  The increasing use of multiple sensors, which produce a large amount of
multi-dimensional data, requires efficient representation and classification
methods. In this paper, we present a new method for multi-dimensional data
classification that relies on two premises: 1) multi-dimensional data are
usually represented by tensors, since this brings benefits from multilinear
algebra and established tensor factorization methods; and 2) multilinear data
can be described by a subspace of a vector space. The subspace representation
has been employed for pattern-set recognition, and its tensor representation
counterpart is also available in the literature. However, traditional methods
do not use discriminative information of the tensors, degrading the
classification accuracy. In this case, generalized difference subspace (GDS)
provides an enhanced subspace representation by reducing data redundancy and
revealing discriminative structures. Since GDS does not handle tensor data, we
propose a new projection called n-mode GDS, which efficiently handles tensor
data. We also introduce the n-mode Fisher score as a class separability index
and an improved metric based on the geodesic distance for tensor data
similarity. The experimental results on gesture and action recognition show
that the proposed method outperforms methods commonly used in the literature
without relying on pre-trained models or transfer learning.
