# Deep Learning-Based Optimal Smart Shoes Sensor Selection for Energy Expenditure and Heart Rate Estimation

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. System Overview

#### 2.2. Experiments

#### 2.3. Data Preparation

## 3. Proposed Model

- The manual feature extraction process is not necessary since a fully automated end-to-end deep learning model was applied;
- The spatiotemporal characteristics of the multivariate time-series data that is complex to process could be effectively extracted using DenseNet and bidirectional GRU (Bi-GRU);
- The importance of each channel in estimating HR and EE could be quantified using the channel-wise attention method, and it can explain the optimal sensors for the task.

**Figure 7.**Structure of the proposed model. The shoe data from 20 channel sensors are fed into the input of the model and the channel-wise attention layer increases the intensity of the significant channels. The spatial features from the multi-channel data are extracted using DenseNet, and the temporal features are produced through Bi-GRU. Finally, HR and EE are estimated after the global average pooling (GAP) layer.

#### 3.1. Channel-Wise Attention

#### 3.2. DenseNet

#### 3.3. Bidirectional Gated Recurrent Unit

#### 3.4. Global Average Pooling

#### 3.5. Model Training Environment

## 4. Results

- Performance evaluation of the HR and EE estimation models;
- Performance analysis with and without the attention mechanism;
- Analysis of the channel significance using the attention weight;

#### 4.1. Energy Expenditure Estimation

#### 4.1.1. Proposed Model Performance

#### 4.1.2. Channel-Wise Attention Effectiveness

#### 4.1.3. Optimal Sensor Analysis

#### 4.2. Heart Rate Estimation

#### 4.2.1. Proposed Model Performance

#### 4.2.2. Channel-Wise Attention Effectiveness

#### 4.2.3. Optimal Sensor Analysis

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

IoT | Internet of Things |

EE | Energy expenditure |

PA | Physical activity |

CVD | Cardiovascular disease |

HRV | Heart rate variability |

HR | Heart rate |

ECG | Electrocardiogram |

PPG | Photoplethysmogram |

ANN | Artificial neural network |

CNN | Convolutional neural network |

GRU | Gated recurrent unit |

GAP | Global average pooling |

Bi-GRU | Bidirectional gated recurrent unit |

FC | Fully connected |

MSE | Mean squared error |

LOSO | Leave-one-subject-out |

RMSE | Root-mean-square error |

MAE | Mean absolute error |

${R}^{2}$ | Coefficient of determination |

LOA | Limit of agreement |

MAPE | Mean absolute percent error |

ANOVA | Analysis of variance |

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**Figure 2.**Locations of the sensors in the smart shoes: (

**a**) a total of 12 sensors (6 sensors on the left and right shoe each) consisting of the pressure, accelerometer, and gyroscope sensors; (

**b**) locations of the pressure sensors on the anatomical sketch: 1st metatarsal head (MH; sensor 1), toe (between the 1st and 2nd phalange; sensor 2), 4th metatarsal head (sensor 3), and heel (sensor 4).

**Figure 3.**Example figures of the experimental equipment and process. During the experiment, participants wore a chest strap and a calorimeter to measure HR and EE, respectively. Each participant ran on a treadmill at a speed varying from 3 to 10 kph, which increased by 1 kph per every 2 min (total 16 min ran) and they were instructed to run at a constant speed as much as possible.

**Figure 4.**Flowchart of the data preprocessing when training the proposed deep learning model. The input shoes’ data were recorded at a 33.3 Hz sampling rate and standardized to have a zero mean and unit variance. The label was created based on the HR and EE information, which were averaged on a 10 s long window with an overlap of 1 s.

**Figure 5.**Application of a linear interpolation method due to the mismatch between the sampling rates of the HR/EE and data of the shoes’ sensors. In the HR and EE graphs, the green dot represents HR and the gold dot represents the EE of the actual measurement, and the dashed line is the estimated value.

**Figure 6.**Distributions of HR and EE labels: (

**a**,

**b**) show the number of EE values per KCal/min and HR values per bpm, respectively.

**Figure 11.**Comparison between the predicted (EST) and ground truths (REF) in EE estimation: (

**a**) is the best case; (

**b**) is the worst case.

**Figure 12.**Bland-Altman plot of EE estimation. The orange line is the limit of agreement (LOA) and the center blue line is the mean of difference error between the actual and estimation.

