Matrix-based vs. vector-based linear discriminant analysis: A comparison of regularized variants on multivariate time series data

Over the past two decades, matrix-based or bilinear discriminant analysis (BLDA) methods have received much attention. However, it has been reported that the traditional vector-based regularized LDA (RLDA) is still quite competitive and could outperform BLDA on some benchmark datasets. A central question is whether the superiority of the vector-based RLDA would always hold for general matrix data, or is there any type of matrix data on which BLDA would perform better than RLDA? Actually, the reported comparisons are found to suffer from two limitations: (i) the comparisons are only limited to image data, and (ii) regularized RLDA is compared with non-regularized BLDA. In this paper, we break the two limitations and investigate the central question on another type of matrix data, namely multivariate time series (MTS) data. We propose a new two-parameter regularized BLDA (RBLDA) for MTS data classification. To choose the two parameters, we develop an efficient model selection algorithm. The newly proposed RBLDA enables us to perform a fair comparison between vector-based RLDA and matrix-based RBLDA. Experiments on a number of real MTS data sets are conducted to compare RBLDA with RLDA and evaluate the proposed algorithm. The results reveal that the superiority of the vector-based RLDA does not always hold for general matrix data, and RBLDA outperforms RLDA on MTS data. Moreover, the proposed model selection algorithm is efficient, and RBLDA can produce better visualization of MTS data than RLDA.