Discrete Metric Learning for Fast Image Set Classification

In the field of image set classification, most existing works focus on exploiting effective latent discriminative features. However, it remains a research gap to efficiently handle this problem. In this paper, benefiting from the superiority of hashing in terms of its computational complexity and memory costs, we present a novel Discrete Metric Learning (DML) approach based on the Riemannian manifold for fast image set classification. The proposed DML jointly learns a metric in the induced space and a compact Hamming space, where efficient classification is carried out. Specifically, each image set is modeled as a point on Riemannian manifold after which the proposed DML minimizes the Hamming distance between similar Riemannian pairs and maximizes the Hamming distance between dissimilar ones by introducing a discriminative Mahalanobis-like matrix. To overcome the shortcoming of DML that relies on the vectorization of Riemannian representations, we further develop Bilinear Discrete Metric Learning (BDML) to directly manipulate the original Riemannian representations and explore the natural matrix structure for high-dimensional data. Different from conventional Riemannian metric learning methods, which require complicated Riemannian optimizations (e.g., Riemannian conjugate gradient), both DML and BDML can be efficiently optimized by computing the geodesic mean between the similarity matrix and inverse of the dissimilarity matrix. Extensive experiments conducted on different visual recognition tasks (face recognition, object recognition, and action recognition) demonstrate that the proposed methods achieve competitive performance in terms of accuracy and efficiency.