文献类型：期刊文献

中文题名：一种新的基于自组织映射的流形学习算法

英文题名：A New Manifold Learning Algorithm Based on SOM

作者：万春红[1];邵超[1]

第一作者：万春红

机构：[1]河南财经学院计算机与信息工程学院

第一机构：河南财经政法大学计算机与信息工程学院

年份：2009

卷号：33

期号：6

起止页码：101-105

中文期刊名：北京交通大学学报

外文期刊名：Journal of Beijing Jiaotong University

收录：CSTPCD;;Scopus;北大核心:【北大核心2008】；CSCD:【CSCD_E2011_2012】；

基金：国家自然科学基金资助项目(60774041);河南省基础与前沿技术研究项目(082300410110);河南省科技攻关项目(072102210001)

语种：中文

中文关键词：流形学习;自组织映射;拓扑缺陷;鲁棒性;邻域大小

外文关键词：manifold learning; self-organizing map （ SO M ） ; topological defect; robustness; neighborhood size

摘要：针对自组织映射(Self-Organizing Map,SOM)算法在进行流形学习时容易陷入局部极值和产生"拓扑缺陷"问题的原因,提出了一种新的基于SOM的流形学习算法:TO-SOM(TrainingOrderly-SOM).根据流形的局部欧氏性,TO-SOM算法从一个局部线性或近似线性的数据子集出发,按照数据的内在流形结构对其进行有序训练,可以避免局部极值、克服"拓扑缺陷".根据SOM算法的鲁棒性,TO-SOM算法在成功学习数据内在流形结构的同时,对邻域大小参数和噪声也不像ISOMAP和LLE等现有流形学习算法那样敏感,从而更容易得到实际应用.
SOM （Self-Organizing Map） can be applied to manifold learning due to its topology preservation property; however, the iterative optimization used by SOM tends to get stuck in local minima and yield the topological defect problem, especially for data sets lying on low-dimensional nonlinear manifolds embedded in a high-dimensional space. To overcome this problem, a new manifold learning algorithm based on SOM, i.e. TO-SOM （Training Orderly-SOM）, was presented in this paper. Based on the locally Euclidean nature of the manifold, TO-SOM trains the data set orderly according to its intrinsic manifold structure, starting from a small neighborhood in which the data points lie on or close to a locally linear patch, and selects the BMU （Best-Matching Unit） in the same way, by which TO- SOM can guide the map onto the manifold surface and overcome the topological defect problem. Additionally, based on the robustness of SOM, TO-SOM can learn the intrinsic manifold structure of the data set more robustly than the traditional manifold learning algorithms such as ISOMAP and LLE, that is, TO-SOM can be less sensitive to the neighborhood size and the noise, which is verified by experimental results finally.