Background: The representational learning of ECG wave complexes has emerged as a powerful approach for capturing clinically salient features from cardiac electrical activity while enabling sub-Nyquist data compression. The topology of the latent space plays a crucial role in maintaining fidelity and preserving the morphological characteristics of reconstructed waveforms.
Methodology: An adaptive Legendre Mixture Model Variational Autoencoder (ALMM-VAE) is proposed for structured and interpretable ECG representation learning. The proposed architecture leverages a Legendre polynomial-based mixture model in the latent space. To ensure that ALMM-VAE learns the optimal combination of Legendre polynomial components , regularization terms are added to the training loss function. Thus, the mixture model consists of various orders of Legendre basis functions capturing both global and local morphological variations of input ECG signals. The orthogonality of Legendre basis functions ensures minimal redundancy in feature extraction while providing a compact and efficient representation of ECG waveforms.
Results: ECG signals from Lead II of the publicly available MIT-BIH dataset are sliced into segments of 200 ms, centered at each R peak. The segments are divided into training and test sets in a 60/40 ratio. Experimental results demonstrate that ALMM-VAE outperforms traditional Gaussian-based VAEs in both reconstruction accuracy and representation quality. Additionally, ectopic beats in the test set are classified using a linear classifier trained on the latent space of ALMM-VAE, achieving sensitivity and precision scores of 87% and 95% are obtained, respectively