Extended variational mode decomposition method and its serialization on collective mixture.

The decomposing problem of collective mixture encompasses various concrete and typical examples, such as mixture models (e.g., GMM), clustering, and HMM, etc. These problems commonly involve latent variables related to sample classification, which is their fundamental characteristic. To address this, researchers typically use the variational inference method (specifically, EM algorithm) to solve the problem. However, this method requires prior information about the cluster number, which can sometimes be difficult to obtain. In this paper, we propose an Extended Variational Mode Decomposition (EVMD) method and its serialized form (SEVMD) to tackle the decomposition issue on collective mixture. These two algorithms correspond to two different prior conditions of the modal number. They are both variational methods and from the perspective of mode decomposition. Our experimental results demonstrate that the EVMD method can effectively recover the original components when the modal number is known. On the other hand, SEVMD successfully extracts the components in a serial manner even when such information is not available.