ECG Classification Based on Wasserstein Scalar Curvature

. 2022 Oct 11;24(10):1450. doi: 10.3390/e24101450

Algorithm 1 WSCEC algorithm

Input: ECG set $T$ ; parameter $k, m, s, ϵ$

Output: Classification result $T = \cup_{j = 0}^{r + 1} {\tilde{T}}_{j} \cup {\tilde{Q}}_{4} = \cup_{j = 0}^{4} {\tilde{Q}}_{j}$

1:
Choose standard normal ECG signal $T_{s}$
2:
For every ECG signal $T_{i}$ in $T$ , acquire point cloud $S_{F} (T_{i})$ after STFFT by Equation (4), where $l = 10$ , $τ = 1$ and $d = 3$
3:
Acquire point cloud $S_{S P D} (T_{i}, k)$ of $T_{i}$ and $S_{S P D} (T_{s}, k)$ of $T_{s}$ by $k N N$ algorithm and Equation (5)
4:
Calculate scalar curvature at each point in $S_{S P D} (T_{s}, k)$ by Equation (11), take b as the minimum of the max scalar curvature and $\frac{3 d (d - 1)}{ϵ}$
5:
Calculate scalar curvature at each point in $S_{S P D} (T_{i}, k)$ by Equation (11) and obtain curvature histogram $H (m, b)$ by Equation (14)
6:
Calculate Wasserstein scalar curvature dispersion $c u r_{T_{i}} (m, b, s)$ of $T_{i}$ by Equation (16)
7:
Give the classification result $T = \cup_{j = 0}^{r + 1} {\tilde{T}}_{j} \cup {\tilde{Q}}_{4} = \cup_{j = 0}^{4} {\tilde{Q}}_{j}$ by symptom description domain partition $D = \cup_{j = 0}^{4} D_{j}$
8:
Output: $T = \cup_{j = 0}^{r + 1} {\tilde{T}}_{j} \cup {\tilde{Q}}_{4} = \cup_{j = 0}^{4} {\tilde{Q}}_{j}$