# Defect-Repairable Latent Feature Extraction of Driving Behavior via a Deep Sparse Autoencoder

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## Abstract

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## 1. Introduction

- We show that DSAE can extract highly correlated low-dimensional time-series of latent features by reducing various degrees of redundancy in different multi-dimensional time-series data of driving behavior.
- We verify that DSAE can reduce the negative effect of defects on the extracted time-series of latent features by repairing the defective sensor time-series data using a BP method.
- We find that the time-series of latent features extracted from the repaired time-series sensor data by DSAE have segmentation results similar to those of non-defective sensor time-series data.

## 2. Background

#### 2.1. Feature Extraction for Driving Behavior Analysis

#### 2.2. Feature Extraction by Deep Learning for Intelligent Vehicles

#### 2.3. Defect Repair for Driving Behavior Analysis

## 3. Proposed Method

#### 3.1. Training Process

#### 3.2. Defect-Repairing Process

#### 3.2.1. DSAE-FP

#### 3.2.2. DSAE-BP

## 4. Experiment 1: Feature Extraction

#### 4.1. Experimental Conditions

#### 4.2. Evaluation of Model Training via Data Reconstruction

#### 4.3. Evaluation of Latent Feature Extraction of Time-Series Using CCA

## 5. Experiment 2: Reducing the Negative Effect of Defects for Feature Extraction

#### 5.1. Experimental Conditions

#### 5.2. Evaluation of Data Repair of Sensor Time-Series Data

#### 5.3. Evaluation of Feature Extraction with Defective Data

## 6. Application: Driving Behavior Segmentation with Defects

## 7. Discussion for Advantages and Limitations of Proposed Method

## 8. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A. Similarity between Two Extracted Time-Series of Latent Features via the Same Trained Model

## Appendix B. Similarity between Two Segment Results

## References

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**Figure 1.**Feature extraction and defect-repairing processes of the deep sparse autoencoder (DSAE), which repairs defects in sensor time-series data by using a back propagation (BP) method.

**Figure 2.**DSAE-FP: Repair the defects in sensor time-series data by updating to the reconstructed time-series data.

**Figure 3.**DSAE-BP: Repair the defects in sensor time-series by a BP method. Weights and biases of DSAE are not changed.

**Figure 4.**Averaged square error between windowing time-series data and reconstructed time-series data of datasets D1 to D12.

**Figure 5.**Three-dimensional time-series of latent features extracted from datasets D1 to D12 by PCA in the three-dimensional feature space.

**Figure 6.**Three-dimensional time-series of latent features extracted from datasets D1 to D12 by DSAE in the three-dimensional feature space.

**Figure 7.**Distance of correlation between each pair of time-series of latent features extracted from the 12 datasets by using PCAs.

**Figure 8.**Distance of correlation between each pair of time-series of latent features extracted from the 12 datasets by using DSAEs.

**Figure 9.**Averaged distance of correlation among pairs of time-series of latent features extracted from D7 to D12 by using PCAs and DSAEs.

**Figure 10.**Square error between the repaired sensor time-series data and non-defective sensor time-series data for C1 to C4 at each update iteration. The plots in the columns on the left and right represent the results obtained by using DSAE-FP and DSAE-BP, respectively.

**Figure 11.**Square error between the repaired sensor time-series data and non-defective sensor time-series data for C5 to C8 at each update iteration. The plots in the columns on the left and right represent the results obtained by using DSAE-FP and DSAE-BP, respectively.

**Figure 12.**Convergence values of squared error with different initial value for each of the datasets when DSAE-FP and DSAE-BP were used.

**Figure 13.**Example of defect repair of the steering angle by DSAE-FP and DSAE-BP for a part of C3 in the time-series, when the defect value was 1. A white background indicates the period of defects. The values in parentheses in the legend represent the defect values.

