Beyond similar and dissimilar relations: A kernel regression formulation for metric learning

Most existing metric learning methods focus on learning a similarity or distance measure relying on similar and dissimilar relations between sample pairs. However, pairs of samples cannot be simply identified as similar or dissimilar in many real-world applications, e.g., multi-label learning, label distribution learning and tasks with continuous decision values. To this end, in this paper we propose a novel relation alignment metric learning (RAML) formulation to handle the metric learning problem in those scenarios. Since the relation of two samples can be measured by the difference degree of the decision values, motivated by the consistency of the sample relations in the feature space and decision space, our proposed RAML utilizes the sample relations in the decision space to guide the metric learning in the feature space. In this way, our RAML method formulates metric learning as a kernel regression problem, which can be efficiently optimized by the standard regression solvers. We carry out several experiments on the single-label classification, multi-label classification, and label distribution learning tasks, to demonstrate that our method achieves favorable performance against the state-of-the-art methods.