Unsupervised deep metric learning (UDML) focuses on learning a semantic
representation space using only unlabeled data. This challenging problem
requires accurately estimating the similarity between data points, which is
used to supervise a deep network. For this purpose, we propose to model the
high-dimensional data manifold using a piecewise-linear approximation, with
each low-dimensional linear piece approximating the data manifold in a small
neighborhood of a point. These neighborhoods are used to estimate similarity
between data points. We empirically show that this similarity estimate
correlates better with the ground truth than the similarity estimates of
current state-of-the-art techniques. We also show that proxies, commonly used
in supervised metric learning, can be used to model the piecewise-linear
manifold in an unsupervised setting, helping improve performance. Our method
outperforms existing unsupervised metric learning approaches on standard
zero-shot image retrieval benchmarks.

无监督深度度量学习通过仅使用无标签数据来学习语义表示空间，其中准确估计数据点之间的相似度是一个具有挑战性的问题。为此，我们提出了使用分段线性逼近来建模高维数据流形的方法，其中每个低维线性段近似于点周围小邻域内的数据流形。通过这些邻域来估计数据点之间的相似度。实验证明，与现有最先进技术的相似度估计相比，我们的方法更好地与真实情况相关。我们还证明，在无监督环境中可以使用代理模型分段线性流形，从而提高性能。我们的方法在标准零样本图像检索基准测试上优于现有的无监督度量学习方法。