We propose a new approach for metric learning by framing it as learning a
sparse combination of locally discriminative metrics that are inexpensive to
generate from the training data. This flexible framework allows us to naturally
derive formulations for global, multi-task and local metric learning. The
resulting algorithms have several advantages over existing methods in the
literature: a much smaller number of parameters to be estimated and a
principled way to generalize learned metrics to new testing data points. To
analyze the approach theoretically, we derive a generalization bound that
justifies the sparse combination. Empirically, we evaluate our algorithms on
several datasets against state-of-the-art metric learning methods. The results
are consistent with our theoretical findings and demonstrate the superiority of
our approach in terms of classification performance and scalability.

本文提出了一种新的度量学习方法，将其框架构建为学习一种稀疏组合的本地判别度量，这种度量可以从训练数据中生成，从而可以自然地推导出全局、多任务和本地的度量学习公式。通过数理分析和实验验证，本方法比现有方法具有更少的参数和更好的可扩展性，从而提高了分类性能。

稀疏组合度量学习

Sparse Compositional Metric Learning

We study the problem of learning local metrics for nearest neighbor
classification. Most previous works on local metric learning learn a number of
local unrelated metrics. While this "independence" approach delivers an
increased flexibility its downside is the considerable risk of overfitting. We
present a new parametric local metric learning method in which we learn a
smooth metric matrix function over the data manifold. Using an approximation
error bound of the metric matrix function we learn local metrics as linear
combinations of basis metrics defined on anchor points over different regions
of the instance space. We constrain the metric matrix function by imposing on
the linear combinations manifold regularization which makes the learned metric
matrix function vary smoothly along the geodesics of the data manifold. Our
metric learning method has excellent performance both in terms of predictive
power and scalability. We experimented with several large-scale classification
problems, tens of thousands of instances, and compared it with several state of
the art metric learning methods, both global and local, as well as to SVM with
automatic kernel selection, all of which it outperforms in a significant
manner.

本文介绍一种新的参数化定向 metric 学习方法，通过学习数据流形上的平滑 metric 矩阵函数，将本地度量作为区域不同点的锚定点上定义的基本度量的线性组合来学习，并应用 manifold 正则化来使学习到的 metric 矩阵函数沿着数据流形的测地线平滑变化，表现出极好的预测能力和可扩展性，并优于多种全局和局部的最先进的度量学习方法以及具有自动内核选择的支持向量机 (SVM)。