Output relevant slow feature extraction using partial least squares

Slow feature analysis (SFA) is an approach that extracts features from a time series dataset in an unsupervised manner based on the temporal slowness principle. These slow features contain relevant information about the dynamics of the process and hence are useful for developing models. For supervised learning objectives, these slow features need to be relevant to the outputs. Partial least squares (PLS) is a method used to perform supervised feature extraction and build models. For time series datasets this approach cannot be used directly as it assumes each sample to be sequentially independent of each other. We propose an approach to perform feature extraction which combines the temporal slowness element of SFA and the output relevance element of PLS. The proposed approach extracts temporally slow features that are relevant to the outputs, which is an essential aspect of supervised learning. The proposed formulations can be solved using the existing PLS algorithms like NIPALS and SIMPLS with proposed modifications. The proposed methods are applied to three case studies: simulated, industrial and experimental case studies to demonstrate their efficacy.