Dynamic mode decomposition: A feature extraction technique based hidden Markov model for detection of Mysticetes' vocalisations

The detection and classification of Mysticetes' vocalisations have evoked the attention of researchers over the years because of their relevance to the marine ecosystem. These vocalisations are gathered employing different passive acoustic monitoring techniques. The vocalisation datasets are accumulated over a period; thus, they are large and cannot be easily analysed manually. Consequently, efficient machine learning (ML) tools such as the hidden Markov models (HMMs) are used extensively to automatically detect and classify these huge vocalisation datasets. As with most ML tools, the detection efficiency of the HMMs depend on the adopted feature extraction technique. Feature extraction techniques such as the Mel-scale frequency cepstral coefficient (MFCC), linear predictive coefficient (LPC), and empirical mode decomposition (EMD) have been adopted with the HMMs to detect different Mysticetes' vocalisations. This article introduces the method of dynamic mode decomposition (DMD) as a feature extraction technique that can be adopted with the HMMs for the detection of Mysticetes' vocalisations. The DMD has emerged as a robust tool for analysing the dynamics of non-stationary and non-linear signals. It is a completely data-driven tool that decomposes a signal over a certain period of time into relevant modes. Here, these spatial-temporal modes are reconstructed mathematically to form reliable feature vectors of the decomposed vocalisation signals. The performance of the proposed DMD-HMM detection technique is demonstrated using the acoustic datasets of two different Mysticetes' vocalisations: Humpback whale songs and Inshore Bryde's whale short pulse calls. In both species, the proposed DMD-HMM exhibits superior sensitivity and false discovery rate performances as compared to the MFCC-HMM, LPC-HMM, and EMD-HMM detection methods. Likewise, this proposed DMD-HMM detection method can be extended to other Mysticetes' that produce characteristics sounds.