自适应邻域值选取的LLE算法研究  

Research of LLE Algorithm of Adaptive Neighborhood Selection

作　　者：高洁[1,2,3] 吴立锋[1,2,3] 关永[1,2,3] 王洪民[1,2,3] 

机构地区：[1]首都师范大学信息工程学院,北京100048 [2]首都师范大学高可靠嵌入式系统技术北京市工程技术研究中心,北京100048 [3]首都师范大学电子系统可靠性技术北京市重点实验室,北京100048

出　　处：《小型微型计算机系统》2017年第2期393-397,共5页Journal of Chinese Computer Systems

基　　金：国家自然科学基金项目(61202027)资助;北京市属高等学校创新团队建设与教师职业发展计划项目(IDHT20150507)资助;北京市留学人员科技项目择优资助

摘　　要：局部线性嵌入(LLE)是一种重要的流形学习算法,已广泛应用于图像处理和多维数据的可视化等领域,但其算法性能一直受邻域选择盲目性的制约.传统的邻域选择算法没有同时考虑高低维数据的分布情况,且没有对无效邻域点做出相应的处理,使自适应结果受初始值影响较大.为此,提出新的自适应流形学习思想,用邻域点到切平面坐标映射函数的一阶泰勒逼近,初步确定出局部邻域值;然后利用关于高低维分布差异性函数的邻域调整策略和权值邻域思想,对初始邻域值进一步调整.该方法提高了LLE邻域选取算法的稳定性,同时减小无效邻域点被选中的可能.仿真表明,基于本文方法确定的自适应结果在不同的初始邻域值下基本一致,在人工数据集Swiss-roll上获得理想稳定的降维效果.Locally linear embedding （ LLE ） is an important manifold learning algorithm, which is widely applied in the image processing, visualization of the multidimensional dataand so on. Butthe blindness of the choiceof neighborhood size always restricts the algorithm performance. The traditional neighborhood selection algorithmsdo not consider the distribution of high and low dimensional data at the same time, and there is no handling of invalid neighborhood points accordingly, which makes adaptive results are greatly influ- enced by the initial value. This paper proposes the new adaptive manifold learning, First it uses the first order Taylor of mapping function from neighborhood points to the tangent plane coordinate to determine the size of neighborhood preliminary, then uses diversity function of distribution of high and low dimensional data and the weights of neighborhood, further adjuststhe value of k. The method improves the stability ofthe neighborhood selection algorithm about LLE, at the same time, reduces the possibility that invalid neigh- borhood point is selected. Simulations show that adaptive results are basically identical under different initial of neighborhood size, and obtain the ideal and stable effect of dimension reduction on the Swiss-roll of artificial data set.

关 键 词：流形学习 权值邻域 降维 局部切平面 

分 类 号：TP311[自动化与计算机技术—计算机软件与理论]