Dimension Reduction: A Guided Tour
Dimension Reduction: A Guided Tour
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DOI：
10.1561/2200000002
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发表时间：
2010-01-01
影响因子：
32.8
通讯作者：
Burges, Christopher J. C.
中科院分区：
文献类型：
--
作者：
Burges, Christopher J. C.
我们给出了几个基本的降维方法的教程概述。我们将方法分为投影方法和方法，模型上的数据所在的流形。对于投影方法，我们回顾投影寻踪，主成分分析（PCA），核PCA，概率PCA，典型相关分析（CCA），核CCA，Fisher判别分析，导向PCA，和几种技术，充分降低维数。对于流形方法，我们回顾了多维标度（MDS），地标MDS，Isomap，局部线性嵌入，拉普拉斯特征映射和谱聚类。虽然这本专著侧重于基础，但我们也提供了一些更现代的技术。我们还描述了关联维数作为一种方法来估计的内在尺寸，我们指出，尺寸的概念可以是一个规模依赖的量。Nystrom方法，其中链接几个流形算法，也进行了审查。我们使用一个公开的数据集来说明一些方法。其目的是提供一个独立的概述的关键概念的基础上，许多这些算法，并给予进一步的阅读的指针。
We give a tutorial overview of several foundational methods for dimension reduction. We divide the methods into projective methods and methods that model the manifold on which the data lies. For projective methods, we review projection pursuit, principal component analysis (PCA), kernel PCA, probabilistic PCA, canonical correlation analysis (CCA), kernel CCA, Fisher discriminant analysis, oriented PCA, and several techniques for sufficient dimension reduction. For the manifold methods, we review multidimensional scaling (MDS), landmark MDS, Isomap, locally linear embedding, Laplacian eigenmaps, and spectral clustering. Although this monograph focuses on foundations, we also provide pointers to some more modern techniques. We also describe the correlation dimension as one method for estimating the intrinsic dimension, and we point out that the notion of dimension can be a scale-dependent quantity. The Nystrom method, which links several of the manifold algorithms, is also reviewed. We use a publicly available data set to illustrate some of the methods. The goal is to provide a self-contained overview of key concepts underlying many of these algorithms, and to give pointers for further reading.