一种新的基于自组织映射的流形学习算法

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（Training Orderly-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．

A New Manifold Learning Algorithm Based on SOM

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.