Slow Down to Go Better: A Survey on Slow Feature Analysis.

Temporal data contain a wealth of valuable information, playing an essential role in various machine-learning tasks. Slow feature analysis (SFA), one of the most classic temporal feature extraction models, has been deeply explored in two decades of development. SFA extracts slowly varying features as high-level representations of temporal data. Its core idea of "slow" has been proven to be consistent with the nature of biological vision and beneficial in capturing significant temporal information for various tasks. So far, SFA has evolved into numerous improved versions and is widely applied in many fields such as computer vision, industrial control, remote sensing, signal processing, and computational biology. However, there currently lacks an insightful review of SFA. In this article, a comprehensive overview of SFA and its extensions is provided for the first time. The formulation and optimization of SFA are introduced. Two mainstream solutions, geometric interpretation, and a gradient-based training method of SFA are presented and discussed. Following that, a taxonomy of the current progress of SFA is proposed. We classify improved versions of SFA into six categories, including dual-input SFA (DISFA), online slow feature analysis (OSFA), probabilistic SFA (PSFA), multimode SFA, nonlinear SFA, and discrete labeled SFA. For each category, we illustrate its main ideas, mathematical principles, and applicable scenarios. In addition, the practical applications of SFA are summarized and presented. Finally, we bring new insights into SFA according to its research status and provide potential research directions, which may serve as a good reference for promoting future work.