Self-supervised lie algebra representation learning via optimal canonical metric

Learning discriminative representation with limited training samples is emerging as an important yet challenging visual categorization task. While prior work has shown that incorporating self-supervised learning can improve performance, we found that the direct use of canonical metric in a Lie group is theoretically incorrect. In this article, we prove that a valid optimization measurement should be a canonical metric on Lie algebra. Based on the theoretical finding, this article introduces a novel self-supervised Lie algebra network (SLA-Net) representation learning framework. Via minimizing canonical metric distance between target and predicted Lie algebra representation within a computationally convenient vector space, SLA-Net avoids computing nontrivial geodesic (locally length-minimizing curve) metric on a manifold (curved space). By simultaneously optimizing a single set of parameters shared by self-supervised learning and supervised classification, the proposed SLA-Net gains improved generalization capability. Comprehensive evaluation results on eight public datasets show the effectiveness of SLA-Net for visual categorization with limited samples.