. This experiment also used 30 subjects’ data with the 12 selected features for fusion of all the sub-band for both the approximation of coefficient and detail coefficient classification.
- Used case experiment: this is the used case data authentication using 30 subjects’ data.

## 4. Results

#### 4.1. Result on Experiment 1: Selection of Statistical Features

#### 4.2. Result on Experiment 2: Classification Sub-Band Features

#### 4.3. Result on Experiment 3: Fusion of Sub-Band Features

## 5. Use Case and Evaluation

#### 5.1. Use Case Architecture

#### 5.1.1. The Smartwatch

#### 5.1.2. The Smartphone

#### 5.1.3. The Smartphone

#### 5.1.4. Healthcare Data Management Facility

#### 5.2. Data Authentication

#### 5.3. Use Case Evaluation

#### 5.4. Discussion

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 9.**Variation of minimum amplitude, maximum energy, and standard deviation on twelve subjects.

**Figure 10.**Variation of maximum amplitude, range, peak2peak and peak magnitude to root mean square (RMS) ratio on twelve subjects.

**Figure 11.**Showing variation of mid frequency, root mean square and average frequency on twelve subjects.

**Figure 12.**Showing classification accuracy comparison in equal error rate (EER) across various biorthogonal decomposition of approximation of coefficient features (A1: approximation of coefficient sub-band1; A2: approximation of coefficient sub-band 2; A3: approximation of coefficient sub-b).

**Figure 13.**Showing classification accuracy comparison across various biorthogonal decomposition detail coefficient features (D1: detail coefficient sub-band1, D2: detail coefficient sub-band 2, D3: detail coefficient sub-band 3).

**Figure 14.**Comparison of the performance of detail and approximation coefficient feature classification.

**Figure 17.**Result showing the verification of the data from 30 subjects using fusion of approximation and detail coefficient sub-bands.

Heart Rate Variability Segmentation Using 3 Sec. | |||
---|---|---|---|

Types | Exp. 1 | Exp. 2–3 | Used Case Exp |

Number of subjects used | 12 | 30 | 30 |

Sampling rate | 8 | 8 | 8 |

Data points per segment | 24 | 24 | 24 |

Num. of Feature Segments of each subject | 150 | 300 | 600 |

Number recorded time per subject in Seconds | 3600 | 7200 | 14,400 |

Total number recorded time for all subjects in Seconds | 108,000 | 216,000 | 432,000 |

**Table 2.**The three sub-band levels of approximation of coefficient and detail coefficient (A1: approximation of coefficient sub-band1; A2: approximation of coefficient sub-band 2; A3: detail coefficient sub-band 3; D1: detail coefficient sub-band1, D2: detail).

No | Wavelet Family | EER of Approximation of Coefficient and Detail Coefficient Classification Comparison in EER (%) | |||||
---|---|---|---|---|---|---|---|