Measured Sensor Information | ||

${I}_{1}$: Accelerator opening rate | ${I}_{2}$: Brake master-cylinder pressure | ${I}_{3}$: Steering angle |

${I}_{4}$: Speed of wheels | ${I}_{5}$: Meter readings of velocity | ${I}_{6}$: Engine speed |

${I}_{7}$: Longitudinal acceleration | ${I}_{8}$: Lateral acceleration | ${I}_{9}$: Yaw rate |

Assumed latent features | ||

V: The feature is related to the velocity | ||

A: The feature is related to the acceleration | ||

D: The feature is related to a change in the driving direction |

**Table 2.**Sensor information included in the 12 datasets we prepared and the PCA and DSAE designs for each of them.

Data Sets | Included Sensor Information | Assumed Latent Features | Encoder Structure of DSAE (with Window Size: 10) | The Structure of PCA (with Window Size: 10) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

${\mathit{I}}_{\mathbf{1}}$ | ${\mathit{I}}_{\mathbf{2}}$ | ${\mathit{I}}_{\mathbf{3}}$ | ${\mathit{I}}_{\mathbf{4}}$ | ${\mathit{I}}_{\mathbf{5}}$ | ${\mathit{I}}_{\mathbf{6}}$ | ${\mathit{I}}_{\mathbf{7}}$ | ${\mathit{I}}_{\mathbf{8}}$ | ${\mathit{I}}_{\mathbf{9}}$ | $\mathit{V}$ | $\mathit{A}$ | $\mathit{D}$ | |||

D1 | √ | √ | ∘ | 2D×10=20D→10D→5D→3D | 2D×10=20D→3D | |||||||||

D2 | √ | ∘ | 1D×10=10D→5D→3D | 1D×10=10D→3D | ||||||||||

D3 | √ | ∘ | 1D×10=10D→5D→3D | 1D×10=10D→3D | ||||||||||

D4 | √ | √ | √ | ∘ | ∘ | 3D×10=30D→15D→7D→3D | 3D×10=30D→3D | |||||||

D5 | √ | √ | ∘ | ∘ | 2D×10=20D→10D→5D→3D | 2D×10=20D→3D | ||||||||

D6 | √ | √ | √ | ∘ | ∘ | 3D×10=30D→15D→7D→3D | 3D×10=30D→3D | |||||||

D7 | √ | √ | √ | √ | ∘ | ∘ | ∘ | 4D×10=40D→20D→10D→5D→3D | 4D×10=40D→3D | |||||

D8 | √ | √ | √ | √ | √ | ∘ | ∘ | ∘ | 5D×10=50D→25D→12D→6D→3D | 5D×10=50D→3D | ||||

D9 | √ | √ | √ | √ | √ | √ | ∘ | ∘ | ∘ | 6D×10=60D→30D→15D→7D→3D | 6D×10=60D→3D | |||

D10 | √ | √ | √ | √ | √ | √ | √ | ∘ | ∘ | ∘ | 7D×10=70D→35D→17D→8D→3D | 7D×10=70D→3D | ||

D11 | √ | √ | √ | √ | √ | √ | √ | √ | ∘ | ∘ | ∘ | 8D×10=80D→40D→20D→10D→3D | 8D×10=80D→3D | |

D12 | √ | √ | √ | √ | √ | √ | √ | √ | √ | ∘ | ∘ | ∘ | 9D×10=90D→45D→22D→11D→3D | 9D×10=90D→3D |

Data Sets | Included Sensor Time-Series Data | ||||||||
---|---|---|---|---|---|---|---|---|---|

${\mathit{I}}_{\mathbf{1}}$ | ${\mathit{I}}_{\mathbf{2}}$ | ${\mathit{I}}_{\mathbf{3}}$ | ${\mathit{I}}_{\mathbf{4}}$ | ${\mathit{I}}_{\mathbf{5}}$ | ${\mathit{I}}_{\mathbf{6}}$ | ${\mathit{I}}_{\mathbf{7}}$ | ${\mathit{I}}_{\mathbf{8}}$ | ${\mathit{I}}_{\mathbf{9}}$ | |

C1 | $(\surd )$ | √ | √ | √ | √ | √ | √ | √ | √ |

C2 | √ | $(\surd )$ | √ | √ | √ | √ | √ | √ | √ |

C3 | √ | √ | $(\surd )$ | √ | √ | √ | √ | √ | √ |

C4 | √ | √ | √ | $(\surd )$ | √ | √ | √ | √ | √ |

C5 | √ | √ | √ | √ | $(\surd )$ | √ | √ | √ | √ |

C6 | √ | √ | √ | √ | √ | $(\surd )$ | √ | √ | √ |

C7 | √ | √ | √ | √ | √ | √ | $(\surd )$ | $(\surd )$ | √ |

C8 | √ | √ | √ | √ | √ | √ | √ | √ | $(\surd )$ |

**Table 4.**${R}^{2}$s between the extracted time-series of latent features of D12 and C1 to C8. The highest value of ${R}^{2}$ is presented in bold font; the second highest value is underlined for each defect value.

