  In recent years, the methods on matrix-based or bilinear discriminant
analysis (BLDA) have received much attention. Despite their advantages, it has
been reported that the traditional vector-based regularized LDA (RLDA) is still
quite competitive and could outperform BLDA on some benchmark datasets.
Nevertheless, it is also noted that this finding is mainly limited to image
data. In this paper, we propose regularized BLDA (RBLDA) and further explore
the comparison between RLDA and RBLDA on another type of matrix data, namely
multivariate time series (MTS). Unlike image data, MTS typically consists of
multiple variables measured at different time points. Although many methods for
MTS data classification exist within the literature, there is relatively little
work in exploring the matrix data structure of MTS data. Moreover, the existing
BLDA can not be performed when one of its within-class matrices is singular. To
address the two problems, we propose RBLDA for MTS data classification, where
each of the two within-class matrices is regularized via one parameter. We
develop an efficient implementation of RBLDA and an efficient model selection
algorithm with which the cross validation procedure for RBLDA can be performed
efficiently. Experiments on a number of real MTS data sets are conducted to
evaluate the proposed algorithm and compare RBLDA with several closely related
methods, including RLDA and BLDA. The results reveal that RBLDA achieves the
best overall recognition performance and the proposed model selection algorithm
is efficient; Moreover, RBLDA can produce better visualization of MTS data than
RLDA.
