基于双邻接图正交近邻保持投影的人脸识别算法

正交保持投影(ONPP)是经典的图嵌入降维技术,已经成功地应用到人脸识别中,其保持了高维数据的局部性和整体几何结构。监督的ONPP通过建立同类邻接图来最小化同类局部重构误差,寻找最优的低维嵌入,但是其只使用了类内信息,这会导致异类数据点间的结构不够明显。因此,提出了基于双邻接图的正交近邻保持投影(DAG-ONPP)算法。通过建立同类邻接图与异类邻接图,在数据嵌入低维空间后同类近邻重构误差尽量小,异类近邻重构误差更加明显。在ORL,Yale,YaleB和PIE人脸库上的实验结果表明,与其他经典算法相比,所提方法有效提高了分类能力。     

Maximal local interclass embedding with application to face recognition

Dimensionality reduction of high dimensional data is involved in many problems in information processing. A new dimensionality reduction approach called maximal local interclass embedding (MLIE) is developed in this paper. MLIE can be viewed as a linear approach of a multimanifolds-based learning framework, in which the information of neighborhood is integrated with the local interclass relationships. In MLIE, the local interclass graph and the intrinsic graph are constructed to find a set of projections that maximize the local interclass scatter and the local intraclass compactness simultaneously. This characteristic makes MLIE more powerful than marginal Fisher analysis (MFA). MLIE maintains all the advantages of MFA. Moreover, the computational complexity of MLIE is less than that of MFA. The proposed algorithm is applied to face recognition. Experiments have been performed on the Yale, AR and ORL face image databases. The experimental results show that owing to the locally discriminating property, MLIE consistently outperforms up-to-date MFA, Smooth MFA, neighborhood preserving embedding and locality preserving projection in face recognition.     

半监督边缘判别嵌入与局部保持的维度约简

为了对高维数据进行降维处理,提出了半监督学习的边缘判别嵌入与局部保持的维度约简算法．通过最小化样本与其所属类别的中心点之间的距离,使得样本在投影子空间中能够保持其领域的拓扑结构;再通过最大化不同类别边缘间的距离,使得类别间的分离度在投影子空间中得到增强．实验结果表明：半监督边缘判别嵌入与局部保持的维度约简算法能够获得初始特征空间的较好的投影子空间．     

基于协作表示和模糊渐进最大边界嵌入的特征抽取方法

针对图嵌入方法在构造邻域关系图的过程中,简单地将样本数据划入某一类的做法并不妥当的问题,提出了模糊渐进的隶属度表示方法。该方法借助模糊数学的思想,通过模糊渐进的隶属度,将样本归属于不同类别。针对图嵌入方法中分类器效率偏低的问题,引入了协作表示分类方法,该分类方法大幅度提高了算法的计算效率。基于这两点,提出了基于协作表示和模糊渐进最大边界嵌入的特征抽取算法。在ORL、AR人脸数据库上,以及USPS数字手写体数据库上的实验表明,该算法优于主成分分析(PCA)、线性鉴别分析(LDA)、局部保留投影(LPP)和边界Fisher分析(MFA)。     

Graph embedding and extensions: a general framework for dimensionality reduction

A large family of algorithms - supervised or unsupervised; stemming from statistics or geometry theory - has been designed to provide different solutions to the problem of dimensionality reduction. Despite the different motivations of these algorithms, we present in this paper a general formulation known as graph embedding to unify them within a common framework. In graph embedding, each algorithm can be considered as the direct graph embedding or its linear/kernel/tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set, with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided. Furthermore, the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms. By utilizing this framework as a tool, we propose a new supervised dimensionality reduction algorithm called marginal Fisher analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class, while the penalty graph connects the marginal points and characterizes the interclass separability. We show that MFA effectively overcomes the limitations of the traditional linear discriminant analysis algorithm due to data distribution assumptions and available projection directions. Real face recognition experiments show the superiority of our proposed MFA in comparison to LDA, also for corresponding kernel and tensor extensions     

一种半监督局部线性嵌入算法的文本分类方法*

针对局部线性嵌入算法（LLE）应用于非监督机器学习中的缺陷,将该算法与半监督思想相结合,提出了一种基于半监督局部线性嵌入算法的文本分类方法。通过使用文本数据的流形结构和少量的标签样本,将LLE中的距离矩阵采用分段形式进行调整;使用调整后的矩阵进行线性重建从而实现数据降维;针对半监督LLE中使用欧氏距离的缺点,采用高斯核函数将欧氏距离进行变换,并用新的核距离取代欧氏距离,提出了基于核的半监督局部线性嵌入算法;最后通过仿真实验验证了改进算法的有效性。     