**Figure 13.**Comparison between predicted (EST) and ground truths (REF) in HR estimation: (

**a**) is the best case; and (

**b**) is the worst case.

**Figure 14.**Bland–Altman plot of HR estimation. The orange line represents the limit of agreement (LOA) and the blue center line is the mean of the difference error between the ground truth and the estimation.

**Figure 15.**Comparison of the average attention weights for each of the x, y, and z axes. (

**A**,

**B**) illustrate the result of EE and HR, respectively.

Input | RMSE | MAE | ${\mathit{R}}^{2}$ |
---|---|---|---|

Acc + Gyro + Pr | 1.05 ± 0.13 | 0.83 ± 0.12 | 0.922 ± 0.005 |

**Table 2.**Mean and standard deviation of RMSE, MAE, and ${R}^{2}$ values obtained using the proposed models with and without the attention mechanism in the EE estimation.

Input | RMSE | MAE | ${\mathit{R}}^{2}$ |
---|---|---|---|

with attention (proposed) | 1.05 ± 0.13 | 0.83 ± 0.12 | 0.922 ± 0.005 |

without attention | 1.17 ± 0.24 | 0.95 ± 0.2 | 0.923 ± 0.12 |

**Table 3.**ANOVA analysis of the channel-wise attention weights in the EE estimation. SS is the sum of squares, df is the degree of freedom, MS is the mean square, and F is the F-statistic.

SS | df | MS | F | p-Value | |
---|---|---|---|---|---|

beetween groups | 1.216 | 19 | 0.064 | 55.107 | 0.000 |

within groups | 22.434 | 19,320 | 0.001 | ||

total | 23.649 | 19,339 |

**Table 4.**Post-hoc Tukey HSD test result for the averaged attention weight for each sensor in EE estimation. Each column 1–10 represents a homogeneous subset for a significance level of $0.05$. The sensor types are pressure (P), accelerometer (A), and gyroscope (G). The first subscript for each sensor type denotes the left (L) and right (R) sides of the shoe. The second subscript is the detailed attachment position of the pressure sensor (see Figure 2) or the x, y, and z axis directions of the accelerometer and gyroscope.

Sensor Type | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

${P}_{L3}$ | 0.4908 | |||||||||

${P}_{R2}$ | 0.4910 | 0.4910 | ||||||||

${P}_{R4}$ | 0.4910 | 0.4910 | ||||||||

${P}_{L4}$ | 0.4918 | 0.4918 | ||||||||

${G}_{RY}$ | 0.4926 | 0.4926 | 0.4926 | |||||||

${P}_{R3}$ | 0.4935 | 0.4935 | 0.4935 | |||||||

${P}_{L1}$ | 0.4944 | 0.4944 | 0.4944 | 0.4944 | ||||||

${A}_{LY}$ | 0.4964 | 0.4964 | 0.4964 | 0.4964 | ||||||

${P}_{L2}$ | 0.4977 | 0.4977 | 0.4977 | 0.4977 | ||||||

${A}_{RX}$ | 0.4979 | 0.4979 | 0.4979 | 0.4979 | ||||||

${A}_{RY}$ | 0.4980 | 0.4980 | 0.4980 | 0.4980 | ||||||

${P}_{R1}$ | 0.4991 | 0.4991 | 0.4991 | |||||||

${A}_{LX}$ | 0.4998 | 0.4998 | 0.4998 | |||||||

${G}_{RX}$ | 0.4999 | 0.4999 | ||||||||

${G}_{LX}$ | 0.5031 | 0.5031 | ||||||||

${G}_{RZ}$ | 0.5070 | 0.5070 | ||||||||

${A}_{RZ}$ | 0.5091 | 0.5091 | ||||||||

${G}_{LY}$ | 0.5137 | 0.5137 | ||||||||

${G}_{LZ}$ | 0.5148 | |||||||||

${A}_{LZ}$ | 0.5155 | |||||||||

p-value | 0.742 | 0.069 | 0.057 | 0.060 | 0.750 | 0.072 | 0.546 | 0.999 | 0.240 | 1.000 |

Input | RMSE | MAE | ${\mathit{R}}^{2}$ |
---|---|---|---|

Acc + Gyro + Pr | 7.81 ± 1.12 | 6.12 ± 0.86 | 0.897 ± 0.017 |

**Table 6.**Comparison of the HR estimation performance of commercial wearable devices and the proposed model. The performance of commercial wearable devices was cited from the study results of Nelson et al. [50].

