  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.
