Subspace Discrimination for Multiway Data

Sampled values of volumetric data are expressed as third-order tensors. Object-oriented data analysis requires us to process and analyse volumetric data without embedding into a higher-dimensional vector space. Multiway forms of volumetric data require quantitative methods for the discrimination of multiway forms. Tensor principal component analysis is an extension of image singular value decomposition for planar images to higher-dimensional images. It is an efficient discrimination analysis method when used with the multilinear subspace method. The multilinear subspace method enables us to analyse spatial textures of volumetric images and spatiotemporal variations of volumetric video sequences. We define a distance metric for subspaces of multiway data arrays using the transport between two probability measures on the Stiefel manifold. Numerical examples show that the Stiefel distance is superior to the Euclidean distance, Grassmann distance and projection-based similarity for the longitudinal analysis of volumetric sequences.