论文标题
强大的几何度量学习
Robust Geometric Metric Learning
论文作者
论文摘要
本文提出了用于公制学习问题的新算法。首先，我们注意到文献中的几种经典度量学习公式可以看作是修改后的协方差矩阵估计问题。然后研究利用这种观点，一种通用方法，称为强大的几何度量学习（RGML）。该方法旨在同时估算每个类别的协方差矩阵，同时将其缩小到（未知）的barycenter。我们专注于两个特定的成本功能：一种与高斯的可能性（RGML高斯）相关，另一个与Tyler的M估计器（RGML Tyler）相关。在这两种情况下，barycenter均以riemannian距离定义，该距离享有地球凸和仿射不变的良好特性。使用对称正定矩阵的riemannian几何形状及其单位决定因素的子序列进行优化。最后，在实际数据集上宣称RGML的性能。表现出强大的性能，同时对错误标记的数据进行了强大的表现。
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.
