Online incremental higher-order partial least squares regression for fast reconstruction of motion trajectories from tensor streams

Abstract

The higher-order partial least squares (HOPLS) is considered as the state-of-the-art tensor-variate regression modeling for predicting a tensor response from a tensor input. However, the standard HOPLS can quickly become computationally prohibitive or merely impossible, especially when huge and time-evolving tensorial streams arrive over time in dynamic application environments. In this paper, we present a computationally efficient online tensor regression algorithm, namely incremental higher-order partial least squares (IHOPLS), for adapting HOPLS to the setting of infinite time-dependent tensor streams. By incrementally clustering the projected latent variables in latent space and summarizing the previous data, IHOPLS is able to recursively update the projection matrices and core tensors over time, resulting in greatly reduced costs in terms of both memory and running time while maintaining high prediction accuracy. To show the effectiveness and scalability of our approach for large databases, we apply IHOPLS to two real-life applications as reconstruction of 3D motion trajectories from video and ECoG streaming signals.