矢量量化地标点的显式监督等距映射算法

Vector Quantization Landmark Points for Supervised Isometric Mapping with Explicit Mapping

针对等距映射(ISOMAP)无监督、不能生成显式映射函数等局限性,提出矢量量化地标点的显式监督等距映射算法.该算法首先在构建的邻域图和测地线距离矩阵中引入类别信息;然后针对在迭代优化处理距离矩阵时引入地标点的问题,运用矢量量化方法代替传统随机选取方法,使选取的地标点更能反映整个流形结构;最后把径向基函数作为函数基,得到降维方法的显式映射表示.在手写数字数据集和UCI数据集上的实验表明,文中算法降维效果快速稳定,识别率较高.

Since isometric mapping （ ISOMAP ） has no supervision and explicit mapping function and other limitations, an improved algorithm, selection of vector quantization landmark points for supervised isometric mapping with explicit mapping （ SE-VQ-ISOMAP ） , is put forward. Firstly, the category information is introduced in the construction of neighborhood graph and geodesic distance matrix. Aiming at the problem that the landmark points are introduced into iterative optimization when distance matrix is processed, a method of vector quantization is employed instead of the traditional random selection. Thus, the whole manifold structure is indicated better by the selected samples. Finally, the radial function is regarded as basis, and consequently explicit mapping of dimensionality reduction method is obtained. On the handwritten digits sets and UCI datasets, the experimental results show that the proposed algorithm is fast and stable with a higher recognition rate.