Noise-Assisted Graph Multivariate Empirical Mode Decomposition With Non-Uniform Projections

Latest advances in multi-agent technology and hardware architecture design have made multivariate or multichannel data, often supported by graphs or networks, ubiquitous in recent scientific and engineering applications. Examples include smart grids management and sensor networks monitoring to cite a few. Multivariate empirical mode decomposition (MEMD), as a fully data-driven technique, has been shown to be effective in the multiscale analysis of non-stationary signals across multiple channels. However, it still lacks the capability to capture the dependency structure of signals over channels when supported by a graph, which limits the relevance of the provided analyses. This work aims to extend MEMD to temporal graph signals. To achieve this, non-uniform projections are processed to preserve smoothness relative to the topology of the graph. A noise-assisted mechanism is also proposed in order to adapt to the randomness of signals on vertices, eliminating mode mixing and misalignment phenomena. To further demonstrate the performance of the proposed graph multivariate empirical mode decomposition (GMEMD), and in particular of its noise-assisted counterpart, we validate its mode alignment property among same-index intrinsic mode functions and its efficacy as a filter bank. Simulations on both synthetic temporal graph signals and real-world electroencephalogram data support the analysis.