WHEN: A Wavelet-DTW Hybrid Attention Network for Heterogeneous Time Series Analysis

Given its broad applications, time series analysis has gained substantial research attention but remains a very challenging task. Recent years have witnessed the great success of deep learning methods, eg., CNN and RNN, in time series classification and forecasting, but heterogeneity as the very nature of time series has not yet been addressed adequately and remains the performance "treadstone." In this light, we argue that the intra-sequence non-stationarity and inter-sequence asynchronism are two types of heterogeneities widely existed in multiple times series, and propose a hybrid attention network called WHEN as deep learning solution. WHEN features in two attention mechanisms in two different modules. In the WaveAtt module, we propose a novel data-dependent wavelet function and integrate it into the BiLSTM network as the wavelet attention, for the purpose of analyzing dynamic frequency components in nonstationary time series. In the DTWAtt module, we transform the dynamic time warping (DTW) technique into the form as the DTW attention, where all input sequences are synchronized with a universal parameter sequence to overcome the time distortion problem in multiple time series. WHEN with the hybrid attentions is then formulated as task-dependent neural network for either classification or forecasting tasks. Extensive experiments on 30 UEA datasets and 3 real-world datasets with rich competitive baselines demonstrate the excellent performance of our model. The ability of WHEN in dealing with time series heterogeneities is also elaborately explored via specially designed analysis.