Metric Learning with A-based Scalar Product for Image-set Recognition

In this paper, we propose a metric learning method for image set recognition using subspace representation. The subspace representation is effective for image set recognition where each image set is compactly represented by a subspace in a high dimensional vector space. In this framework, the similarity between two given image sets is measured by the canonical angles between the two corresponding subspaces. Many types of methods utilizing the concept of canonical angles have been developed and studied extensively. However, there still remains large potential in improving the ability to measure canonical angles. Our key idea is to learn a general scalar product space (metric space) that produces more valid canonical angles between two subspaces. To realize this idea, we first introduce an A-based scalar product instead of the standard scalar product, where A is a symmetric positive definite matrix and the canonical angles between two subspaces are measured through the A-based scalar product. We learn a discriminative metric space by optimizing metric A in terms of the Fisher ratio from local Fisher discriminant analysis. Besides, we introduce a mechanism to automatically reduce the dimension of the metric space by imposing a low-rank constraint on metric A. The effectiveness of the proposed methods is validated through extensive classification experiments on three real-world datasets.