有监督Mahalanobis远程学习者的核化研究

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摘要翻译：
本文主要研究一个已有监督马氏远程学习者的核化问题。本文包括以下特点。首先，对三种常用的无核学习算法，即“邻域分量分析”、“大边界最近邻”和“判别邻域嵌入”进行了核化，以提高它们的分类性能。其次，提出了一种可供选择的核化框架“KPCA技巧”。与标准框架相比，在新框架中实现学习器具有许多优点，例如，内核实现不需要数学公式和重新编程，避免了奇异性等麻烦问题。第三，在以往的相关论文中，表示定理的真实性只是假设，本文对表示定理进行了形式化证明。在Mahalanobis远程学习环境下，证明了核技巧和KPCA技巧的有效性。第四，与以往的核选择方法不同，我们研究了两种方法，可以有效地为给定的数据集构造合适的核。最后给出了在各种实际数据集上的数值结果。
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英文标题：
《On Kernelization of Supervised Mahalanobis Distance Learners》
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作者：
Ratthachat Chatpatanasiri, Teesid Korsrilabutr, Pasakorn
  Tangchanachaianan and Boonserm Kijsirikul
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最新提交年份：
2009
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Machine Learning        机器学习
分类描述：Papers on all aspects of machine learning research (supervised, unsupervised, reinforcement learning, bandit problems, and so on) including also robustness, explanation, fairness, and methodology. cs.LG is also an appropriate primary category for applications of machine learning methods.
关于机器学习研究的所有方面的论文（有监督的，无监督的，强化学习，强盗问题，等等），包括健壮性，解释性，公平性和方法论。对于机器学习方法的应用，CS.LG也是一个合适的主要类别。
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一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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英文摘要：
  This paper focuses on the problem of kernelizing an existing supervised Mahalanobis distance learner. The following features are included in the paper. Firstly, three popular learners, namely, "neighborhood component analysis", "large margin nearest neighbors" and "discriminant neighborhood embedding", which do not have kernel versions are kernelized in order to improve their classification performances. Secondly, an alternative kernelization framework called "KPCA trick" is presented. Implementing a learner in the new framework gains several advantages over the standard framework, e.g. no mathematical formulas and no reprogramming are required for a kernel implementation, the framework avoids troublesome problems such as singularity, etc. Thirdly, while the truths of representer theorems are just assumptions in previous papers related to ours, here, representer theorems are formally proven. The proofs validate both the kernel trick and the KPCA trick in the context of Mahalanobis distance learning. Fourthly, unlike previous works which always apply brute force methods to select a kernel, we investigate two approaches which can be efficiently adopted to construct an appropriate kernel for a given dataset. Finally, numerical results on various real-world datasets are presented.
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PDF链接：
https://arxiv.org/pdf/0804.1441

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关键词：Mahalanobis mahal 远程学习 Alan LAN previous KPCA 本文 性能 内核