Multilinear decomposition of human walking paths

In a previous work, the authors have shown how the Principal Components Analysis (PCA) of a set of human walking paths provides sufficient information to derive a linear human-like path generator based on examples. The present work aims to provide an analysis of human walking paths from the perspective of multilinear algebra, using the n-mode Singular Value Decomposition (SVD). This decomposition subsumes the conventional PCA and extends its capabilities to study the interaction between the different vector spaces attached to the data. The training set consists of sixty routes performed three times by five different subjects for a total of 900 examples. The outcome of this decomposition is a novel multilinear model capable of revealing the global shape variations between the different vector spaces, particularly, exhibiting the planning strategies that each subject seemed to use to approach to the different targets. In addition, we sketch how the multilinear model may be used to synthesize new routes for the hypothetical case of a subject trying to reach a moving target.