A simple scalable linear time algorithm for horizontal visibility graphs

Abstract

Horizontal Visibility Graphs establish a connection between time series and complex networks. As a feature, they have shown strong results in time series classification. For real-world applications, algorithms for computing HVGs are necessary that work efficiently on streamed data, that can be parallelized, and whose runtime is independent of the type of time series. Our proposed algorithm extends the fast horizontal visibility algorithm of Zhu et al. satisfying all these desirable properties. The extended version stays worst-case in O(n), works additionally efficiently on streamed data, and becomes parallelizable. Contrary to recent publications, it does not require a complex data structure. This approach enables the computation of HVGs with millions of vertices in a short period, opening up new application areas of HVGs for time series generated batch-wise or resulting from measurements with a high sampling rate.