Deep metric learning is a supervised learning paradigm to construct a meaningful vector space to represent complex objects. A successful application of deep metric learning to pointsets means that we can avoid expensive retrieval operations on objects such as documents and can significantly facilitate many machine learning and data mining tasks involving pointsets. We propose a self-supervised deep metric learning solution for pointsets. The novelty of our proposed solution lies in a self-supervision mechanism that makes use of a distribution distance for set ranking called the Earth’s Mover Distance (EMD) to generate pseudo labels and a pointset augmentation method for supporting the learning solution. Our experimental studies on documents, graphs, and point clouds datasets show that our proposed solutions outperform baselines and state-of-the-art approaches under the unsupervised settings. The learned self-supervised representation can also be used as a pre-trained model, which can boost downstream tasks with a fine-tuning step and outperform state-of-the-art language models.