关键词: 流形学习, 等距特征映射, 最速梯度下降, 小世界模型, 标志点

Abstract: Isometric Feature Mapping (ISOMAP) not only has high complexity but also can not learn new samples. L-ISOMAP has lower complexity by only preserving the geodesic distances between some landmark points. However, landmark point set randomly selected often leads to worse embedding results. A manifold learning algorithm based on the small world model was proposed, which only preserve the geodesic distances between each point and its k nearest neighbors as well as some distant points randomly chosen according to the small world model. The deepest gradient descent method was used to optimize the iterative process to obtain the low dimensional representation of data. The theoretic analysis demonstrates that the complexity of the proposed algorithm is far below one of ISOMAP. The stress function and the residual variance were used to compare the three methods. The experiments show that the results from the new method are close to those from ISOMAP and are superior to those from L-ISOMAP. Moreover, the algorithm can treat new data and is also not sensitive to noise.

Key words: manifold learning, Isometric Feature Mapping (ISOMAP), deepest gradient descent, small world model, landmark point