距离保持投影非线性降维技术的可视化与分类

Non-Linear Dimensionality Reduction Techniques of Distance-Preserving Projection for Visualization and Classification

本文对高维数据距离保持投影方法进行了改进和扩展,采用测地线距离代替欧氏距离,能够正确地展开数据所在的流形,同时又准确地保留了每个数据点到其最近邻点和部分近邻点之间的距离.为了减少邻域大小难以选取问题,采取了对邻域大小不甚敏感的P-ISOMAP算法.与原方法和ISOMAP等高维数据降维方法相比,本文方法能更好地对数据进行降维和可视化.并且,为了进行分类,本文扩展了新的分类技术.实验表明本文方法在可视化、降维和分类方面效果不错.

This paper has extended and improved the method of distance-preserving projection which substitutes an estimated geodesic distance for the conventional Euclidean distance. It can nuroll the data of nonlinear surface correctly and preserves exact distances of each data point to its nearest neighbor point and to some other near neighbors. In order to choose a suitable neighborhood size effectively, the P-ISOMAP algorithm which is much less sensitive to the neighborhood size is used. Contrasted with the original method and ISOMAP and other methods, this paper can reduce dimensionality and visualize more effectively. For classification, this paper develops new classification techniques. The experiments prove that the method has taken the excellent effect in visualization, dimensionality reduction and classification.