鲁棒几何度量学习
Robust Geometric Metric Learning
摘要：
本文提出了度量学习问题的新算法。我们首先注意到，从文献中的几个经典的度量学习公式可以被视为修改后的协方差阵估计问题。利用这一观点，一般的方法，称为鲁棒几何度量学习（RGML），然后研究。该方法的目的是同时估计的协方差阵的每一类，而收缩他们的（未知的）重心。我们专注于两个特定的成本函数：一个与高斯似然（RGML高斯），一个与泰勒的M -估计（RGML泰勒）。在这两种方法中，重心都是用黎曼距离定义的，黎曼距离具有良好的测地凸性和仿射不变性。利用对称正定矩阵及其单位行列式子流形的黎曼几何进行优化。最后，RGML的性能断言在真实的数据集。表现出强大的性能，同时对错误标记的数据具有鲁棒性。
英文摘要：
This paper proposes new algorithms for the metric learning problem. We start by noticing that several classical metric learning formulations from the literature can be viewed as modified covariance matrix estimation problems. Leveraging this point of view, a general approach, called Robust Geometric Metric Learning (RGML), is then studied. This method aims at simultaneously estimating the covariance matrix of each class while shrinking them towards their (unknown) barycenter. We focus on two specific costs functions: one associated with the Gaussian likelihood (RGML Gaussian), and one with Tyler's M -estimator (RGML Tyler). In both, the barycenter is defined with the Riemannian distance, which enjoys nice properties of geodesic convexity and affine invariance. The optimization is performed using the Riemannian geometry of symmetric positive definite matrices and its submanifold of unit determinant. Finally, the performance of RGML is asserted on real datasets. Strong performance is exhibited while being robust to mislabeled data.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
