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Establishing a sparse set of keypoint correspon dences between images is a fundamental task in many computer vision pipelines. Often, this translates into a computationally expensive nearest neighbor search, where every keypoint descriptor at one image must be compared with all the descriptors at the others. In order to lower the computational cost of the matching phase, we propose a deep feature extraction network capable of detecting a predefined number of complementary sets of keypoints at each image. Since only the descriptors within the same set need to be compared across the different images, the matching phase computational complexity decreases with the number of sets. We train our network to predict the keypoints and compute the corresponding descriptors jointly. In particular, in order to learn complementary sets of keypoints, we introduce a novel unsupervised loss which penalizes intersections among the different sets. Additionally, we propose a novel descriptor-based weighting scheme meant to penalize the detection of keypoints with non-discriminative descriptors. With extensive experiments we show that our feature extraction network, trained only on synthetically warped images and in a fully unsupervised manner, achieves competitive results on 3D reconstruction and re-localization tasks at a reduced matching complexity.