Distance Metric Learning with Eigenvalue Optimization
Distance Metric Learning with Eigenvalue Optimization
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DOI：
10.5555/2503308.2188386
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Yiming Ying;Peng Li
中科院分区：
文献类型：
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作者：
Yiming Ying;Peng Li
本文的主题是开发一个新型的特征值优化框架来学习摩alano虫指标。在这种情况下，我们介绍了一种称为DML-EIG的新型度量学习方法，该方法被证明等同于众所周知的特征值优化问题，称为对称矩阵的最大特征值（Overton，1988; Lewis and Overton，1996）。此外，我们制定了LMNN（Weinberger等，2005），这是最先进的度量学习方法之一，作为类似的特征值优化问题。这个新颖的框架不仅为公制学习提供了新的见解，而且为有效的度量学习算法设计开辟了新的途径。实际上，针对DML-EIG和LMNN开发了一阶算法，该算法仅需要计算按迭代矩阵的最大特征向量。它们的收敛特征是严格确定的。基准数据集的各种实验表明我们的新方法的竞争性能。此外，我们报告了一个令人鼓舞的结果，这是一个艰难而充满挑战的面部验证数据集，称为野外标记的面孔（LFW）。
The main theme of this paper is to develop a novel eigenvalue optimization framework for learning a Mahalanobis metric. Within this context, we introduce a novel metric learning approach called DML-eig which is shown to be equivalent to a well-known eigenvalue optimization problem called minimizing the maximal eigenvalue of a symmetric matrix (Overton, 1988; Lewis and Overton, 1996). Moreover, we formulate LMNN (Weinberger et al., 2005), one of the state-of-the-art metric learning methods, as a similar eigenvalue optimization problem. This novel framework not only provides new insights into metric learning but also opens new avenues to the design of efficient metric learning algorithms. Indeed, first-order algorithms are developed for DML-eig and LMNN which only need the computation of the largest eigenvector of a matrix per iteration. Their convergence characteristics are rigorously established. Various experiments on benchmark data sets show the competitive performance of our new approaches. In addition, we report an encouraging result on a difficult and challenging face verification data set called Labeled Faces in the Wild (LFW).