Tensor Analysis with n-Mode Generalized Difference Subspace

Abstract

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.

Delta Descriptors: Change-Based Place Representation for Robust Visual Localization

“…In particular, it would be interesting to see how a framework that learns underlying descriptors would change its behaviour if optimized for place recognition performance using the subsequent Delta Descriptors. The concept of using a difference space [18] is not well-explored in the place recognition literature but is a promising avenue for future research applied to other similar problems where inferring or learning the changes might be more relevant than the representation itself [19], [20], [47]. We believe that our research contributes to the continued understanding of deep-learnt image description techniques and opens up new opportunities for developing and learning robust representations of places that leverage temporal information.…”

“…[19] proposed a novel discriminant analysis based on GDS demonstrating its utility as discriminative feature extractor for face recognition. Recently, [20] extended the concept of GDS to tensors for representing and classifying gestures and actions. [47] used difference subspace analysis to maximize inter-class discrimination for effective face recognition as an alternative approach to improving representation ability of samples.…”

“…This is of particular importance to a mobile robot or autonomous vehicle operating in a new environment that may undergo significant variations in visual appearance during a repeated route traversal. Previously, difference-based approaches have been explored for recognizing objects [18], faces [19] and actions [20]. In this research, the concept of differencebased description is based on measuring the changes across an observed sequence of places which is repeatable across traverses.…”