黎曼流形上的保局投影在图像集匹配中的应用

目的提出了黎曼流形上局部结构特征保持的图像集匹配方法。方法该方法使用协方差矩阵建模图像集合,利用对称正定的非奇异协方差矩阵构成黎曼流形上的子空间,将图像集的匹配转化为流形上的点的匹配问题。通过基于协方差矩阵度量学习的核函数将黎曼流形上的协方差矩阵映射到欧几里德空间。不同于其他方法黎曼流形上的鉴别分析方法,考虑到样本分布的局部几何结构,引入了黎曼流形上局部保持的图像集鉴别分析方法,保持样本分布的局部邻域结构的同时提升样本的可分性。结果在基于图像集合的对象识别任务上测试了本文算法,在ETH80和YouTube Celebrities数据库分别进行了对象识别和人脸识别实验,分别达到91.5%和65.31%的识别率。结论实验结果表明,该方法取得了优于其他图像集匹配算法的效果。     

基于等角映射的多样本增量流形学习算法

目前一些经典的降维流形学习方法以距离来度量数据间的相似度,难以处理噪音造成的子空间偏离.针对此问题,文中提出一种基于等角映射的多样本增量流形学习算法,将以样本均值为中心的高维样本数据的协方差矩阵变为以邻域均值为中心的协方差矩阵,消除基于距离度量对子空间带来的误差,并对协方差矩阵进行加权,减少不规则新增样本或噪音对降维造成的影响.实验证明该算法与其他算法相比,具有更好的抗噪能力及降维效果,可更好地应用于图像识别问题.     

核邻域保持判别嵌入在人脸识别中的应用

为更有效地进行数据降维,将核映射思想引入到邻域保持判别嵌入中,提出一种核邻域保持判别嵌入的流形学习算法。以类内相似度矩阵与类间散度矩阵之差作为鉴别准则,使类间散度矩阵不受满秩的约束,从而解决人脸数据的非线性和小样本问题。在ORL和Yale人脸库上的实验结果表明,该算法具有较好的人脸识别性能。     

有效的协方差判别学习算法

在基于视频的图像集分类中,类内样本多样性问题是影响算法分类性能的一个主要原因.为了尝试解决该问题,提出了一种图像集分类算法,其目标体现在2个方面:(1)使得算法在时间效率上相较于协方差判别学习(CDL)等具有代表性的图像集分类算法有进一步的提升;(2)使得算法在分类精度上也仍然具有可比性.首先利用双向二维主成分分析对原始的协方差特征进行降维,使其变得更加紧凑.同时,为了抽取到更具判别性的特征信息,对每一个低维紧凑的协方差矩阵应用QR分解,使其变换成一个正交基矩阵和一个非奇异的上三角矩阵.考虑数据分布空间的黎曼流形特性,通过定义函数的方式使得上三角矩阵仍然分布在由对称正定(SPD)矩阵张成的SPD流形之上.此时,原始的样本空间就转化成了一个由正交基矩阵张成的Grassmann流形和一个特征分布更加紧凑的新的SPD流形.为了更好地整合这2种黎曼流形特征,首先利用Stein散度以及对数欧氏距离导出一个黎曼流形测地线距离度量;然后,利用该度量设计一个正定的核函数将上述特征映射到一个高维Hilbert核空间;最后,利用核判别分析算法进行判别子空间特征学习.文中算法在5个基准视频集YTC, Honda, ETH-80, MDSD以及AFEW上均取得了较好的分类结果,同时在计算效率上也优于CDL等对比算法,从而表明了其可行性和有效性.     

基于等维度独立多流形的DC-ISOMAP算法

流形学习已经成为机器学习与数据挖掘领域中一个重要的研究课题.目前的流形学习算法都假设所研究的高维数据存在于同一个流形上,并不能支持或者应用于大量存在的采样于多流形上的高维数据.针对等维度的独立多流形DC-ISOMAP算法,首先通过从采样密集点开始扩展切空间的方法将多流形准确分解为单个流形,并逐个计算其低维嵌入,然后基于各子流形间的内部位置关系将其低维嵌入组合起来,得到最终的嵌入结果.实验结果表明,该算法在人造数据和实际的人脸图像数据上都能有效地计算出高维数据的低维嵌入结果.     

