Latent Mode Decomposition

TL;DR

This work tackles the limitations of Multivariate Mode Decomposition by introducing Latent Mode Decomposition (LMD) and the Variational Latent Mode Decomposition (VLMD) algorithm. VLMD operates in a low-dimensional latent space to jointly recover sparse connectivity across channels and AM-FM latent modes, incorporating reconstruction fidelity, sparsity, and a frequency-regularization constraint via ADMM. The approach generalizes existing MMD methods, improves robustness to noise and parameter settings, and delivers interpretable connectivity patterns; it demonstrates superior accuracy and efficiency on synthetic data and provides meaningful insights in exchange-rate and electric-grid datasets. Such a framework holds promise for scalable, interpretable analysis of high-dimensional, structured multivariate signals in finance, energy, and beyond.

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.

Figures (9)

• Figure 1: Performance comparison. IMs correlation error and frequency MAPE for the MEMD, MVMD and VLMD algorithms across the three main studied scenarios for different level of noise. Each bar shows the average results corresponding to the 10 different studied cases for each studied scenario and noise seeds.
• Figure 2: Estimated frequencies per iteration. Evolution of the central frequencies, $\omega_{k}$, estimated by VLMD and MVMD respectively per iteration for Scenario A and B for different level of noise. Each line depicts the average central frequency estimated by each algorithm per iteration for all the studied cases. The horizontal dashed lines correspond to the ground truth.
• Figure 3: Overestimation of the number of modes. IMs correlation error of VLMD and MVMD algorithms for varying numbers of selected modes. The results belong to the analysis of the data from Scenario A, where $K=5$ corresponds to the ground truth (see Table \ref{['tab:SynthParameters']}). The figure also displays several panels (A-D), corresponding to varying noise levels. Each bar represents the average correlation error for 5 different studied cases with different initialization seeds.
• Figure 4: IMs for four selected countries. This figure illustrates the obtained IMs for four selected countries. Each subplot also depict the main period (central frequency) associated with each IM.
• Figure 5: Coefficient matrix of the exchange rate dataset. Heatmap of the values from the coefficient matrix from VLMD. Each row corresponds to a specific channel from the data associated with each studied country, whereas each column corresponds to a specific latent channel.