中文摘要：

主曲线是主成分的非线性推广，其基本思想是要寻找通过数据分布的中间，并满足自相合特性的光滑曲线．本文在极限意义下提出了一种基于局部切空间的主曲线构建算法，并证明了构建的主曲线不仅满足自相合特性，而且对于任意的开覆盖，主曲线唯一存在．多种数据集上的模拟实验结果证明了算法的有效性．

英文摘要：

Principal curves are defined as self-consistent smooth one-dimensional curves which pass through the middle of a multidimensional data set. They are nonlinear generalization of the first Principal Components. In this paper, a new practical algorithm for constructing principal curves based on local tangent space is proposed in the sense of limit. It is also proved that these principal curves not only satisfy the self-consistenoy property, but also are the unique existence for any given open cover. The new principal curve construction algorithm is illustrated with some simulated data sets.