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摘要翻译：
我们引入了一种新的谱降维方法，将这些方法看作是高斯马尔可夫随机场(GRFs)。我们的统一观点是基于最大熵原理，它反过来又受到最大方差展开的启发。我们称之为最大熵展开(MEU)模型是主成分分析的非线性推广。我们将该模型与拉普拉斯本征图和ISOMAP联系起来。我们证明了局部线性嵌入(LLE)中的参数拟合是近似最大似然MEU。我们介绍了一种完全执行极大似然的LLE的变体：无环LLE(ALE)。我们表明MEU和ALLE在机器人导航可视化和人体运动捕捉数据集上与领先的光谱方法具有竞争力。最后，从最大似然的角度出发，提出了一种基于L1正则化的高斯随机场降维方法。
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英文标题：
《A Unifying Probabilistic Perspective for Spectral Dimensionality
Reduction: Insights and New Models》
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作者：
Neil D. Lawrence
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最新提交年份：
2012
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分类信息：
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：
We introduce a new perspective on spectral dimensionality reduction which views these methods as Gaussian Markov random fields (GRFs). Our unifying perspective is based on the maximum entropy principle which is in turn inspired by maximum variance unfolding. The resulting model, which we call maximum entropy unfolding (MEU) is a nonlinear generalization of principal component analysis. We relate the model to Laplacian eigenmaps and isomap. We show that parameter fitting in the locally linear embedding (LLE) is approximate maximum likelihood MEU. We introduce a variant of LLE that performs maximum likelihood exactly: Acyclic LLE (ALLE). We show that MEU and ALLE are competitive with the leading spectral approaches on a robot navigation visualization and a human motion capture data set. Finally the maximum likelihood perspective allows us to introduce a new approach to dimensionality reduction based on L1 regularization of the Gaussian random field via the graphical lasso.
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PDF链接：
https://arxiv.org/pdf/1010.4830
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