CAJ | 학술논문

已有的流形学习方法仅能建立点对点的降维嵌入,而未建立高维数据流形空间与低维表示空间之间的相互映射.此缺陷已限制了流形学习方法在诸多数据挖掘问题中的进一步应用.针对这一问题,文中提出了两种新型高效的流形结构重建算法:快速算法与稳健算法.其均以经典的Isomap方法内在运行机理为出发点,进而推导出高维流形空间与低维表示空间之间双向的显式映射函数关系,基于此函数即可实现流形映射的有效重建.理论分析与实验结果证明,所提算法在计算速度、噪音敏感性、映射表现等方面相对已有方法具有明显优势.
이유적류형학습방법부능건립점대점적강유감입,이미건립고유수거류형공간여저유표시공간지간적상호영사.차결함이한제료류형학습방법재제다수거알굴문제중적진일보응용.침대저일문제,문중제출료량충신형고효적류형결구중건산법:쾌속산법여은건산법.기균이경전적Isomap방법내재운행궤리위출발점,진이추도출고유류형공간여저유표시공간지간쌍향적현식영사함수관계,기우차함수즉가실현류형영사적유효중건.이론분석여실험결과증명,소제산법재계산속도、조음민감성、영사표현등방면상대이유방법구유명현우세.
Most of the existing nonlinear dimensionality reduction methods only realize data embedding from high-dimensional to low-dimensional data spaces hut not data mapping between them,which restrict their applications to approximation and prediction tasks.This paper proposes two new data mapping methods,fast method and robust method respectively,which realizes data mapping from data embedding based on the intrinsic executive mechanism of Isomap,one of the most well known nonlinear dimensionality reduction method.It also presents theoretical estimations for the approximation precision and computational complexity of the new methods.Some experiment results on synthetic and real-world data sets are demonstrated,which verifies the feasibility and effectiveness of the new data mapping methods.Particularly,the simulations,which apply the new methods on feature movie description problem and pattern classification problem,are designed.The results further shows the potential usefulness of the new methods.