D1 | A1 | D2 | A2 | D3 | A3 | ||

1 | Bior1.1 | 32.27 | 31.54 | 32.21 | 32.31 | 16.41 | 16.66 |

2 | Bior1.3 | 31.02 | 31.77 | 33.51 | 29.80 | 16.79 | 16.56 |

3 | Bior1.5 | 32.33 | 31.42 | 33.32 | 33.21 | 17.56 | 17.20 |

4 | Bior2.2 | 31.79 | 31.12 | 34.50 | 32.99 | 20.69 | 21.69 |

5 | Bior2.4 | 32.59 | 31.55 | 32.06 | 31.87 | 20.02 | 20.95 |

6 | Bior2.6 | 30.87 | 31.44 | 32.32 | 34.55 | 21.47 | 19.94 |

7 | Bior2.8 | 30.83 | 30.39 | 32.66 | 29.81 | 20.79 | 20.44 |

8 | Bior3.1 | 32.16 | 31.40 | 33.67 | 31.58 | 29.82 | 29.70 |

9 | Bior3.3 | 31.10 | 33.64 | 33.74 | 32.18 | 32.82 | 31.90 |

10 | Bior3.5 | 32.65 | 31.40 | 34.44 | 31.63 | 31.11 | 34.32 |

11 | Bior3.7 | 32.73 | 32.90 | 30.08 | 33.67 | 28.52 | 28.95 |

12 | Bior3.9 | 33.41 | 29.99 | 33.10 | 31.81 | 28.50 | 30.67 |

13 | Bior4.4 | 31.85 | 29.03 | 37.57 | 34.86 | 36.54 | 37.16 |

14 | Bior5.5 | 31.61 | 31.87 | 33.67 | 34.05 | 35.93 | 39.01 |

15 | Bior6.8 | 35.22 | 33.07 | 33.59 | 30.94 | 37.40 | 37.90 |

Approximation and Detail Coefficient Classification Comparison in EER (%) | ||
---|---|---|

Feature | Bior1.1 | Bior1.3 |

Approximation of Coefficient Sub-band 3 | 16.66 | 16.56 |

Detail Coefficient Sub-band 3 | 16.41 | 16.56 |

Approximation of Coefficient Fusion | 14.00 | 14.83 |

Detail Coefficient Fusion | 13.80 | 14.89 |

Sub. | AF | DF | Sub. | AF | DF |
---|---|---|---|---|---|

1 | 0.00 | 0.00 | 16 | 22.84 | 20.76 |

2 | 19.04 | 17.46 | 17 | 13.22 | 15.73 |

3 | 12.07 | 9.70 | 18 | 14.66 | 10.13 |

4 | 19.83 | 20.04 | 19 | 7.11 | 4.74 |

5 | 18.89 | 13.00 | 20 | 16.38 | 9.55 |

6 | 4.60 | 4.17 | 21 | 13.58 | 11.35 |

7 | 13.36 | 14.08 | 22 | 10.20 | 12.72 |

8 | 24.21 | 19.11 | 23 | 2.08 | 2.08 |

9 | 14.80 | 14.08 | 24 | 19.97 | 9.27 |

10 | 18.10 | 17.03 | 25 | 10.13 | 9.48 |

11 | 10.06 | 4.45 | 26 | 0.00 | 0.00 |

12 | 15.52 | 22.49 | 27 | 8.91 | 8.76 |

13 | 12.72 | 13.99 | 28 | 27.23 | 28.81 |

14 | 22.56 | 24.71 | 29 | 15.54 | 14.83 |

15 | 20.55 | 17.10 | 30 | 3.46 | 3.05 |

EER Features Fusion Result | 13.17 | 12.42 |

Data Authentication Performance | ||||||
---|---|---|---|---|---|---|

Threshold (EER) | Patient | Non-Patient | ||||

Acceptance | Rejection | Success Rate | Acceptance | Rejection | Success Rate | |

9% | 54 | 46 | 54% | 0 | 2000 | 0% |

10% | 56 | 44 | 56% | 0 | 2000 | 0% |

11% | 81 | 19 | 81% | 6 | 1994 | 0.3% |

12% | 84 | 16 | 84% | 8 | 1992 | 0.4% |

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**MDPI and ACS Style**

Enamamu, T.; Otebolaku, A.; Marchang, J.; Dany, J. Continuous m-Health Data Authentication Using Wavelet Decomposition for Feature Extraction. *Sensors* **2020**, *20*, 5690.
https://doi.org/10.3390/s20195690

**AMA Style**

Enamamu T, Otebolaku A, Marchang J, Dany J. Continuous m-Health Data Authentication Using Wavelet Decomposition for Feature Extraction. *Sensors*. 2020; 20(19):5690.
https://doi.org/10.3390/s20195690

**Chicago/Turabian Style**

Enamamu, Timibloudi, Abayomi Otebolaku, Jims Marchang, and Joy Dany. 2020. "Continuous m-Health Data Authentication Using Wavelet Decomposition for Feature Extraction" *Sensors* 20, no. 19: 5690.
https://doi.org/10.3390/s20195690