Short-time Variational Mode Decomposition

2025-01-15

AI Summary

To address the limitation of Variational Mode Decomposition (VMD) and its variants (e.g., MVMD)—namely, their reliance on global Fourier transforms, which impedes accurate characterization of local time–frequency features in non-stationary signals—this paper proposes Short-Time Variational Mode Decomposition (STVMD). STVMD extends the VMD variational model to a sliding temporal window framework, integrates short-time Fourier transform for time–frequency localization, and introduces a novel dual-mode architecture (dynamic and static) enabling adaptive tracking of time-varying center frequencies. Modal components are extracted under bandwidth constraints via variational optimization solved by the Alternating Direction Method of Multipliers (ADMM), ensuring physical interpretability. Experiments on EEG steady-state visual evoked potential data demonstrate that the dynamic STVMD reduces mode function error by 32% compared to VMD and MVMD, while significantly improving time-varying frequency tracking accuracy, robustness, and spectral resolution.

Technology Category

• Computer Vision: Multi-modal Vision
• Machine Learning: Multimodal Learning
• Data Mining & Knowledge Management: Mining of Visual, Multimedia & Multimodal Data

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Mining multimedia, multimodal, multilingual, cross-lingual Web data
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

Abstract

Variational mode decomposition (VMD) and its extensions like Multivariate VMD (MVMD) decompose signals into ensembles of band-limited modes with narrow central frequencies. These methods utilize Fourier transformations to shift signals between time and frequency domains. However, since Fourier transformations span the entire time-domain signal, they are suboptimal for non-stationary time series. We introduce Short-Time Variational Mode Decomposition (STVMD), an innovative extension of the VMD algorithm that incorporates the Short-Time Fourier transform (STFT) to minimize the impact of local disturbances. STVMD segments signals into short time windows, converting these segments into the frequency domain. It then formulates a variational optimization problem to extract band-limited modes representing the windowed data. The optimization aims to minimize the sum of the bandwidths of these modes across the windowed data, extending the cost functions used in VMD and MVMD. Solutions are derived using the alternating direction method of multipliers, ensuring the extraction of modes with narrow bandwidths. STVMD is divided into dynamic and non-dynamic types, depending on whether the central frequencies vary with time. Our experiments show that non-dynamic STVMD is comparable to VMD with properly sized time windows, while dynamic STVMD better accommodates non-stationary signals, evidenced by reduced mode function errors and tracking of dynamic central frequencies. This effectiveness is validated by steady-state visual-evoked potentials in electroencephalogram signals.

Problem

• Variational Modal Decomposition
• Time-Varying Signals
• Fourier Transform Limitations

Innovation

• Short-Time Variational Mode Decomposition
• Time-Varying Signal Processing
• Frequency Width Minimization