Mixed-Curvature Metric Learning for Image Retrieval

Distance metric learning is a key field of machine learning, which aims at improving the performance of pattern classification and data discrimination by optimizing features to make samples of the same category closer in the feature space and samples of different classes farther apart. Most existing metric learning methods work in Euclidean space with zero curvature due to its simple and convenient characteristics. The latest studies show that non-zero curvature geometric spaces can better capture discriminative information. In this paper, to explore and form a more generalized feature space that is capable of matching complex data structure of samples, we look into metric learning problem in the mixed curvature space and present a new method called mixed-curvature metric learning (MCML). By simulating dimensionality reduction operations in different curvature spaces and conducting sample mining in mixed curvature space, our metric learning method is extended to feature spaces with a mixture of positive curvature, zero curvature, and negative curvature. Extensive experimental results show that our MCML approach achieves the superior performance in image retrieval task on multiples benchmark datasets, demonstrating the effectiveness of the proposed MCML method.