Defect Values | Mehods | C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 |
---|---|---|---|---|---|---|---|---|---|

1 | LI+PCA | 0.958 | 0.970 | 0.962 | 0.990 | 0.989 | 0.976 | 0.825 | 0.948 |

1 | LI+DSAE | 0.864 | 0.945 | 0.938 | 0.944 | 0.997 | 0.988 | 0.890 | 0.992 |

1 | MF+PCA | 0.950 | 0.952 | 0.957 | 0.951 | 0.945 | 0.976 | 0.893 | 0.960 |

1 | MF+DSAE | 0.855 | 0.916 | 0.933 | 0.725 | 0.989 | 0.990 | 0.924 | 0.995 |

1 | PCA | 0.581 | −0.173 | 0.520 | 0.637 | 0.595 | 0.481 | −0.269 | 0.174 |

1 | DSAE | −0.233 | −0.671 | 0.213 | −0.791 | 0.916 | 0.729 | 0.579 | 0.874 |

1 | PCA-FP | 0.832 | −1.01 | −177 | −0.858 | −0.055 | 0.337 | – | – |

1 | DSAE-FP | 0.968 | 0.975 | 0.906 | 0.750 | 1.00 | 0.997 | 0.987 | 0.999 |

1 | PCA-BP | 0.985 | 0.975 | 0.987 | 0.998 | 0.996 | 0.989 | 0.953 | 0.986 |

1 | DSAE-BP | 0.964 | 0.983 | 0.974 | 0.992 | 1.00 | 0.997 | 0.990 | 0.999 |

0 | LI+PCA | 0.958 | 0.970 | 0.962 | 0.990 | 0.989 | 0.976 | 0.825 | 0.948 |

0 | LI+DSAE | 0.864 | 0.945 | 0.938 | 0.944 | 0.997 | 0.988 | 0.890 | 0.992 |

0 | MF+PCA | 0.950 | 0.952 | 0.957 | 0.951 | 0.945 | 0.976 | 0.893 | 0.960 |

0 | MF+DSAE | 0.855 | 0.916 | 0.933 | 0.725 | 0.989 | 0.990 | 0.924 | 0.995 |

0 | PCA | 0.904 | 0.745 | 0.970 | 0.949 | 0.930 | 0.925 | 0.912 | 0.961 |

0 | DSAE | 0.641 | 0.553 | 0.955 | 0.692 | 0.986 | 0.960 | 0.947 | 0.995 |

0 | PCA-FP | 0.832 | −1.01 | −177 | −0.858 | −0.055 | 0.337 | – | – |

0 | DSAE-FP | 0.968 | 0.975 | 0.916 | 0.653 | 1.00 | 0.997 | 0.987 | 0.999 |

0 | PCA-BP | 0.985 | 0.975 | 0.987 | 0.998 | 0.996 | 0.989 | 0.953 | 0.986 |

0 | DSAE-BP | 0.969 | 0.983 | 0.981 | 0.992 | 1.00 | 0.997 | 0.990 | 0.999 |

−1 | LI+PCA | 0.958 | 0.970 | 0.962 | 0.990 | 0.989 | 0.976 | 0.825 | 0.948 |

−1 | LI+DSAE | 0.864 | 0.945 | 0.938 | 0.944 | 0.997 | 0.988 | 0.890 | 0.992 |

−1 | MF+PCA | 0.950 | 0.952 | 0.957 | 0.951 | 0.945 | 0.976 | 0.893 | 0.960 |

−1 | MF+DSAE | 0.855 | 0.916 | 0.933 | 0.725 | 0.989 | 0.990 | 0.924 | 0.995 |

−1 | PCA | 0.949 | 0.961 | 0.642 | 0.814 | 0.870 | 0.901 | −0.581 | 0.351 |

−1 | DSAE | 0.862 | 0.930 | 0.385 | −0.080 | 0.976 | 0.954 | 0.430 | 0.904 |

−1 | PCA-FP | 0.832 | −1.01 | −177 | −0.858 | −0.055 | 0.337 | – | – |

−1 | DSAE-FP | 0.970 | 0.975 | 0.921 | 0.489 | 1.00 | 0.997 | 0.987 | 0.999 |

−1 | PCA-BP | 0.985 | 0.975 | 0.987 | 0.998 | 0.996 | 0.989 | 0.953 | 0.986 |