基于推广流形学习的高分辨遥感影像目标分类

针对传统的流形学习算法不能对位于黎曼流形上的协方差描述子进行有效降维这一问题,本文提出一种推广的流形学习算法,即基于Log-Euclidean黎曼核的自适应半监督正交局部保持投影（Log-Euclidean Riemannian kernel-based adaptive semi-supervised orthogonal locality preserving projection,LRK-ASOLPP）,并将其成功用于高分辨率遥感影像目标分类问题.首先,提取图像每个像素点处的几何结构特征,计算图像特征的协方差描述子;其次,通过采用Log-Euclidean黎曼核将协方差描述子投影到再生核Hilbert空间;然后,基于流形学习理论,建立黎曼流形上半监督正交局部保持投影算法模型,利用交替迭代更新算法对目标函数进行优化求解,同时获得相似性权矩阵和低维投影矩阵;最后,利用求得的低维投影矩阵计算测试样本的低维投影,并用K—近邻、支持向量机（Support victor machine,SVM）等分类器对其进行分类.三个高分辨率遥感影像数据集上的实验结果说明了该算法的有效性与可行性.     

一种基于局部线性嵌入的多流形学习算法

针对局部线性嵌入算法在处理多流形数据时失效问题,提出一种新的基于局部线性嵌入的多流形学习算法.采用cam分布寻找数据点的近邻,避免了近邻选取方向的缺失;同时在获取重建权值矩阵的过程中引入一个正则项约束,从而降低了算法对噪声的敏感度.通过对分布在不同流形上的高维数据实验后发现改进算法具有很好的降维效果.为了进一步验证算法的有效性,将改进后的算法对COIL-20数据库进行图像检索,结果表明该算法不仅有较好的降维效果而且在多类别多形状流形学习中有很好的实用价值.     

基于增量式最大方差展开的水下控制系统故障诊断

对于复杂工业系统的故障诊断,由于非线性的存在,使得利用核函数的多元统计方法存在因核函数选择不同导致诊断结果不同的问题.本文采用最大方差展开的方法,作为一种流形学习方法,该方法在处理非线性数据时通过学习确定核矩阵,因而无需人为选择核函数.针对该方法难以对新增数据进行处理,本文提出了最大方差展开的增量式改进方法,利用正常样本进行学习建模,对检测样本通过增量的方式降维构造出低维空间,在该空间中构造监控统计量来完成故障的检测.最后,本文将该方法应用在水下控制系统的故障诊断中,通过仿真分析验证了该方法应用的有效性.     

流形学习方法中的若干问题分析

流形学习是近年来机器学习与认知科学中的一个新的研究热点,其本质在于根据有限的离散样本学习和发现嵌入在高维空间中的低维光滑流形,从而揭示隐藏在高维数据中的内在低维结构,以实现非线性降维或者可视化.介绍了几种主要的流形学习算法,分析了它们的优势与不足,总结了流形学习方法中需要解决的若干问题及其研究现状,并展望了流形学习未来的研究前景.     

黎曼流形上半调图像的协方差建模与贝叶斯分类方法

针对半调图像分类问题,提出黎曼流形上的协方差建模方法和贝叶斯分类策略.根据半调图像傅立叶频谱的特点,提出一种基于模板矩阵的特征获取方法,并结合频谱信息形成协方差矩阵描述方法.通过引入有效图像判决规则和分块技术,提出一种协方差矩阵提取算法.利用样本的局部特性和核密度估计方法,实现黎曼流形上的贝叶斯分类策略.实验中研究阈值参数的选择策略,与5个相似方法进行分类性能比较,探讨有关参数对性能的影响.实验结果表明,所提出的方法在Q=32或64和L=10~15时其分类错误率低于4%,建模时间开销低于100ms,且优于5个相似方法.     

