基于邻近局部切空间相似性的多流形学习研究

项目名称： 基于邻近局部切空间相似性的多流形学习研究

项目编号： No.61202285

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 计算机科学学科

项目作者： 邵超

作者单位： 河南财经政法大学

项目金额： 22万元

中文摘要： 为了学习高维多流形数据集的内在低维几何结构，人们提出了监督和无监督多流形学习算法，能比较有效地实现多流形的分类和聚类，但在成功展现各流形的内在几何结构、鲁棒性、泛化能力、准确划分各流形进而有效判定流形个数等方面的能力还比较有限。本项目根据流形的局部欧氏特性，研究基于邻近局部切空间相似性的监督和无监督多流形学习算法，具体包括多流形下的最短路径算法研究，基于邻近局部切空间相似性的泛化能力研究，基于期望距离的鲁棒性研究和基于邻近局部切空间相似性的谱聚类算法研究。一方面，研究多流形下的最短路径算法，使各流形的内在几何结构得以成功展现，并研究采用对噪音具有一定抑制能力的期望距离，增强算法的鲁棒性；另一方面，根据邻近局部切空间的相似性能更准确地判别新数据点所属的流形，提高算法的泛化能力，并能创建合适的邻域图，进而准确划分各流形并有效判定流形的个数。预期研究结果将为多流形学习的研究和应用注入新的活力。

中文关键词： 多流形学习；局部切空间；通勤时间距离；鲁棒性；泛化能力

英文摘要： To learn the intrinsic low-dimensional geometric structure of high-dimensional multi-manifold datasets effectively, several supervised and unsupervised multi-manifold learning algorithms were presented. These multi-manifold learning algorithms can classify or cluster multiple manifolds relatively effectively, but may not display the intrinsic geometric structure of some manifolds successfully, have relatively poor robustness and generalization, may not partition all the manifolds precisely and then cannot judge the number of manifolds existing in the data effectively. To solve these problems, according to the locally Euclidean nature of the manifold, this project studies the supervised and unsupervised multi-manifold learning algorithms based on the similarities between neighboring local tangent spaces, including the study of shortest path algorithm suitable for the multi-manifold structure, the generalization study of multi-manifold learning algorithms based on the similarities between neighboring local tangent spaces, the robustness study of multi-manifold learning algorithms based on mean distance, and the study of spectral clustering algorithm based on the similarities between neighboring local tangent spaces. On the one hand, the intrinsic geometric structure of each manifold can be displayed in the low-dim

英文关键词： Multi-manifold learning；local tangent space；commute time distance；robustness；generalization ability