Segment Growing Neural Gas for Nonlinear Time Series Analysis

In this work we propose an extension to Growing Neural Gas (GNG) for dealing with the spatiotemporal quantization of time series. The two main changes to the original GNG algorithm are the following. First, the basic unit of the GNG network is changed from a node to a linear segment joining two nodes. Secondly, temporal connections between neighboring units in time are added. The proposed algorithm called Segment GNG (SGNG) is compared with the original GNG and Merge GNG algorithms using three benchmark time series: Rossler, Mackey-Glass and \(\text {NH}_{3}\) Laser. The algorithms are applied to the quantization of trajectories in the state space representation of these time series. The results show that the SGNG outperforms both GNG and Merge GNG in terms of quantization error and temporal quantization error.