Abstract: A novel clustering algorithm for ordered data, called unsupervised order learning (UOL), is proposed in this paper. First, we develop the ordered $k$-means to group objects into ordered clusters by reducing the deviation of an object from consecutive clusters. Then, we train a network to construct an embedding space, in which objects are sorted compactly along a chain of line segments, determined by the cluster centroids. We alternate the clustering and the network training until convergence. Moreover, we perform unsupervised rank estimation via a simple nearest neighbor search in the embedding space. Extensive experiments on various ordered datasets demonstrate that UOL provides reliable ordered clustering results and decent rank estimation performances with no supervision.