Tensor Analysis with n-Mode Generalized Difference Subspace

The increasing use of multiple sensors requires more efficient methods to represent and classify multi-dimensional data, since these applications produce a large amount of data, demanding modern techniques for data processing. Considering these observations, we present in this paper a new method for multi-dimensional data classification which relies on two premises: 1) multi-dimensional data are usually represented by tensors, due to benefits from multilinear algebra and the established tensor factorization methods; and 2) this kind of data can be described by a subspace lying within a vector space. Subspace representation has been consistently employed for pattern-set recognition, and its tensor representation counterpart is also available in the literature. However, traditional methods do not employ discriminative information of the tensors, which degrades the classification accuracy. In this scenario, generalized difference subspace (GDS) may provide an enhanced subspace representation by reducing data redundancy and revealing discriminative structures. Since GDS is not able to directly handle tensor data, we propose a new projection called n-mode GDS, which efficiently handles tensor data. In addition, n-mode Fisher score is introduced as a class separability index and an improved metric based on the geodesic distance is provided to measure the similarity between tensor data. To confirm the advantages of the proposed method, we address the problem of representing and classifying tensor data for gesture and action recognition. The experimental results have shown that the proposed approach outperforms methods commonly used in the literature without adopting pre-trained models or transfer learning.