关键词: 流形学习, 自组织映射, 拓扑缺陷, 局部欧氏性, 邻域结构

Abstract: Self-Organizing Map (SOM) tends to yield the topological defect problem when learning and visualizing the intrinsic low-dimensional manifold structure of high-dimensional data sets. To solve this problem, a manifold learning algorithm, Dynamic Self-Organizing MAP (DSOM), was presented in this paper. In the DSOM, the training data set was expanded gradually according to its neighborhood structure, and thus the map was trained step by step, by which local minima could be avoided and the topological defect problem could be overcome. Meanwhile, the map size was increased dynamically, by which the time cost of the algorithm could be reduced greatly. The experimental results show that DSOM can learn and visualize the intrinsic low-dimensional manifold structure of high-dimensional data sets more faithfully than SOM. In addition, compared with traditional manifold learning algorithms, DSOM can obtain more concise visualization results and be less sensitive to the neighborhood size and the noise, which can also be verified by the experimental results. The innovation of this paper lies in that DSOM expands the map size and the training data set synchronously according to its intrinsic neighborhood structure, by which the intrinsic low-dimensional manifold structure of high-dimensional data sets can be learned and visualized more concisely and faithfully.

Key words: manifold learning, Self-Organizing Map (SOM), topological defect, locally Euclidean nature, neighborhood structure