基于图感知学习的多流形分析方法及实证研究

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 feature extraction framework is studied by intergating characteristics of both multi-manifold learning and supervised learning.In addition, it is constructed a nearest feature space distance classifier model based on multi-manifold local structure affine invariance. At last, face data, palmprint data, tumor gene expressive data and strip steel surface defects images data can all be taken to validate the presented methods. The proposed project will make progresses in multi-manifold learning methods and push forward their wide applications in personal identification, tumor diagnosis and inspection in metallurgical industry.

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。

本项目根据同一类别数据分布在同一流形、不同类别数据分布在不同流形上的科学假设，为了克服传统K近邻方法和L1图方法不能从某一个流形局部选择近邻点的缺陷，提出两层感知图模型，其中任一样本点，存在两层邻域：一层邻域表示同一流形近邻点，另一层邻域表示不同流形近邻点，实现多流形数据的局部结构的充分学习，并且在感知图的基础上，建立一种基于感知图的多流形聚类方法，即局部线性表示的流形边距方法。另外，利用样本数据的类别标签信息，提出多种基于多流形判别学习的特征提取或维数约减方法，包括非参判别多流形学习方法、最大非参边距投影方法、约束判别近邻嵌入方法和局部特征空间距离度量学习方法，构建集成流形学习和监督学习的广义Fisher框架方法。最后，提出基于多流形仿射结构不变的点到特征空间距离分类器模型。同时，将这些多流形学习方法和分类器应用于人脸数据、肿瘤基因表达数据、带钢表面缺陷图像数据、超谱图像数据、视频数据等，以实证方法的效果。本项目的开展，一方面提出了几种多流形学习方法，丰富了流形学习方法，促进了机器学习方法的发展；另一方面也推动了流形学习方法在新领域的应用，拓展了应用领域范围，提高了应用效果。

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