Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model in Li et al. (2015). By decomposing the distance metric A as L T L, the problem can be cast as looking for a linear map between two sets of points in different spaces, meanwhile maintaining some data structures. The ordinal relation of the labels can be maintained via classical multidimensional scaling, a popular tool for dimension reduction in statistics. A least squares fitting term is then introduced to the cost function, which can also maintain the local data structure. The resulting model is an unconstrained problem, and can better fit the data structure. Extensive numerical results demonstrate the improvement of the new approach over the linear distance metric learning model both in speed and ranking performance.Ordinal Distance Metric Learning with MDS
IntroductionGiven a labeled image dataset (referred as the training set), image ranking is to find the most relevant images for a query image based on the training set. Different from binary classification and multiclassification, the labels of the training set in image ranking often have an order, for example, age. The two important and challenging aims for image ranking are as follows. The first aim is to find which class the query image belongs to, and the second is to find the most relevant images in the specific class. The first aim actually falls into ordinal regression in statistics, where different approaches have been proposed, see Gutierrez et al. (2016) for a survey on ordinal regression and Qiao (2015), Wang et al. (2017) for the recent development. However, the second aim makes image ranking different from ordinal regression since the training images having the same label with query image need to be further ranked. Therefore, a direct extension of methods for ordinal regression is not appropriate for image ranking.As for the second aim, to find the most relevant images, a natural way is to use Euclidean distance between images to measure their dissimilarities. However, as we will show later, in most cases, Euclidean distance is not appropriate for dissimilarity. A practical way is to learn a distance metric (denoted as A) to measure the distances between images. This is referred as distance metric learning (DML). Then for a query image, the most relevant images are those with smallest distances under metric A. Many DML methods have been developed for image classification and clustering tasks. For example, the SDP approach proposed by Xing et al. (2003), an online learning algorithm proposed by Shalev-Shwartz et al. (2004), a neighborhood component analysis (NCA) by Goldberger et al. (2004), and so on (Bar-hillel et al. (2003); Shen et al. (2010); Yang et al. ( 2007)). However, most of these methods didn't assume the labels are ordered. Therefore, they can not be directly used for image ranking.Recently, Li et al. (2015) firstly introduced ordin...