基于切丛联络的主曲线构建算法  

Principle Curves Construction Algorithm Based on Connection of Tangent Bundle

作　　者：张炯 李凡长[2] 何书萍[2] 曾劲涛[3] 

机构地区：[1]苏州市劳动和社会保障信息中心,江苏苏州215006 [2]苏州大学计算机科学与技术学院,江苏苏州215006 [3]井冈山大学信息科学与传媒学院,江西吉安343009

出　　处：《微电子学与计算机》2009年第10期151-153,157,共4页Microelectronics & Computer

基　　金：国家自然科学基金项目(60775045)

摘　　要：寻找嵌入在高维空间的低维流形是机器学习、模式识别等领域的一个基本问题.主曲线可以看作一维主流形,是第一主成分的非线性推广,其基本思想是寻找通过数据分布中间的光滑曲线.文中通过构造数据集合的切丛及其联络,提出并分析一种新的主曲线构建思想及方法——基于切丛联络的主曲线构建算法,证明由切丛联络算法构造的主曲线符合自相合特性.一组在多个不同数据集上的实验结果证明了算法的有效性.In many fields such as machine learning and pattern recognition, finding the low-dimensional manifold that embedded in high- dimensional space is vital. Principal curves, judged as one - dimensional principal manifold, are non-linear generalizations of the first linear principal component. The basic idea is to find smooth curves that pass through the middle of a multidimensional data set. By constructing the tangent bundle and the cormection on it, this paper aims at proposing and analysing a new method to construct the principal curves, that is a new method to build principle curves construction algorithm based on connection of tangent bundle. Also the paper will demonstrate that the principle curves is generated by the algorithm satisfy‘self -consistent＇. The results of a series of experiments on many different datasets illustrate their effect.

关 键 词：主曲线 自相合 切丛 联络 流形学习 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]