Pseudo Bidirectional Linear Discriminant Analysis for Multivariate Time Series Classification

Multivariate time series (MTS) is a kind of matrix data, typically consisting of multiple variables measured at multiple time points. Due to the high dimensionality of MTS data, many methods for MTS classification have been proposed within the literature to reduce the redundancy in time or variable mode, but there is relatively little work on exploring the redundancy in both modes concurrently. In this paper we propose a new method for MTS classification based on bidirectional linear discriminant analysis (BLDA). The advantage is that BLDA can utilize label information in reducing the redundancy in time and variable modes simultaneously. Moreover, the existing procedures for BLDA suffer from two problems: (i) BLDA cannot be performed when one of the within-class matrices is singular; (ii) the computational burden could be very heavy when one of the data dimensionality is high. A new procedure for BLDA based on pseudo-inverse (PBLDA) and an efficient algorithm for PBLDA are proposed in this paper to overcome the two problems. The performance of our proposed method is illustrated through the experiments on a number of real MTS datasets.