Generalized subspace distance for set-to-set image classification

Recent research in visual data classification often involves image sets and the measurement of dissimilarity between each pair of them. An effective solution is to model each image set using a subspace and compute the distance between these two subspaces as the dissimilarity between the sets. Several subspace similarity measures have been proposed in the literature. However, their relationships have not been well explored and most of them do not fully utilize the different importance of individual bases of each subspace. To consolidate this family of subspace-based measures, we propose a generalized subspace distance (GSD) framework and show that most existing subspace similarity measures can be considered as its special cases. To better utilize the different importance, we further propose a new fractional order weighted subspace distance (FOWSD) method within the GSD framework, by assigning different weights to the bases of each subspace and thus characterizing their different importance in similarity measurement. Experimental results on two image classification tasks including face recognition and object recognition are presented to show the effectiveness of the proposed method.