基于特征点提取的三维点云模型水印算法

为了有效提高三维水印的透明性、抗噪能力和水印提取准确度,针对三维网格中不固定点云数据,提出一种基于局部特征点提取的三维点云模型水印算法。根据协方差分析提取出三维模型初始特征点,以初始特征点为核心,在它K近邻邻域中,构建不跨越区域最小三角形为嵌入单元的底面,将剩余顶点按照升序排列,寻找合适的嵌入顶点,构建局部嵌入单元,通过改变嵌入顶点信息来嵌入水印。其中通过顶点在平面投影产生的夹角确定水印索引值,实现盲水印。算法通过保留特征点信息,改变非特征点嵌入水印信息能有效提高透明性和抗噪能力,通过限制嵌入单元区域提高水印提取准确率,同时实现了盲水印检测。     

Manifold-Based Learning and Synthesis

This paper proposes a new approach to analyze high-dimensional data set using low-dimensional manifold. This manifold-based approach provides a unified formulation for both learning from and synthesis back to the input space. The manifold learning method desires to solve two problems in many existing algorithms. The first problem is the local manifold distortion caused by the cost averaging of the global cost optimization during the manifold learning. The second problem results from the unit variance constraint generally used in those spectral embedding methods where global metric information is lost. For the out-of-sample data points, the proposed approach gives simple solutions to transverse between the input space and the feature space. In addition, this method can be used to estimate the underlying dimension and is robust to the number of neighbors. Experiments on both low-dimensional data and real image data are performed to illustrate the theory.     

Spectral embedding of graphs

In this paper we explore how to embed symbolic relational graphs with unweighted edges in a pattern-space. We adopt a graph-spectral approach. We use the leading eigenvectors of the graph adjacency matrix to define eigenmodes of the adjacency matrix. For each eigenmode, we compute vectors of spectral properties. These include the eigenmode perimeter, eigenmode volume, Cheeger number, inter-mode adjacency matrices and intermode edge-distance. We embed these vectors in a pattern-space using two contrasting approaches. The first of these involves performing principal or independent components analysis on the covariance matrix for the spectral pattern vectors. The second approach involves performing multidimensional scaling on the L2 norm for pairs of pattern vectors. We illustrate the utility of the embedding methods on neighbourhood graphs representing the arrangement of corner features in 2D images of 3D polyhedral objects. Two problems are investigated. The first of these is the clustering of graphs representing distinct objects viewed from different directions. The second is the identification of characteristic views of single objects. These two studies reveal that both embedding methods result in well-structured view spaces for graph-data extracted from 2D views of 3D objects.     

A generative model for graph matching and embedding

This paper shows how to construct a generative model for graph structure through the embedding of the nodes of the graph in a vector space. We commence from a sample of graphs where the correspondences between nodes are unknown ab initio. We also work with graphs where there may be structural differences present, i.e. variations in the number of nodes in each graph and their edge structure. We characterise the graphs using the heat-kernel, and this is obtained by exponentiating the Laplacian eigensystem with time. The idea underpinning the method is to embed the nodes of the graphs into a vector space by performing a Young-Householder decomposition of the heat-kernel into an inner product of node co-ordinate matrices. The co-ordinates of the nodes are determined by the eigenvalues and eigenvectors of the Laplacian matrix, together with a time-parameter which can be used to scale the embedding. Node correspondences are located by applying Scott and Longuet-Higgins algorithm to the embedded nodes. We capture variations in graph structure using the covariance matrix for corresponding embedded point positions. We construct a point-distribution model for the embedded node positions using the eigenvalues and eigenvectors of the covariance matrix. We show how to use this model to both project individual graphs into the eigenspace of the point position covariance matrix and how to fit the model to potentially noisy graphs to reconstruct the Laplacian matrix. We illustrate the utility of the resulting method for shape analysis using data from the Caltech–Oxford and COIL databases.     

Spectral estimation by least-squares optimization based on rational covariance extension

This paper proposes a new spectral estimation technique based on rational covariance extension with degree constraint. The technique finds a rational spectral density function that approximates given spectral density data under constraint on a covariance sequence. Spectral density approximation problems are formulated as nonconvex optimization problems with respect to a Schur polynomial. To formulate the approximation problems, the least-squares sum is considered as a distance. Properties of optimization problems and numerical algorithms to solve them are explained. Numerical examples illustrate how the methods discussed in this paper are useful in stochastic model reduction and stochastic process modeling.     

