Visibility graph-based segmentation of multivariate time series data and its application

In this paper, we propose an efficient segmentation approach in order to divide a multivariate time series through integrating principal component analysis (PCA), visibility graph theory, and community detection algorithm. Based on structural characteristics, we can automatically divide the high-dimensional time series into several stages. First, we adopt the PCA to reduce the dimensions; thus, a low dimensional time series can be obtained. Hence, we can overcome the curse of dimensionality conduct, which is incurred by multidimensional time sequences. Later, the visibility graph theory is applied to handle these multivariate time series, and corresponding networks can be derived accordingly. Then, we propose a community detection algorithm (the obtained communities correspond to the desired segmentation), while modularity $Q$ is adopted as an objective function to find the optimal. As indicated, the segmentation determined by our method is of high accuracy. Compared with the state-of-art models, we find that our proposed model is of a lower time complexity $(O( n 3))$⁠, while the performance of segmentation is much better. At last, we not only applied this model to generated data with known multiple phases but also applied it to a real dataset of oil futures. In both cases, we obtained excellent segmentation results.