An ensemble of shapelet-based classifiers on inter-class and intra-class imbalanced multivariate time series at the early stage

Early classification of time series will weaken the accuracy to some degree. If the time series data are imbalanced, it will be also challenging to accurately identify minority class examples. Up to now, these two problems have been intensively addressed separately on univariate time series data, but yet to be well studied when they occur together. Compared with univariate time series, multivariate time series (MTS) is more complex, which contains multiple variables, and the interconnections between variables are hidden. Therefore, it is even more challenging to handle the combination of both problems on multivariate time series. In this paper, we propose an adaptive classification ensemble method called early prediction on imbalanced MTS to deal with early classification on inter-class and intra-class imbalanced MTS data simultaneously. First, an adaptive ensemble framework is designed to learn an early classification model on imbalanced MTS data. Based on a multiple under-sampling approach and dynamical subspace generation method, the diversity of base classifiers is realized as well as all majority class examples being fully utilized. Second, to deal with the implicit issue of intra-class imbalance in the training data, a cluster-based shapelet selection method is introduced to obtain an optimal set of stable and robust shapelets. Finally, an associate-pattern mining approach is designed to efficiently learn base classifiers, which could enhance the interpretability of classification. Experimental results show that our proposed method can achieve effective early prediction on inter-class and intra-class imbalanced MTS data.