Linear-time online visibility graph transformation algorithm: for both natural and horizontal visibility criteria

Visibility graph (VG) transformation is a technique used to convert a time series into a graph based on specific visibility criteria. It has attracted increasing interest in the fields of time series analysis, forecasting, and classification. Optimizing the VG transformation algorithm to accelerate the process is a critical aspect of VG-related research, as it enhances the applicability of VG transformation in latency-sensitive areas and conserves computational resources. In the real world, many time series are presented in the form of data streams. Despite the proposal of the concept of VG's online functionality, previous studies have not thoroughly explored the acceleration of VG transformation by leveraging the characteristics of data streams. In this paper, we propose that an efficient online VG algorithm should adhere to two criteria and develop a linear-time method, termed the LOT framework, for both natural and horizontal visibility graph transformations in data stream scenarios. Experiments are conducted on two datasets, comparing our approach with five existing methods as baselines. The results demonstrate the validity and promising computational efficiency of our framework.