# Latent Mode Decomposition

arXiv: https://arxiv.org/abs/2505.17797 · HTML: https://mlsanity.com/paper/2505.17797/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 22 references that are in the map.
- First posted on arXiv 23 May 2025.

## Builds on (most cited first, 4 of 4)

- [Convolutional Dictionary Learning: A Comparative Review and New Algorithms](https://mlsanity.com/paper/1709.02893/) (2017)
- [Multivariate Variational Mode Decomposition](https://mlsanity.com/paper/1907.04509/) (2019)
- [Simultaneously sparse and low-rank abundance matrix estimation for hyperspectral image unmixing](https://mlsanity.com/paper/1504.01515/) (2015)
- [Data-driven Signal Decomposition Approaches: A Comparative Analysis](https://mlsanity.com/paper/2208.10874/) (2022)

## Abstract (arXiv)

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.