Algorithm 1. Automated non-Delineation Feature Extraction Pipeline

Input: Raw ECG data

$X\in {\mathbb{R}}^{T\times 12}$

Output: $F\in {\mathbb{R}}^{10}$

Step 1: lead selection

Lead II is extracted

$x=X_{:,2}\in {\mathbb{R}}^T$

Whereas $X_{:,2}$, represents second column for any given row for T samples. Therefore $x={\mathbb{R}}^T$. The signals are resized $s=\mathrm{Resize}\left(x,L\right),s\in {\mathbb{R}}^L,$ where $\mathrm{Resize}\left(\cdot \right)$ denotes truncation for signals longer than L samples and zero-padding for shorter signals.

Step 2: Automatic R-Peak Detection

$d_{min}=max\left(1, ⌊{\displaystyle \frac{f_s}{2}}⌋\right)$, located in $R=\left\{r_1,r_2,r_3,\dots r_p,\right\}, r_p\in \left\{1,\dots L\right\},$

Step 3: RR Rhythm Descriptors

If $P\ge 2$, RR interval vector

$q={\left[q_1,q_2,q_3, \dots q_N\right]}^T\in {\mathbb{R}}^N$

For $q_i{\displaystyle \frac{r_{i+1}-r_i}{f_s}}$ $i=\left\{1,\dots ,N\right\}$

All RR Descriptors

$F_1={\mu }_q={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N}{q}_i,$ $F_2={\sigma }_q=\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N}(q_i-{\mu }_q{)}^2},$ $F_3=\mathrm{R}\mathrm{M}\mathrm{S}\left(q\right)=\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N}{q}_i^2},$ $F_4={\displaystyle \frac{1}{\mathrm{m}\mathrm{a}\mathrm{x}(1,N-1)}}{\displaystyle \sum _{i=1}^{N-1}}\mathbb{I}\left(\mid q_{i+1}-q_i\mid >0.05\right),$

If $\mathrm{P}<2$,

$F_1=F_2=F_3=F_4=0.$

Step 4: QRS-Width Proxy Descriptors

If $P\ge 1$, the peak-width vector is

$\mathbf{w}=[w_1,w_2,\dots ,w_K{]}^T\in {\mathbb{R}}^K,$

where each width is estimated at half-maximum peak prominence. The extracted descriptors are

$F_5={\mu }_w={\displaystyle \frac{1}{K}}{\displaystyle \sum _{k=1}^K}{w}_k,$ $F_6={\sigma }_w=\sqrt{{\displaystyle \frac{1}{K}}{\displaystyle \sum _{k=1}^K}(w_k-{\mu }_w{)}^2}.$

If no valid widths are available,

$F_5=F_6=0.$

These are QRS-width proxy descriptors. As such, they do not rely on explicit delineation of the onset and offset of the QRS complexes.

Step 5: Global Spectral Descriptors

The FFT magnitude spectrum of the aligned ECG signal is

$\mathbf{m}=\mid \mathcal{F}\left(s\right)\mid =[m_1,m_2,\dots ,m_L{]}^T\in {\mathbb{R}}^L.$

The extracted spectral descriptors are

$F_7={\mu }_m={\displaystyle \frac{1}{L}}{\displaystyle \sum _{j=1}^L}{m}_j,$ $F_8={\sigma }_m=\sqrt{{\displaystyle \frac{1}{L}}{\displaystyle \sum _{j=1}^L}(m_j-{\mu }_m{)}^2},$ $F_9=\mathrm{skew}\left(\mathbf{m}\right),$ $F_{10}=\mathrm{kurtosis}\left(\mathbf{m}\right).$

If

${\sigma }_m=0,$

then

$F_9=F_{10}=0.$

Step 6: Feature Vector Assembly

The final handcrafted descriptor vector is

$F={\left[\begin{array}{cccccccccc}{F}_1& F_2& F_3& F_4& F_5& F_6& F_7& F_8& F_9& F_{10}\end{array}\right]}^T\in {\mathbb{R}}^{10}.$