# Generating Synthetic Health Sensor Data for Privacy-Preserving Wearable Stress Detection

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## Abstract

**:**

## 1. Introduction

- We achieve data generation models based on GANs that produce synthetic multimodal time-series sequences corresponding to available smartwatch health sensors. Each data point presents a moment of stress or non-stress and is labeled accordingly.
- Our models generate realistic data that are close to the original distribution, allowing us to effectively expand or replace publicly available, albeit limited, data collections for stress detection while keeping their characteristics and offering privacy guarantees.
- With our solutions for training stress detection models with synthetic data, we are able to improve on state-of-the-art results. Our private synthetic data generators for training DP-conform classifiers help us in applying DP with much better utility–privacy trade-offs and lead to higher performance than before. We give a quick overview regarding the improvements over related work in Table 1.
- Our approach enables applications for stress detection via smartwatches while safeguarding user privacy. By incorporating DP, we ensure that the generated health data can be leveraged freely, circumventing privacy concerns of basic anonymization. This facilitates the development and deployment of accurate models across diverse user groups and enhances research capabilities through increased data availability.

## 2. Background

#### 2.1. Stress Detection from Physiological Measurements

#### 2.2. Generative Adversarial Network

#### 2.3. Differential Privacy

#### 2.4. Differentially Private Stochastic Gradient Descent

## 3. Related Work

#### 3.1. Synthetic Data for Stress Detection

#### 3.2. Privacy of Synthetic Data

#### 3.3. Stress Detection on WESAD Dataset

## 4. Methodology

#### 4.1. Environment

#### 4.2. Dataset Description

#### 4.3. Data Preparation

#### 4.4. Generative Models

- Time-series data: Instead of singular and individual input samples, we find continuous time-dependent data recorded over a specific time interval. Further, each data point is correlated to the rest of the sequence before and after it.
- Multimodal signal data: For each point in time, we find not a single sample but one each for all of our six signal modalities. Artificially generating this multimodality is further complicated by the fact that the modalities correlate to each other and to their labels.
- Class labels: Each sample also has a corresponding class label as stress or non-stress. This is solvable with standard GANs by training a separate GAN for each class, like when using the Time-series GAN (TimeGAN) [32]. However, with such individual models, some correlation between label and signal data might be lost.

#### 4.4.1. Conditional GAN

#### 4.4.2. DoppelGANger GAN

#### 4.4.3. DP-CGAN

#### 4.5. Synthetic Data Quality Evaluation

- Principal Component Analysis (PCA) [39]. As a statistical technique for simplifying and visualizing a dataset, PCA converts many correlated statistical variables into principal components to reduce the dimensional space. Generally, PCA is able to identify the principal components that identify the data while preserving their coarser structure. We restrict our analysis to calculating the first two PCs, which is a feasible representation since the major PCs capture most of the variance.
- t-Distributed Stochastic Neighbor Embedding (t-SNE) [40]. Another method for visualizing high-dimensional data is using t-SNE. Each data point is assigned a position in a two-dimensional space. This reduces the dimension while maintaining significant variance. Unlike PCA, it is less qualified at preserving the location of distant points, but can better represent the equality between nearby points.
- Signal correlation and distribution. To validate the relationship between signal modalities and to their respective labels, we analyze the strength of the Pearson correlation coefficients [41] found inside the data. A successful GAN model should be able to output synthetic data with a similar correlation as the original training data. Even though correlation does not imply causation, the correlation between labels and signals can be essential to train classification models. Additionally, we calculate the corresponding p-values (probability values) [42] to our correlation coefficients to analyze if our findings are statistically significant. As a further analysis, we also take a look at the actual distribution of signal values to see if the GANs are able to replicate these statistics.
- Classifier Two-Sample Test (C2ST). To evaluate whether the generated data are overall comparable to real WESAD data, we employ a C2ST mostly as described by Lopez-Paz and Oquab [43]. The C2ST uses a classification model that is trained on a portion of both real and synthetic data, with the task of differentiating between the two classes. Afterward, the model is fed with a test set that again consists of real and synthetic samples in equal amounts. Now, if the synthetic data are close to the real data, the classifier would have a hard time correctly labeling the different samples, leaving it with a low accuracy result. In an optimal case, the classifier would label all given test samples as real and thus only achieve 0.5 of accuracy. This test method allows us to see if the generated data are indistinguishable from real data for a trained classifier. For our C2ST model, we decided on a Naive Bayes approach.