Nonlinear Dimensionality Reduction by Topologically Constrained Isometric Embedding

Many manifold learning procedures try to embed a given feature data into a flat space of low dimensionality while preserving as much as possible the metric in the natural feature space. The embedding process usually relies on distances between neighboring features, mainly since distances between features that are far apart from each other often provide an unreliable estimation of the true distance on the feature manifold due to its non-convexity. Distortions resulting from using long geodesics indiscriminately lead to a known limitation of the Isomap algorithm when used to map non-convex manifolds. Presented is a framework for nonlinear dimensionality reduction that uses both local and global distances in order to learn the intrinsic geometry of flat manifolds with boundaries. The resulting algorithm filters out potentially problematic distances between distant feature points based on the properties of the geodesics connecting those points and their relative distance to the boundary of the feature manifold, thus avoiding an inherent limitation of the Isomap algorithm. Since the proposed algorithm matches non-local structures, it is robust to strong noise. We show experimental results demonstrating the advantages of the proposed approach over conventional dimensionality reduction techniques, both global and local in nature.     

Distinguishing variance embedding

Nonlinear dimensionality reduction is a challenging problem encountered in a variety of high dimensional data analysis. Based on the different geometric intuitions of manifolds, maximum variance unfolding (MVU) and Laplacian eigenmaps are designed for detecting the different aspects of data set. In this paper, combining the ideas of MVU and Laplacian eigenmaps, we propose a new nonlinear dimensionality reduction method called distinguishing variance embedding (DVE), which unfolds the data manifold by maximizing the global variance subject to the proximity relation preservation constraint originated in Laplacian eigenmaps. We illustrate the algorithm on easily visualized examples of curves and surfaces, as well as on actual images of faces, handwritten digits, and rotating objects.     

基于方差约束控制的专家系统故障预测技术研究

基于方差约束控制理论和专家系统的相关知识,研究了动态组合系统内部故障的预测问题。首先根据组合系统的运行情况在线提取故障点在各个子系统的状态观测值,定义了故障点的状态观测均值、误差以及误差和参数结构并进行了分析;然后在给出故障判定定理的基础上,利用专家系统加权算法得到的故障点状态误差和约束容许值,设计了故障预测的流程图;最后根据流程图给出一种新的故障预测算法。理论分析结果表明,这种算法与传统的故障诊断方法和已有的故障预测方法相比有比较明显的优势。     

基于协方差矩阵降维稀疏表示的二维波达方向估计

针对稀疏重构下二维波达方向（2D-DOA）估计存在计算量大的问题,提出一种基于协方差矩阵降维稀疏表示的二维波达方向估计方法。首先引入空间角构造流形矢量矩阵冗余字典,将方位角和俯仰角组合从二维空间映射到一维空间,降低了字典的长度和求解复杂度,并且能自动实现俯仰角和方位角配对;其次改进了样本协方差矩阵的稀疏表示模型,对该模型进行了降维处理;然后由协方差矩阵稀疏重构的残差约束特性得到约束残差项置信区间,避免采用正则化方法导致参数选取困难;最后通过凸优化包实现了二维波达方向的估计。仿真实验表明,待选取的协方差矩阵列数达到某个阈值（在只有两个入射信号情况下该值为3）时,可准确实现入射信号角的估计;当信噪比（SNR）较小（<5dB）时,该方法估计精度优于基于空间角的特征矢量算法;低快拍数（<100）下该方法估计精度略低于特征矢量法,但小间隔角度下估计精度与后者相当。     

Discrete optimisation based on the combined use of reinforcement and constraint satisfaction schemes

A new approach is presented for finding near-optimal solutions to discrete optimisation problems that is based on the cooperation of two modules: an optimisation module and a constraint satisfaction module. The optimisation module must be able to search the problem state space through an iterative process of sampling and evaluating the generated samples. To evaluate a generated point, first a constraint satisfaction module is employed to map that point to another one satisfying the problem constraints, and then the cost of the new point is used as the evaluation of the original one. The scheme that we have adopted for testing the effectiveness of the method uses a reinforcement learning algorithm in the optimisation module and a general deterministic constraint satisfaction algorithm in the constraint satisfaction module. Experiments using this scheme for the solution of two optimisation problems indicate that the proposed approach is very effective in providing feasible solutions of acceptable quality.