Detection of Cardiac Arrhythmia from ECG Sequence

In the posted 1.2 version several demonstrations were included in the distribution. This notebook recreates the ECG demonstration.

This uses both the static (predict_proba) and sequence (predict_sequence) detection methods on ECG data. The specific data can be downloaded here selecting Select MIT-BIH Arrhythmia Database ( mitdb ), and export as a CSV.

The data was initially prepared from the CSV by applying a median filter with a kernel size of 301:

X = np.loadtxt(
    "data/MIT_physionet_sample.csv", skiprows=2, usecols=(1, 2), delimiter=","
)

# Apply a median filter with a window size of 301
X[:, 0] = X[:, 0] - scipy.signal.medfilt(X[:, 0], kernel_size=301)
X[:, 1] = X[:, 1] - scipy.signal.medfilt(X[:, 1], kernel_size=301)

For efficiency, the data used here has the median filter applied and is in /notebooks/filtered_ecg.json.



In [1]:

    
import os
import numpy as np
from pathlib import Path

cwd = os.getcwd()
os.chdir(Path(cwd).parents[1])

from lsanomaly import LSAnomaly
import lsanomaly.notebooks.dynamic as demo

Data Prep



In [2]:

    
X_train, X_test = demo.data_prep(
    data_file=os.path.join(
        os.getcwd(), "lsanomaly", "notebooks", "filtered_ecg.json"
    )
)

Anomaly Models



In [3]:

    
anomaly_model = LSAnomaly(rho=1, sigma=0.5)
anomaly_model.fit(X_train)









    Out[3]:





LSAnomaly(gamma=4.0,
          kernel_pos=array([[ 0.055,  0.05 ,  0.05 ,  0.03 ],
       [-0.03 , -0.05 ,  0.93 ,  0.66 ],
       [-0.355,  0.355, -3.16 , -2.985],
       ...,
       [ 0.235,  0.155,  0.865,  1.56 ],
       [-0.01 , -0.025, -0.255, -0.245],
       [ 0.09 ,  0.075,  0.765,  1.395]]),
          n_kernels_max=500, rho=1, seed=None, sigma=0.5)

Static Detection



In [4]:

    
y_pred_static = anomaly_model.predict_proba(X_test)

Dynamic Detection

Because the dynamic model uses an HMM, a state transition matrix $A$ and an initial probability vector $\pi$ are required. We set

$$ \begin{equation*} A = \begin{pmatrix} 0.999 & 0.001 \\ 0.01 & 0.99 \\ \end{pmatrix} \end{equation*} $$

and $$\pi = (0.5, .05)$$



In [5]:

    
A = np.array([[0.999, 0.001], [0.01, 0.99]])
pi = np.array([0.5, 0.5])



In [6]:

    
y_pred_dynamic = anomaly_model.predict_sequence(
    X_test, A, pi, inference="smoothing"
)

RESULTS



In [7]:

    
demo.plot_results(X_test, y_pred_static, y_pred_dynamic);