Latent Mode Decomposition

--We introduce V ariational 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 the interpretability of extracted structures. ONST A TIONARY signal decomposition techniques constitute an essential tool in Signal Processing for analyzing complex signals. Among them, Mode Decomposition (MD) has emerged as a fundamental framework, enabling the extraction of meaningful intrinsic oscillatory components [1]. Over the last couple of decades, a wide range of MD methods and algorithms have been developed and successfully applied across a wide range of interdisciplinary applications, such as biomedical signal analysis, structural health monitoring, and financial time-series analysis. This particular trend dates back to the late nineties with the introduction of Empirical Mode Decomposition (EMD) [1], which was followed by the development of other similar alternatives, such as Synchro-squeezed Transform (SST) [2], V ariational Mode Decomposition (VMD) [3] and Sliding-window Singular Spectrum Analysis (SSA) [4]. Originally designed for single-channel time series analysis, some of these methods were later extended to handle multivariate time series. Notable multivariate algorithms include Multivariate Empirical Mode Decomposition (MEMD) [5], multivariate nonlinear chirp mode decomposition [6], iterative filtering [7], as well as Multivariate V ariational Mode Decomposition (MVMD) [8].