%0 Journal Article
%T Nonlinear Dimensionality Reduction for Data on Manifold with Rings<br>针对环状流形数据的非线性降维
%A MENG De-Yu
%A GU Nan-Nan
%A XU Zong-Ben
%A LEUNG Yee
%A <br>孟德宇
%A 古楠楠
%A 徐宗本
%A 梁怡
%J 软件学报
%D 2008
%I 
%X Isomap has attracted attentions recently due to its prominent performance on nonlinear dimensionality reduction.However,how to implement effective learning for data on manifold with rings is still a remaining problem.To solve this problem,a systemic strategy is presented in this study.Based on the intrinsic implementation principle of Isomap,a theorem is presented which gives a sufficient and necessary condition to judge whether a manifold is with rings.Besides,an algorithm for detecting ring structures in the manifold is constructed and a nonlinear dimensionality reduction strategy is developed through polar coordinates transformation.A series of simulation results implemented on a series of synthetic and real-world data sets generated by manifolds with or without rings verify the prominent performance of the new method.
%K manifold with rings
%K manifold learning
%K nonlinear dimensionality reduction<br>环状流形
%K 流形学习
%K 非线性降维
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=5B3AB970F71A803DEACDC0559115BFCF0A068CD97DD29835&cid=8240383F08CE46C8B05036380D75B607&jid=7735F413D429542E610B3D6AC0D5EC59&aid=1C1712B0FEFE0555A2DA3FBB24055061&yid=67289AFF6305E306&vid=2A8D03AD8076A2E3&iid=708DD6B15D2464E8&sid=6F6DB7E6345096DE&eid=917ED002A95B58B8&journal_id=1000-9825&journal_name=软件学报&referenced_num=0&reference_num=11