促进一致性的距离度量学习：凸松弛及其理论分析
Orthogonality-Promoting Distance Metric Learning: Convex Relaxation and Theoretical Analysis
摘要：
距离度量学习（DML），从标记的“相似”和“不相似”的数据对学习距离度量，被广泛使用。最近，一些工作研究了正交性促进正则化（OPR），它鼓励DML中的投影向量接近正交，以实现三个效果：（1）高平衡性-在频繁和不频繁类上都实现相当的性能;（2）高紧凑性-使用少量投影向量来实现"好"度量;（3）良好的推广性--减轻对训练数据的过拟合。虽然显示出有希望的结果，但这些方法存在三个问题。首先，它们涉及解决非凸优化问题，其中实现全局最优是NP难的。第二，缺乏对OPR为什么能导致平衡的理论理解。第三，目前对OPR的泛化误差分析不是直接针对正则化器。在本文中，我们解决这三个问题：（1）寻求凸松弛的原始非凸问题，使全局最优是保证可实现的;（2）提供一个正式的分析OPR的能力，促进平衡;（3）提供一个理论分析，直接揭示OPR和泛化性能之间的关系。在各种数据集上的实验表明，与非凸方法相比，我们的凸方法在促进平衡性，紧凑性和泛化方面更有效，并且计算效率更高。
英文摘要：
Distance metric learning (DML), which learns a distance metric from labeled "similar" and "dissimilar" data pairs, is widely utilized. Recently, several works investigate orthogonality-promoting regularization (OPR), which encourages the projection vectors in DML to be close to being orthogonal, to achieve three effects: (1) high balancedness -- achieving comparable performance on both frequent and infrequent classes; (2) high compactness -- using a small number of projection vectors to achieve a "good" metric; (3) good generalizability -- alleviating overfitting to training data. While showing promising results, these approaches suffer three problems. First, they involve solving non-convex optimization problems where achieving the global optimal is NP-hard. Second, it lacks a theoretical understanding why OPR can lead to balancedness. Third, the current generalization error analysis of OPR is not directly on the regularizer. In this paper, we address these three issues by (1) seeking convex relaxations of the original nonconvex problems so that the global optimal is guaranteed to be achievable; (2) providing a formal analysis on OPR's capability of promoting balancedness; (3) providing a theoretical analysis that directly reveals the relationship between OPR and generalization performance. Experiments on various datasets demonstrate that our convex methods are more effective in promoting balancedness, compactness, and generalization, and are computationally more efficient, compared with the nonconvex methods.
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。
