Correlation network from multivariate time series: a new method for characterizing nonlinear dynamic behavior in marine acoustic signal

Marine acoustic signal detection is significant as it constitutes potential real-time monitoring of severe underwater threats. There is still a lack of an efficient approach to achieve weak acoustic signal detection with nonparametric and non-information priors. During the last decade, the complex network has emerged as a new multidisciplinary methodology for characterizing complex systems. It does not need to obtain information priors to analyze time series, which makes the marine acoustic signal detection of non-information priors possible. However, most existing research on complex networks focuses on noiseless ideal univariate time series. Further research needs to be conducted to extend complex network reconstruction from univariate time series to multivariate time series under a noise background. For this purpose, this paper proposes an algorithm to convert multivariate time series into an undirected complex network termed the correlation network method. Meanwhile, to realize the effective representation of the complex network, we further study the spectral characteristics. The correlation network method and the investigation of the spectral characteristics are demonstrated by simulation and applied to actual recorded data. The results indicate that the correlation network and graph spectral domain methods can effectively characterize nonlinear dynamic behavior in marine acoustic signals.