An improved LDA dimension reduction algorithm for multivariate time series classification

In recent years, multivariate time series (MTS) classification has gradually become a research hotspot. However, due to the high-dimensional nature of MTS, directly classifying them often leads to suboptimal results. As a result, existing methods typically apply dimension reduction to the MTS dataset before classification. But the traditional MTS dimension reduction methods often lead to significant information redundancy or loss when dealing with unequal-length MTS dataset. To minimize information loss, this paper proposes a novel extraction method that helps transform unequal-length MTS dataset into equal-length MTS dataset. Furthermore, since existing dimension reduction methods ignore the fact that different MTS may have the same feature points at different time moments, this paper proposes a supervised dimension reduction method based on Linear Discriminant Analysis (LDA). This method aims to find the projection plane at each time point that minimizes the within-class scatter and maximizes the between-class scatter, thereby improving the effectiveness of dimension reduction. Experiments were conducted on 16 publicly available datasets. The results show that the proposed method effectively enhances classification performance after dimension reduction, achieving good experimental results.