#### 4.6. Use Case Specific Evaluation

- Train Synthetic Test Real (TSTR). The TSTR framework is commonly used in the synthetic data domain, which means that the classification model is trained on just the synthetic data and then evaluated on the real data for testing. We implement this concept by generating synthetic subject data in differing amounts, i.e., the number of subjects. We decide to first use the same size as the WESAD set of 15 subjects to simulate a synthetic replacement of the dataset. We then evaluate a larger synthetic set of 100 subjects. Complying with the LOSO method, the model is trained using the respective GAN model, leaving out the test subject on which it is then tested. The average overall subject results are then compared to the original WESAD LOSO result. Private TSTR models can use our already privatized DP-CGAN data in normal training.
- Synthetic Data Augmentation (AUGM). The AUGM strategy focuses on enlarging the original WESAD dataset with synthetic data. For each LOSO run of a WESAD subject, we combine the respective original training data and our LOSO-conform GAN data in differing amounts. As before in TSTR, we consider 15 and 100 synthetic subjects. Testing is also performed in the LOSO format. With this setup, we evaluate if adding more subjects, even though synthetic and of the same nature, helps the classification. Private training in this scenario takes the privatized DP-CGAN data but also has to consider the not-yet-private original WESAD data they are combined with. Therefore, the private AUGM models still undergo a DP-SGD training process to guarantee DP.

#### 4.7. Stress Classifiers

#### 4.7.1. Pre-Processing for Classification

#### 4.7.2. Time-Series Classification Transformer

#### 4.7.3. Convolutional Neural Network

#### 4.7.4. Hybrid Convolutional Neural Network

#### 4.8. Private Training

#### 4.8.1. For Generative Models

#### 4.8.2. For Classification Models

## 5. Results

#### 5.1. Synthetic Data Quality Results

#### 5.1.1. Two-Dimensional Visualization

#### 5.1.2. Signal Correlation and Distribution

#### 5.1.3. Indistinguishability

#### 5.2. Stress Detection Use Case Results

#### 5.2.1. Baseline Approach

#### 5.2.2. Deep Learning Approach

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Expanded Results

#### Appendix A.1. Signal Distribution Plots

**Figure A1.**An overview of the histograms giving the distribution density of signal values, while comparing generated and original data. This covers the omitted signals from Figure 8, which solely focused on EDA.

#### Appendix A.2. Per Subject LOSO Classification Results

**Table A1.**The averaged LOSO results broken down per subject and measured by F1-score (%). We compare the achieved scores based on the original WESAD data and on the best synthetically enhanced models. This extends the before presented extract of the results in Table 5.

WESAD Subject | WESAD | CGAN | CGAN + WESAD | DP-CGAN $\mathit{\epsilon}=10$ | DP-CGAN $\mathit{\epsilon}=1$ | DP-CGAN $\mathit{\epsilon}=0.1$ |
---|---|---|---|---|---|---|

ID2 | 91.76 | 95.59 | 92.35 | 88.24 | 93.67 | 96.47 |

ID3 | 74.04 | 70.00 | 77.65 | 65.39 | 61.86 | 66.57 |

ID4 | 98.14 | 93.59 | 100.00 | 80.71 | 100.00 | 80.29 |

ID5 | 97.15 | 96.29 | 97.43 | 100.00 | 100.00 | 86.57 |

ID6 | 93.43 | 98.29 | 97.43 | 100.00 | 97.14 | 99.71 |

ID7 | 90.12 | 92.29 | 91.43 | 97.14 | 84.26 | 86.86 |

ID8 | 94.85 | 96.29 | 96.57 | 89.14 | 90.54 | 88.86 |

ID9 | 97.14 | 97.71 | 98.86 | 100.00 | 97.14 | 90.96 |

ID10 | 99.03 | 96.80 | 95.83 | 100.00 | 100.00 | 88.49 |

ID11 | 79.84 | 83.77 | 90.43 | 73.58 | 79.89 | 78.89 |

ID13 | 99.72 | 93.89 | 96.39 | 99.44 | 85.81 | 99.72 |

ID14 | 54.46 | 74.88 | 77.22 | 69.44 | 61.00 | 57.22 |

ID15 | 100.00 | 100.00 | 100.00 | 97.22 | 94.82 | 86.94 |

ID16 | 96.73 | 89.17 | 95.00 | 95.13 | 91.18 | 71.94 |

ID17 | 53.57 | 91.39 | 88.61 | 65.18 | 43.04 | 83.33 |

Average | 88.00 | 91.33 | 93.01 | 88.04 | 85.36 | 84.19 |

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**Figure 1.**A brief description of the basic GAN architecture: The generator, denoted as G, creates an artificial sample ${x}^{\prime}$ using a random noise input z. These artificial samples ${x}^{\prime}$ and the real samples x are fed into the discriminator D, which categorizes each sample as either real or artificial. The classification results are used to compute the loss, which is then used to update both the generator and the discriminator through backpropagation.

