Table 2 Nomenclature table for problem formulations.
From: DeepECG-Net: a hybrid transformer-based deep learning model for real-time ECG anomaly detection
Notation | Description | Notation | Description |
|---|---|---|---|
\(\:S,{S}_{t},T\) | ECG signal sequence, its time step \(\:t\), and total length | \(\:{f}_{\theta\:},{\theta\:}^{\text{*}}\) | DeepECG-Net model and its optimal parameters |
\(\:\widehat{y}\) | Predicted ECG class (normal/anomaly) | \(\:{\mathcal{L}}_{ECG},{\mathcal{L}}_{adaptive}\) | ECG classification and adaptive anomaly detection loss functions |
\(\:{\lambda\:}_{1},{\lambda\:}_{2}\) | Regularization coefficients | \(\:{W}_{\text{CNN}},{W}_{\text{Transformer}}\) | CNN and transformer layer weights |
\(\:{F}_{\text{CNN}}^{\left(l\right)}\) | Features extracted by CNN layer \(\:l\) | \(\:\sigma\:\) | Activation function |
\(\:{\mathbf{A}}_{h},H\) | Attention score for head \(\:h\) and number of attention heads | \(\:\mathbf{M}\mathbf{H}\mathbf{A}\) | Multi-head attention output |
\(\:P{E}_{\left(t,2i\right)}\) | Positional encoding for sequence modelling | \(\:{W}_{\text{out}},{b}_{\text{out}}\) | Output layer weights and bias |
\(\:{D}_{i},M\) | Distributed ECG dataset for client \(\:i\) and the number of edge devices | \(\:{\theta\:}_{i}^{\left(t\right)},\eta\:\) | Model parameters of client \(\:i\) at iteration \(\:t\) and learning rate |
\(\:\text{KL}\left(P\parallel\:Q\right)\) | Kullback-Leibler divergence for feature representation regularization | \(\:{W}_{j},\gamma\:\) | Learnable weights for ECG denoising and adaptive noise filtering coefficient |
\(\:\text{softmax}\left(\cdot\:\right)\) | Softmax function for classification | \(\:\nabla\:{S}_{i}\) | Gradient of ECG feature representation |
