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Local principal curves

机译：局部主曲线

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摘要

Principal components are a well established tool in dimension reduction. The extension to principal curves allows for general smooth curves which pass through the middle of a multidimensional data cloud. In this paper local principal curves are introduced, which are based on the localization of principal component analysis. The proposed algorithm is able to identify closed curves as well as multiple curves which may or may not be connected. For the evaluation of the performance of principal curves as tool for data reduction a measure of coverage is suggested. By use of simulated and real data sets the approach is compared to various alternative concepts of principal curves.
机译：主要组件是减少尺寸方面的完善工具。主曲线的扩展允许一般的平滑曲线通过多维数据云的中间。本文介绍了基于主成分分析的局部主曲线。所提出的算法能够识别闭合曲线以及可能连接或不连接的多条曲线。为了评估主曲线作为减少数据量的工具的性能，建议使用覆盖率的度量。通过使用模拟和真实数据集，将该方法与主曲线的各种替代概念进行了比较。

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