基于图感知学习的多流形分析方法及实证研究

项目名称： 基于图感知学习的多流形分析方法及实证研究

项目编号： No.61273303

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 李波

作者单位： 武汉科技大学

项目金额： 80万元

中文摘要： 近年来多流形学习方法受到越来越多的关注，其关键和难点在于如何通过图构建充分地学习多流形局部结构。K近邻图和L1图都不能有效地解决该问题。本项目以此为切入点，构建两层邻域感知图。首先通过K近邻确定局部邻域，再设计局部邻域切空间线性表示误差L1范数最小和线性表示系数L1范数最小的L1/L1模型，从局部邻域中自适应地选取与样本点分布于同一流形的近邻点，组成流形局部邻域，有效学习多流形局部结构。然后根据感知图两层邻域，定义流形间子图和流形内子图，进行多谱聚类。利用类别信息，定义流形局部邻域距离，提出多流形判别学习方法。在此基础上，集成多流形学习和监督学习，研究感知图特征提取框架。建立基于多流形局部结构仿射不变的最小特征空间距离分类器。最后采用人脸、掌纹、肿瘤基因表达和带钢表面缺陷图像等数据进行实证研究。本项目的展开将推动多流形学习方法的发展，促进在身份识别、肿瘤诊断和冶金工业检测等领域的广泛应用。

中文关键词： 感知图；聚类；多流形学习；监督学习；特征空间距离

英文摘要： Recently, multi-manifold learning methods are being paid increasing attention to，whose key problem lies in how to fully explore multi-manifold local structure by graph construction. Currently, both KNN graph and L1 graph fail to solve the problem efficiently. Aiming to overcome this problem, a sensing graph with two kinds of neighborhood, i.e.local neighborhood and manifold local neighborhood, is constructed in the proposed project.The local neighborhood is determined by KNN criterion firstly, then a L1/L1 model is presented to simultaneously minimize both L1 norm of local neighborhood tangent space linear representation errors and L1 norm of linear representation weights, by which the neighbor points on the same manifold can be adaptively selected from the local neighborhood and consist of manifold local neighborhood, thus the multi-manifold local structure can be well approached. Later, according to two kinds of neighborhood in the sensing graph, an intra-manifold subgraph and an inter-manifold subgraph are defined to conduct multi-spectrum clustering. Moreover, distances between manifold local nighborhood can be advanced by taking sample labels into account and a multi-manifold discrminant learning method with the proposed distances is put forword. On the basis of above mentioned algorithms, a sesing graph fe

英文关键词： Sensing graph；Clustering；Multi-manifold learning；Supervised learning；Feature space distance