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.
出处
《北京交通大学学报》
CAS
CSCD
北大核心
2009年第6期101-105,共5页
JOURNAL OF BEIJING JIAOTONG UNIVERSITY
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)
关键词
流形学习
自组织映射
拓扑缺陷
鲁棒性
邻域大小
manifold learning
self-organizing map （ SO M ）
topological defect
robustness
neighborhood size
