A Review of Dimension Reduction Techniques
A Review of Dimension Reduction Techniques
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发表时间：
2009
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通讯作者：
M. A. Carreira-Perpiñán
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作者：
M. A. Carreira-Perpiñán
降维问题是在处理高维空间中的矢量数据时克服维度诅咒的一种方式，也是这种数据的建模工具。它被定义为寻找嵌入高维数据的低维流形。提出了一种降维问题的分类。综述了几种降维技术，包括主成分分析、投影寻踪和投影寻踪回归、主曲线和基于拓扑连续图的降维方法，如Kohonen图或广义地形图。还回顾了其中几种技术的神经网络实现，如投影寻踪学习网络和具有目标函数的BCM神经元。几个附录补充了正文的数学处理。
The problem of dimension reduction is introduced as a way to overcome the curse of the dimensionality when dealing with vector data in high-dimensional spaces and as a modelling tool for such data. It is defined as the search for a low-dimensional manifold that embeds the high-dimensional data. A classification of dimension reduction problems is proposed. A survey of several techniques for dimension reduction is given, including principal component analysis, projection pursuit and projection pursuit regression, principal curves and methods based on topologically continuous maps, such as Kohonen’s maps or the generalised topographic mapping. Neural network implementations for several of these techniques are also reviewed, such as the projection pursuit learning network and the BCM neuron with an objective function. Several appendices complement the mathematical treatment of the main text.