Revisiting PCA for time series reduction in temporal dimension

Abstract: Revisiting PCA for Time Series Reduction in Temporal Dimension; Jiaxin Gao, Wenbo Hu, Yuntian Chen; Deep learning has significantly advanced time series analysis (TSA), enabling the extraction of complex patterns for tasks like classification, forecasting, and regression. Although dimensionality reduction has traditionally focused on the variable space-achieving notable success in minimizing data redundancy and computational complexity-less attention has been paid to reducing the temporal dimension. In this study, we revisit Principal Component Analysis (PCA), a classical dimensionality reduction technique, to explore its utility in temporal dimension reduction for time series data. It is generally thought that applying PCA to the temporal dimension would disrupt temporal dependencies, leading to limited exploration in this area. However, our theoretical analysis and extensive experiments demonstrate that applying PCA to sliding series windows not only maintains model performance, but also enhances computational efficiency. In auto-regressive forecasting, the temporal structure is partially preserved through windowing, and PCA is applied within these windows to denoise the time series while retaining their statistical information. By preprocessing time-series data with PCA, we reduce the temporal dimensionality before feeding it into TSA models such as Linear, Transformer, CNN, and RNN architectures. This approach accelerates training and inference and reduces resource consumption. Notably, PCA improves Informer training and inference speed by up to 40% and decreases GPU memory usage of TimesNet by 30%, without sacrificing model accuracy. Comparative analysis against other reduction methods further highlights the effectiveness of PCA in improving the efficiency of TSA models.