I am currently searching for methods of feature extraction from an ECG signal and I've stumbled upon the Karhunen–Loeve Transform. I've read some papers and I think I get the basics but my question though is, how do I extract the features(i.e R wave variability) based on the KLT transformed matrix?

Thank you in advance!


The Karhunen–Loeve Transform is the equivalent of PCA analysis for continuous signals, you could seek more informations on this type of Feature extraction.

1/The idea is to compute the covariance matrix on known signals (i don't know, maybe the ECG of a person suffering from a particular heart disease).

$C = (x-\bar{x})(x-\bar{x})^T$

where X is your dataset Matrix (idk, maybe k pattern each composed of N samples), $\bar{x}$ the mean value vector (size : k,1).

2/ Decompose this matrix in eigenvector ($V$) and eigenvalue ($D$):

$V^{-1}CV = D$

3/ Extract the main features (direction of highest variablility), depending on the eigenvalues, let's imagine that the first 7 eigenvalues will represent 99% of the energy used to represent the ECG signals.

4/ Projected data $= [V^T(X-\bar{x})^T]^T$ in a more meaningful feature space

see : https://machinelearningmastery.com/calculate-principal-component-analysis-scratch-python/

  • $\begingroup$ Thank you! it made it a bit clearer! $\endgroup$ – Ali Co. May 18 '20 at 11:19

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