Integrating Convolutional Variational Autoencoders and the Gaussian Mixture Model for efficient manifold learning and clustering of spatially preserved EEG topographic maps

Abstract

EEG microstate analysis segments continuous brain activity into brief, quasi-stable topographic configurations whose quantity, duration, and transition dynamics index cognitive state and neuropsychiatric conditions. The standard algorithm, modified k-means (ModKMeans), operates in electrode space. However, it focuses on hard partitioning where each data point is assigned to exactly one cluster and provides neither a learned representation, a generative decoder where output data are typically transformed into a compact internal representation, nor probabilistic soft assignment. In this research, a Convolutional Variational Deep Embedding model (Conv-VaDE) is designed, a topographic-map adaptation of Variational Deep Embedding (VaDE) that places a Gaussian Mixture Model (GMM) prior on the latent space of a convolutional variational autoencoder and jointly trains the encoder, decoder, and GMM. Microstate polarity invariance, the property that a topography x and its sign-inverted counterpart -x index the same underlying configuration, is preserved through three coordinated mechanisms: sign-flip augmentation of the training set, a polarity-invariant reconstruction loss, and an encoder regulariser on the latent embedding. The model is evaluated on a sample of healthy participants (N = 203 healthy adults, eyes-closed) from the LEMON resting-state EEG dataset using a multi-quadrant evaluation framework, with each method assessed in its native frame and cross-method comparisons performed via rank-based Wilcoxon signed-rank tests. Conv-VaDE's focused set of capabilities that the standard ModKMeans pipeline does not provide: a learned generative latent manifold (silhouette 0.232 at K=3, with very narrow cross-subject interquartile-range width approx 0.02 across the 203 participants, indicating highly reproducible latent geometry), decoded GMM cluster centres inspectable as scalp topographies, probabilistic soft assignment for transitional states, and a generative framework supporting downstream representation analysis. A rank-based meta-criterion over silhouette, Calinski-Harabasz, and Davies-Bouldin yields modal K=4 for Conv-VaDE (39.4%) and K=3 for ModKMeans (29.6%); K=4 is adopted to align with the canonical Lehmann A/B/C/D literature. Within the classical cluster-validity register, ModKMeans attains a higher silhouette and 4-5 percentage points higher Global Explained Variance (GEV) at every K (Wilcoxon, BH-corrected, p < 10^-30); the two methods occupy distinct positions in the methodological design space, with the cross-method comparison characterising the trade-off between direct electrode-space optimisation and learned generative representation rather than adjudicating method superiority.