Tri-Partition Alphabet-Based State Prediction for Multivariate Time-Series

Recently, predicting multivariate time-series (MTS) has attracted much attention to obtain richer semantics with similar or better performances. In this paper, we propose a tri-partition alphabet-based state (tri-state) prediction method for symbolic MTSs. First, for each variable, the set of all symbols, i.e., alphabets, is divided into strong, medium, and weak using two user-specified thresholds. With the tri-partitioned alphabet, the tri-state takes the form of a matrix. One order contains the whole variables. The other is a feature vector that includes the most likely occurring strong, medium, and weak symbols. Second, a tri-partition strategy based on the deviation degree is proposed. We introduce the piecewise and symbolic aggregate approximation techniques to polymerize and discretize the original MTS. This way, the symbol is stronger and has a bigger deviation. Moreover, most popular numerical or symbolic similarity or distance metrics can be combined. Third, we propose an along-across similarity model to obtain the k-nearest matrix neighbors. This model considers the associations among the time stamps and variables simultaneously. Fourth, we design two post-filling strategies to obtain a completed tri-state. The experimental results from the four-domain datasets show that (1) the tri-state has greater recall but lower precision; (2) the two post-filling strategies can slightly improve the recall; and (3) the along-across similarity model composed by the Triangle and Jaccard metrics are first recommended for new datasets.