#### Divide and Conquer the Embedding Space for Metric Learning

##### Artsiom Sanakoyeu, Vadim Tschernezki, Uta Büchler, Björn Ommer

Learning the embedding space, where semantically similar objects are located close together and dissimilar objects far apart, is a cornerstone of many computer vision applications. Existing approaches usually learn a single metric in the embedding space for all available data points, which may have a very complex non-uniform distribution with different notions of similarity between objects, e.g. appearance, shape, color or semantic meaning. Approaches for learning a single distance metric often struggle to encode all different types of relationships and do not generalize well. In this work, we propose a novel easy-to-implement divide and conquer approach for deep metric learning, which significantly improves the state-of-the-art performance of metric learning. Our approach utilizes the embedding space more efficiently by jointly splitting the embedding space and data into $K$ smaller sub-problems. It divides both, the data and the embedding space into $K$ subsets and learns $K$ separate distance metrics in the non-overlapping subspaces of the embedding space, defined by groups of neurons in the embedding layer of the neural network. The proposed approach increases the convergence speed and improves generalization since the complexity of each sub-problem is reduced compared to the original one. We show that our approach outperforms the state-of-the-art by a large margin in retrieval, clustering and re-identification tasks on CUB200-2011, CARS196, Stanford Online Products, In-shop Clothes and PKU VehicleID datasets.

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