Abstract: A novel clustering algorithm for orderable 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 orderable datasets demonstrate that UOL provides reliable ordered clustering results and decent rank estimation performances with no supervision. The source codes are available at https://github.com/seon92/UOL.