TE-ESN: Time Encoding Echo State Network for Prediction Based on Irregularly Sampled Time Series Data

Abstract: Prediction based on Irregularly Sampled Time Series (ISTS) is of wide concern in the real-world applications. For more accurate prediction, the methods had better grasp more data characteristics. Different from ordinary time series, ISTS is characterised with irregular time intervals of intra-series and different sampling rates of inter-series. However, existing methods have suboptimal predictions due to artificially introducing new dependencies in a time series and biasedly learning relations among time series when modeling these two characteristics. In this work, we propose a novel Time Encoding (TE) mechanism. TE can embed the time information as time vectors in the complex domain. It has the the properties of absolute distance and relative distance under different sampling rates, which helps to represent both two irregularities of ISTS. Meanwhile, we create a new model structure named Time Encoding Echo State Network (TE-ESN). It is the first ESNs-based model that can process ISTS data. Besides, TE-ESN can incorporate long short-term memories and series fusion to grasp horizontal and vertical relations. Experiments on one chaos system and three real-world datasets show that TE-ESN performs better than all baselines and has better reservoir property.