作　　者： ; ; ;

机构地区： 湖南大学电气与信息工程学院

出　　处： 《计算机研究与发展》 2009年第9期1515-1522,共8页

摘　　要： Isomap算法嵌入向量求解依赖于所有的初始样本,在增加新数据时需要较长时间重新计算所有数据样本间的测地距离.为了提高运算速度,提出一种基于核函数的增量学习Isomap算法,将测地距离矩阵当作一个核矩阵,并通过常数增加的方法保证测地距离矩阵满足Mercer条件,算法只需要计算新增点与原有数据点间的测地距离.与核主成分算法一样,新增点的投影值计算变为核矩阵上的特征分解.在Swiss,Helix和多姿态人脸数据中的实验结果表明,算法大大降低了计算复杂度,有利于快速发现隐藏在高维空间的低维流形分布. The Isomap algorithm operates in batch mode, meaning that all data should to be available when training is done. However, in many scenarios the data come sequentially and the effect of the data is accumulated. When new data is added, it takes a long time to update the geodesic distance matrix including all data points. In order to improve the computing speed, a kernel based incremental learning Isomap algorithm （ILIsomap） is proposed. The geodesic distance matrix can be interpreted as a kernel matrix, and then ILIsomap exploits a constant-shifting method to guarantee that the geodesic distance matrix satisfy the Mercer kernel. ILIsomap only needs to calculate the geodesic distance between new data and the original data, making it possible to project test data points onto low-dimensional manifold embedding using a kernel trick as in kernel PCA. Experimental results on Swiss data sets, Helix data sets, and multi-posture face data set demonstrate that ILIsomap reduces the computational complexity, making it possible to quickly visualize low-dimensional manifolds embedding in high-dimensional space.

关 键 词： 流形学习 算法 测地距离 增量学习 核矩阵

领　　域： [自动化与计算机技术] [自动化与计算机技术]