**Figure 2.**Our experimental methods are illustrated by the given workflow. In the first step, we load and pre-process the WESAD dataset. We then train different GAN models for our data augmentation purposes. Each resulting model generates synthetic data, which are evaluated on data quality and, finally, compared on their ability to improve our stress detection models.

**Figure 3.**The individual signal modalities plotted for Subject ID4 after resampling, relabeling, and normalizing the data. The orange line shows the label, which equals 0 for non-stress and 1 for stress.

**Figure 4.**The spectrum plots from the FFT calculations of all subwindows in a 60-s window (

**a**), and the plot of the averaged spectrum representation over these subwindows (

**b**).

**Figure 5.**Visualization of synthetic data from our GANs using PCA and t-SNE to cluster data points against original WESAD data. Generated data are more realistic when they fit the original data points.

**Figure 6.**The signal contributions to the two PCs of our PCA model fitted on the original WESAD data. A high positive or negative contribution signifies that the feature greatly influences the variance explained by that component.

**Figure 7.**The matrices showing the Pearson correlation between the available signals. We compare real WESAD data and data from each of our GANs. In each matrix, the diagonal and all values to the right of it represent the correlation between signals. A higher value signifies a stronger correlation. The lower half of the matrices, left of the diagonal, shows the corresponding p-values for the signal correlation. A lower p-value translates to a higher statistical significance.

**Figure 8.**Histograms showing the distribution density of EDA signal values compared between original and generated data. The y-axis gives the density as $y=[0,12]$, and on the x-axis, the normalized signal value is $x=[0,1]$. The plots for all signal modalities are located in Figure A1 of Appendix A.

**Figure 9.**The results of our baseline experiment on stress detection using spectral power features. We employ a Logistic Regression (LR) model and test the effectiveness of various signal combinations.

**Table 1.**Performance results of relevant related work evaluated on WESAD dataset for modalities collected from wrist devices regarding binary (stress vs. non-stress) classification task. We compare accuracy (%) and F1-score (%) and include achieved $\epsilon $-guarantee regarding DP.

Reference | Model | Data | Accuracy | F1-Score | Privacy Budget $\mathit{\epsilon}$ |
---|---|---|---|---|---|

[20] | RF | WESAD | 87.12 | 84.11 | ∞ |

[21] | LDA | WESAD | 87.40 | N/A | ∞ |

[22] | CNN | WESAD | 92.70 | 92.55 | ∞ |

[19] | TSCT | WESAD | 91.89 | 91.61 | ∞ |

Ours | CNN-LSTM | CGAN + WESAD | 92.98 | 93.01 | ∞ |

[19] | DP-TSCT | WESAD | 78.88 | 76.14 | 10 |

Ours | CNN | DP-CGAN | 88.08 | 88.04 | 10 |

[19] | DP-TSCT | WESAD | 78.16 | 71.26 | 1 |

Ours | CNN | DP-CGAN | 85.46 | 85.36 | 1 |

[19] | DP-TSCT | WESAD | 71.15 | 68.71 | 0.1 |

Ours | CNN-LSTM | DP-CGAN | 84.16 | 84.19 | 0.1 |

**Table 2.**The subwindow length per signal depending on its frequency range and the resulting number of inputs for the classification model, as described by Gil-Martin et al. [22].

Signal | Frequency Range | Subwindow Length | # Inputs |
---|---|---|---|

ACC (x,y,z) | 0–30 Hz | 7 s | 210 |

BVP | 0–7 Hz | 30 s | 210 |

EDA | 0–7 Hz | 30 s | 210 |

TEMP | 0–6 Hz | 35 s | 210 |

**Table 3.**The results of the classifier two-sample test (C2ST), where a low accuracy closer to 0.5 is better. We also include the results of the unseen WESAD test data, which constitute an empirical lower bound.

WESAD (Unseen) | DGAN | CGAN | DP-CGAN $\mathit{\epsilon}=10$ | DP-CGAN $\mathit{\epsilon}=1$ | DP-CGAN $\mathit{\epsilon}=0.1$ | |
---|---|---|---|---|---|---|

Both | 0.59 | 0.93 | 0.61 | 0.93 | 0.77 | 0.75 |

Stress | 0.72 | 0.94 | 0.77 | 1.00 | 0.90 | 0.85 |

Non-stress | 0.70 | 0.90 | 0.71 | 0.99 | 0.83 | 0.91 |

**Table 4.**A summarization of our stress classification results in a comparison of our strategies using synthetic data with the results using just the original WESAD data. We include different counts of generated subjects, privacy budgets, and classification models. Each setting is compared on the F1-score (%) as our utility metric.

