Fig 1.
The hierarchy of the data and the VAE used in this study.
Data were processed and split up into epochs of 512 samples with 6 dimensions (triaxial acceleration and angular velocity). The encoder (green) and the decoder (blue) consisted of 3 mirrored convolutional layers with a size of 256, 128 and 64 nodes. These layers were configured with 32, 64, and 128 filters, respectively, and employed a kernel size of 3. The activation function used throughout the model was a hyperbolic tangent. The latent layer contained 12 normally distributed latent features. The model was trained by comparing the input to the reconstructed output. An Adam optimizer with a learning rate of 0.001 was used. The loss function consisted of two aspects: 1) the difference between the original and reconstructed signal; 2) the difference between the distribution of the latent features and a Gaussian distribution. The VAE was created in Python using TensorFlow version 2.11.0 and is available via: https://zenodo.org/doi/10.5281/zenodo.10878458 [29]. * The actual sensor data consisted of a two-minute measurement with six dimensions. For demonstration purposes a one-dimensional signal was visualized for ten seconds.
Fig 2.
Visualization of the type of data that is used per research question.
The dataset included both test-retest data from people after stroke (red) and healthy individuals (green), and longitudinal data from people after stroke (blue). The data from the people after stroke was used to train, test, and validate the VAE. The trained VAE was then used to evaluate the model fit, via the reconstruction error, on the data of the healthy control group. Next, the average value per latent feature was calculated for each measurement. These averaged latent features scores were used to 1) determine the between-day test-retest reliability using the test-retest data of the people after stroke and the healthy controls; 2) determine if people after stroke significantly changed during rehabilitation using the longitudinal data; and 3) evaluate the differences between the healthy control group and the stroke group.
Table 1.
Characteristics.
Fig 3.
Example of an original signal and its reconstructed version.
The original signal is a 512 X 6 epoch that consists of a 5.12 seconds (s) measurement with triaxial acceleration (Ax, Ay, Az) and angular velocity (Gx, Gy, Gz) data. The upper panel displays the normalized original and reconstructed acceleration. The lower panel shows the normalized original and reconstructed angular velocity. The reconstructed signal has a strong resemblance to the original signal, as indicated by visual inspection. Overall, this image demonstrates the effectiveness of using a VAE to reduce the dimensionality of a complex signal while maintaining its important features, such as the distinct strides visible in the original signal. More examples are available via: edu.nl/p3kv4.
Fig 4.
Distribution of the reconstruction error of gait people after stroke (blue) and healthy controls (orange).
The reconstruction error was expressed as the Mean Squared error (MSE). The data is normalized on a group level to facilitate comparison between groups. The majority of the epochs from people after stroke were reconstructed with an error below 0.004, while the average reconstruction error of the healthy control group was substantially larger. This indicates that the VAE was less accurate in the data-reduction and reconstruction of the data of the healthy controls.
Table 2.
Reliability and difference between healthy controls and people after stroke.
Fig 5.
Distribution of the latent features (L0-L11) and gait speed (z-normalised).
The results of the healthy participants are colored in orange, the results for people after stroke are colored in blue. The * indicates a variable with a high-excellent reliability. The # indicates a significant difference between healthy participants and people after stroke. The height of the distributions on the y-axis indicates the range of the latent variable. The width of the distribution on the x-axis indicates the height of the peak. Since the latent variables are computed with a VAE, the distributions of the stroke group are roughly normally distributed around 0 and are roughly normally distributed. Visual inspection indicates some differences between the healthy and stroke group. First, for the healthy participants, L0 appears to follow a bi-modal distribution. Second, L1 demonstrates a peak at another height than the peak of the stroke group.
Table 3.
Changes over time in gait speed and latent-feature scores in people after stroke during clinical rehabilitation.