−1 | DSAE-BP | 0.975 | 0.983 | 0.982 | 0.992 | 1.00 | 0.997 | 0.990 | 0.999 |

**Table 5.**Average segmentation distances between D12 and C1 to C8 with defect values of 1, 0, and $-1$. The shortest average segmentation distance (best performance) is shown in bold font; the second shortest average segmentation distance is shown in underlined.

Defect Value | Methods | C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 |
---|---|---|---|---|---|---|---|---|---|

1 | RAW | 381 | 524 | 578 | 402 | 358 | 321 | 312 | 338 |

1 | PCA | 306 | 408 | 295 | 300 | 304 | 322 | 342 | 326 |

1 | DSAE | 351 | 424 | 332 | 344 | 226 | 288 | 325 | 277 |

1 | PCA-BP | 153 | 167 | 98.4 | 87.9 | 98.4 | 151 | 187 | 94.3 |

1 | DSAE-FP | 132 | 149 | 196 | 235 | 50.4 | 89.5 | 143 | 59.1 |

1 | DSAE-BP | 126 | 125 | 133 | 142 | 46.3 | 81.8 | 132 | 56.5 |

0 | RAW | 325 | 437 | 166 | 321 | 224 | 210 | 108 | 117 |

0 | PCA | 252 | 329 | 93.1 | 199 | 207 | 237 | 231 | 113 |

0 | DSAE | 310 | 352 | 126 | 281 | 137 | 213 | 196 | 72.6 |

0 | PCA-BP | 155 | 171 | 92.3 | 90.0 | 94.5 | 145 | 194 | 91.7 |

0 | DSAE-FP | 132 | 155 | 233 | 328 | 46.3 | 89.1 | 146 | 56.4 |

0 | DSAE-BP | 123 | 123 | 141 | 142 | 43.6 | 84.2 | 132 | 58.8 |

−1 | RAW | 158 | 177 | 352 | 347 | 260 | 203 | 344 | 317 |

−1 | PCA | 116 | 174 | 288 | 263 | 218 | 249 | 342 | 316 |

−1 | DSAE | 137 | 181 | 322 | 377 | 118 | 213 | 332 | 275 |

−1 | PCA-BP | 152 | 170 | 93.5 | 88.3 | 95.3 | 147 | 189 | 91.2 |

−1 | DSAE-FP | 131 | 154 | 228 | 305 | 44.1 | 88.1 | 144 | 57.0 |

−1 | DSAE-BP | 123 | 125 | 144 | 142 | 43.8 | 82.9 | 129 | 55.7 |

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**MDPI and ACS Style**

Liu, H.; Taniguchi, T.; Takenaka, K.; Bando, T. Defect-Repairable Latent Feature Extraction of Driving Behavior via a Deep Sparse Autoencoder. *Sensors* **2018**, *18*, 608.
https://doi.org/10.3390/s18020608

**AMA Style**

Liu H, Taniguchi T, Takenaka K, Bando T. Defect-Repairable Latent Feature Extraction of Driving Behavior via a Deep Sparse Autoencoder. *Sensors*. 2018; 18(2):608.
https://doi.org/10.3390/s18020608

**Chicago/Turabian Style**

Liu, HaiLong, Tadahiro Taniguchi, Kazuhito Takenaka, and Takashi Bando. 2018. "Defect-Repairable Latent Feature Extraction of Driving Behavior via a Deep Sparse Autoencoder" *Sensors* 18, no. 2: 608.
https://doi.org/10.3390/s18020608