Strategy | Dataset (s) | Subject Counts | Privacy Budget $\mathit{\epsilon}$ | TSCT | CNN | CNN-LSTM |
---|---|---|---|---|---|---|

Original | WESAD | 15 | ∞ | 80.65 | 88.00 | 86.48 |

TSTR | DGAN | 15 | ∞ | 80.60 | 85.89 | 85.33 |

TSTR | CGAN | 15 | ∞ | 87.04 | 88.50 | 90.24 |

TSTR | DGAN | 100 | ∞ | 73.90 | 84.46 | 79.31 |

TSTR | CGAN | 100 | ∞ | 86.97 | 87.96 | 91.33 |

AUGM | DGAN + WESAD | 15 + 15 | ∞ | 82.86 | 88.45 | 90.67 |

AUGM | CGAN + WESAD | 15 + 15 | ∞ | 88.00 | 91.13 | 90.83 |

AUGM | DGAN + WESAD | 100 + 15 | ∞ | 86.94 | 87.28 | 88.14 |

AUGM | CGAN + WESAD | 100 + 15 | ∞ | 90.67 | 91.40 | 93.01 |

Original | WESAD | 15 | 10 | 59.81 | 46.21 | 73.18 |

TSTR | DP-CGAN | 15 | 10 | 87.55 | 88.04 | 84.84 |

TSTR | DP-CGAN | 100 | 10 | 85.28 | 86.41 | 85.19 |

AUGM | DP-CGAN + WESAD | 15 + 15 | 10 | 64.24 | 73.66 | 71.70 |

AUGM | DP-CGAN + WESAD | 100 + 15 | 10 | 71.96 | 73.50 | 69.59 |

Original | WESAD | 15 | 1 | 58.31 | 26.82 | 71.82 |

TSTR | DP-CGAN | 15 | 1 | 82.90 | 85.36 | 78.07 |

TSTR | DP-CGAN | 100 | 1 | 83.75 | 77.43 | 83.94 |

AUGM | DP-CGAN + WESAD | 15 + 15 | 1 | 68.55 | 75.76 | 71.70 |

AUGM | DP-CGAN + WESAD | 100 + 15 | 1 | 50.06 | 62.03 | 71.75 |

Original | WESAD | 15 | 0.1 | 58.81 | 28.32 | 71.70 |

TSTR | DP-CGAN | 15 | 0.1 | 76.27 | 81.35 | 76.53 |

TSTR | DP-CGAN | 100 | 0.1 | 76.54 | 83.00 | 84.19 |

AUGM | DP-CGAN + WESAD | 15 + 15 | 0.1 | 68.99 | 73.89 | 71.70 |

AUGM | DP-CGAN + WESAD | 100 + 15 | 0.1 | 35.05 | 61.99 | 71.70 |

**Table 5.**LOSO results for Subject ID14 and ID17 from the WESAD dataset. We compare the achieved F1-scores (%) based on the original WESAD data and on the best synthetically enhanced models. The full coverage of all subject results is found in Table A1 of Appendix A.

WESAD Subject | WESAD | CGAN | CGAN + WESAD | DP-CGAN $\mathit{\epsilon}=10$ | DP-CGAN $\mathit{\epsilon}=1$ | DP-CGAN $\mathit{\epsilon}=0.1$ |
---|---|---|---|---|---|---|

ID14 | 54.46 | 74.88 | 77.22 | 69.44 | 61.00 | 57.22 |

ID17 | 53.57 | 91.39 | 88.61 | 65.18 | 43.04 | 83.33 |

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## Share and Cite

**MDPI and ACS Style**

Lange, L.; Wenzlitschke, N.; Rahm, E.
Generating Synthetic Health Sensor Data for Privacy-Preserving Wearable Stress Detection. *Sensors* **2024**, *24*, 3052.
https://doi.org/10.3390/s24103052

**AMA Style**

Lange L, Wenzlitschke N, Rahm E.
Generating Synthetic Health Sensor Data for Privacy-Preserving Wearable Stress Detection. *Sensors*. 2024; 24(10):3052.
https://doi.org/10.3390/s24103052

**Chicago/Turabian Style**

Lange, Lucas, Nils Wenzlitschke, and Erhard Rahm.
2024. "Generating Synthetic Health Sensor Data for Privacy-Preserving Wearable Stress Detection" *Sensors* 24, no. 10: 3052.
https://doi.org/10.3390/s24103052