Device | Condition | Device Error | Bland–Altman Analysis | |||
---|---|---|---|---|---|---|

MAE | MAPE | ME | Lower LOA | Upper LOA | ||

Fitbit Charge 2 | walking | 9.55 | 9.21 | −6.85 | −28.51 | 14.81 |

running | 14.73 | 9.88 | −14.73 | −29.77 | 0.31 | |

Apple Watch 3 | walking | 4.77 | 4.64 | 0.11 | −14.18 | 14.41 |

running | 4.05 | 3.01 | 1.77 | −9.78 | 13.33 | |

proposed model | walking + running | 6.12 | 5.40 | 0.39 | −15.12 | 15.90 |

**Table 7.**Mean and standard deviation of RMSE, MAE, and ${R}^{2}$ values of models with (proposed model) and without the attention for HR estimation.

Input | RMSE | MAE | ${\mathit{R}}^{2}$ |
---|---|---|---|

with attention | 7.81 ± 1.12 | 6.12 ± 0.86 | 0.897 ± 0.017 |

without attention | 9.19 ± 3.16 | 7.72 ± 3.67 | 0.878 ± 0.037 |

**Table 8.**ANOVA analysis of the channel-wise attention weights in the HR estimation. SS denotes the sum of squares, df denotes the degree of freedom, MS denotes the mean square, and F denotes the F-statistic.

SS | df | MS | F | p-Value | |
---|---|---|---|---|---|

beetween groups | 2.145 | 19 | 0.113 | 90.706 | 0.000 |

within groups | 24.049 | 19,320 | 0.001 | ||

total | 26.194 | 19,339 |

**Table 9.**Post-hoc Tukey HSD test result for the average attention weight for each sensor in HR estimation. Each column 1–8 represents a homogeneous subset for a significance level of $0.05$.

Sensor Type | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

${P}_{R3}$ | 0.4864 | |||||||

${P}_{L3}$ | 0.4871 | |||||||

${P}_{R1}$ | 0.4888 | |||||||

${P}_{R4}$ | 0.4893 | |||||||

${P}_{R2}$ | 0.4900 | 0.4900 | ||||||

${P}_{L4}$ | 0.4901 | 0.4901 | ||||||

${G}_{RY}$ | 0.4911 | 0.4911 | 0.4911 | |||||

${A}_{LX}$ | 0.4952 | 0.4952 | ||||||

${A}_{RY}$ | 0.4954 | 0.4954 | ||||||

${P}_{L1}$ | 0.4956 | 0.4956 | ||||||

${A}_{RX}$ | 0.4961 | |||||||

${P}_{L2}$ | 0.4963 | |||||||

${G}_{RX}$ | 0.5032 | |||||||

${A}_{LY}$ | 0.5064 | 0.5064 | ||||||

${G}_{LX}$ | 0.5067 | 0.5067 | ||||||

${G}_{RZ}$ | 0.5084 | 0.5084 | 0.5084 | |||||

${G}_{LZ}$ | 0.5099 | 0.5099 | ||||||

${G}_{LY}$ | 0.5141 | 0.5141 | ||||||

${A}_{RZ}$ | 0.5167 | |||||||

${A}_{LZ}$ | 0.5229 | |||||||

p-value | 0.288 | 0.061 | 0.122 | 0.130 | 0.794 | 0.056 | 0.986 | 1.000 |

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## Share and Cite

**MDPI and ACS Style**

Eom, H.; Roh, J.; Hariyani, Y.S.; Baek, S.; Lee, S.; Kim, S.; Park, C.
Deep Learning-Based Optimal Smart Shoes Sensor Selection for Energy Expenditure and Heart Rate Estimation. *Sensors* **2021**, *21*, 7058.
https://doi.org/10.3390/s21217058

**AMA Style**

Eom H, Roh J, Hariyani YS, Baek S, Lee S, Kim S, Park C.
Deep Learning-Based Optimal Smart Shoes Sensor Selection for Energy Expenditure and Heart Rate Estimation. *Sensors*. 2021; 21(21):7058.
https://doi.org/10.3390/s21217058

**Chicago/Turabian Style**

Eom, Heesang, Jongryun Roh, Yuli Sun Hariyani, Suwhan Baek, Sukho Lee, Sayup Kim, and Cheolsoo Park.
2021. "Deep Learning-Based Optimal Smart Shoes Sensor Selection for Energy Expenditure and Heart Rate Estimation" *Sensors* 21, no. 21: 7058.
https://doi.org/10.3390/s21217058