Weighted Undirected Similarity Network Construction and Application for Nonlinear Time Series Detection

Detecting weak nonlinear time series is critical in various applications, such as ocean monitoring, port security, coastal operations, and offshore activities. However, traditional methods for detecting such signals often require informative priors, leading to inefficiencies. This study proposes a novel approach that transforms nonlinear time series detection into network characterization through a weighted undirected similarity network construction method. The method integrates symmetric Kullback-Leibler divergence and complex network theory, transforming the node similarity measurement problem into a geometric problem on matrix manifolds. This method constructs a network representation of the time series data by measuring the similarity between data at different time scales. To demonstrate the effectiveness of our proposed approach, we conducted simulations and applied it to actual recorded data collected in the South China Sea. The synthetic data study showed that our method has a significant advantage in detecting weak nonlinear time series from ambient noise. Additionally, our approach successfully distinguished ship signals from marine ambient noise by comparing the network spectral values.