Analysis of Choosing the Initial Value of Principal Curve Algorithm
主曲线算法初始值选取的分析

Principal Curves are very useful approaches of feature extraction and data compression,they are nonlinear generalizations of the first linear principal component which can be thought of as 'optimal' linear 1-d summarization of the data.Up to now several algorithms for constructing principal curves have been proposed.They are all initialized by the first principal component for the close relation between principal curves and the principal components.Taking example for the HS and the polygonal line algorithms,this paper analyzes how the initial line affects the principal curves.We conclude the first principal component line is not always the best choice of the initialization step.The experiments show the HS algorithm will produce perfect results if it starts with the origin,and the polygonal line algorithm should choose proper initial value according to different global structure of the data.It proves that local optimization can not always lead to global optimization.