Metric learning aims at finding a suitable distance metric over the input
space, to improve the performance of distance-based learning algorithms. In
high-dimensional settings, metric learning can also play the role of
dimensionality reduction, by imposing a low-rank restriction to the learnt
metric. In this paper, instead of training a low-rank metric on
high-dimensional data, we consider a randomly compressed version of the data,
and train a full-rank metric there. We give theoretical guarantees on the error
of distance-based metric learning, with respect to the random compression,
which do not depend on the ambient dimension. Our bounds do not make any
explicit assumptions, aside from i.i.d. data from a bounded support, and
automatically tighten when benign geometrical structures are present.
Experimental results on both synthetic and real data sets support our
theoretical findings in high-dimensional settings.

在高维背景下，本文通过对数据的随机压缩版本进行训练和全秩度量，在距离度量学习的错误方面提供了理论保证，这不依赖于环境维度，同时假定数据来自有界支持并自动在存在良好几何结构时收缩。合成和真实数据集的实验结果支持我们在高维背景下的理论发现。