关键词: 等距映射, 数据可视化, 拓扑稳定, 数据流形

Abstract: The Isomap (isometric mapping) and its variant algorithm are much influenced by static parameters and the nearest neighbor judgment logic. As a result, there are problems such as computational waste, numerical sensitivity or unstable data topology. In the practical application of interactive data visualization, it is very difficult to fulfill the requirement of real-time interaction and accurate visualization. Therefore, this paper makes an improvement on the original computing framework of isometric mapping, and proposes a global adaptive algorithm called GA-Isomap (global adaptive-Isomap). In the aspect of neighborhood construction, this paper proposes an incremental construction method and region selection method, by means of the new designed method of local density calculation and the       region division. In the aspect of low-dimensional embedding, this paper proposes a mapping calculation method based on two-layer graph, which takes the framework graph of landmarks and the relative position relationship into consideration. Compared with original Isomap, L-Isomap, Isomap with dynamic neighbor and Isomap with NC, simulation results show that the GA-Isomap algorithm can effectively balance the data topology stability and operational efficiency in visualization.

Key words: isometric mapping, data visualization, topological stability, data manifold