A novel approach to blind image quality assessment, called quality comparison network (QCN), is proposed in this paper, which sorts the feature vectors of input images according to their quality scores in an embedding space. QCN employs comparison transformers (CTs) and score pivots, which act as the centroids of feature vectors of similar-quality images. Each CT updates the score pivots and the feature vectors of input images based on their ordered correlation. To this end, we adopt four loss functions. Then, we estimate the quality score of a test image by searching the nearest score pivot to its feature vector in the embedding space. Extensive experiments show that the proposed QCN algorithm yields excellent image quality assessment performances on various datasets. Furthermore, QCN achieves great performances in cross-dataset evaluation, demonstrating its superb generalization capability. The source codes are available at https://github.com/nhshin-mcl8/QCN.

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.

A novel ordinal regression algorithm, called moving window regression (MWR), is proposed in this paper. First, we propose the notion of relative rank ($\rho$-rank), which is a new order representation scheme for input and reference instances. Second, we develop global and local relative regressors ($\rho$-regressors) to predict$\rho$-ranks within entire and specific rank ranges, respectively. Third, we refine an initial rank estimate iteratively by selecting two reference instances to form a search window and then estimating the$\rho$-rank within the window. Extensive experiments results show that the proposed algorithm achieves the state-of-the-art performances on various benchmark datasets for facial age estimation and historical color image classification. The codes are available at https://github.com/nhshin-mcl/MWR.

A novel approach to rank estimation, called geometric order learning (GOL), is proposed in this paper. First, we construct an embedding space, in which the direction and distance between objects represent order and metric relations between their ranks, by enforcing two geometric constraints: the order constraint compels objects to be sorted according to their ranks, while the metric constraint makes the distance between objects reflect their rank difference. Then, we perform the simple $k$ nearest neighbor ($k$-NN) search in the embedding space to estimate the rank of a test object. Moreover, to assess the quality of embedding spaces for rank estimation, we propose a metric called discriminative ratio for ranking (DRR). Extensive experiments on facial age estimation, historical color image (HCI) classification, and aesthetic score regression demonstrate that GOL constructs effective embedding spaces and thus yields excellent rank estimation performances. The source codes are available at https://github.com/seon92/GOL