Latent Mode Decomposition

TL;DR

VLMD is a novel algorithm that efficiently extracts oscillatory modes and connectivity structures from multivariate signals, improving robustness, scalability, and interpretability over existing methods.

Contribution

It introduces Latent Mode Decomposition, a new model blending sparse coding with mode decomposition, enabling lower-dimensional, noise-robust analysis of multichannel signals.

Findings

VLMD outperforms existing MMD methods in accuracy.

VLMD is more computationally efficient.

VLMD provides more interpretable results.

Abstract

We introduce Variational Latent Mode Decomposition (VLMD), a new algorithm for extracting oscillatory modes and associated connectivity structures from multivariate signals. VLMD addresses key limitations of existing Multivariate Mode Decomposition (MMD) techniques -including high computational cost, sensitivity to parameter choices, and weak modeling of interchannel dependencies. Its improved performance is driven by a novel underlying model, Latent Mode Decomposition (LMD), which blends sparse coding and mode decomposition to represent multichannel signals as sparse linear combinations of shared latent components composed of AM-FM oscillatory modes. This formulation enables VLMD to operate in a lower-dimensional latent space, enhancing robustness to noise, scalability, and interpretability. The algorithm solves a constrained variational optimization problem that jointly enforces reconstruction fidelity, sparsity, and frequency regularization. Experiments on synthetic and real-world datasets demonstrate that VLMD outperforms state-of-the-art MMD methods in accuracy, efficiency, and interpretability of extracted structures.