Locally Minimizing Embedding and Globally Maximizing Variance: Unsupervised Linear Difference Projection for Dimensionality Reduction

Recently, many dimensionality reduction algorithms, including local methods and global methods, have been presented. The representative local linear methods are locally linear embedding (LLE) and linear preserving projections (LPP), which seek to find an embedding space that preserves local information to explore the intrinsic characteristics of high dimensional data. However, both of them still fail to nicely deal with the sparsely sampled or noise contaminated datasets, where the local neighborhood structure is critically distorted. On the contrary, principal component analysis (PCA), the most frequently used global method, preserves the total variance by maximizing the trace of feature variance matrix. But PCA cannot preserve local information due to pursuing maximal variance. In order to integrate the locality and globality together and avoid the drawback in LLE and PCA, in this paper, inspired by the dimensionality reduction methods of LLE and PCA, we propose a new dimensionality reduction method for face recognition, namely, unsupervised linear difference projection (ULDP). This approach can be regarded as the integration of a local approach (LLE) and a global approach (PCA), so that it has better performance and robustness in applications. Experimental results on the ORL, YALE and AR face databases show the effectiveness of the proposed method on face recognition.     

Adaptive Graph Embedding Discriminant Projections

Graph embedding based learning method plays an increasingly significant role on dimensionality reduction (DR). However, the selection to neighbor parameters of graph is intractable. In this paper, we present a novel DR method called adaptive graph embedding discriminant projections (AGEDP). Compared with most existing DR methods based on graph embedding, such as marginal Fisher analysis which usually predefines the intraclass and interclass neighbor parameters, AGEDP applies all the homogeneous samples for constructing the intrinsic graph, and simultaneously selects heterogeneous samples within the neighborhood generated by the farthest homogeneous sample for constructing the penalty graph. Therefore, AGEDP not only greatly enhances the intraclass compactness and interclass separability, but also adaptively performs neighbor parameter selection which considers the fact that local manifold structure of each sample is generally different. Experiments on AR and COIL-20 datasets demonstrate the effectiveness of the proposed method for face recognition and object categorization, and especially under the interference of occlusion, noise and poses, it is superior to other graph embedding based methods with three different classifiers: nearest neighbor classifier, sparse representation classifier and linear regression classifier.     

基于随机子空间的局部鉴别投影*

针对高维数据容易对噪声敏感及容易造成维数灾难问题,文中提出基于随机子空间的局部鉴别投影算法(RSLDP).利用随机子空间方法对高维的原始数据进行特征选择,在生成的低维特征子空间构造近邻图,降低噪声影响.RSLDP通过最大化局部类间加权散度和最小化局部类内加权散度,同时最小化样本的总体局部散度,改进局部最大间距鉴别嵌入算法,较好刻画样本与其类间类内近邻中心点的关系,有利于鉴别特征的提取.在CMU PIE和AR这2个人脸数据库上的实验表明文中算法的有效性.     

Locality preserving embedding for face and handwriting digital recognition

Most supervised manifold learning-based methods preserve the original neighbor relationships to pursue the discriminating power. Thus, structure information of the data distributions might be neglected and destroyed in low-dimensional space in a certain sense. In this paper, a novel supervised method, called locality preserving embedding (LPE), is proposed to feature extraction and dimensionality reduction. LPE can give a low-dimensional embedding for discriminative multi-class sub-manifolds and preserves principal structure information of the local sub-manifolds. In LPE framework, supervised and unsupervised ideas are combined together to learn the optimal discriminant projections. On the one hand, the class information is taken into account to characterize the compactness of local sub-manifolds and the separability of different sub-manifolds. On the other hand, at the same time, all the samples in the local neighborhood are used to characterize the original data distributions and preserve the structure in low-dimensional subspace. The most significant difference from existing methods is that LPE takes the distribution directions of local neighbor data into account and preserves them in low-dimensional subspace instead of only preserving the each local sub-manifold’s original neighbor relationships. Therefore, LPE optimally preserves both the local sub-manifold’s original neighborhood relationships and the distribution direction of local neighbor data to separate different sub-manifolds as far as possible. The criterion, similar to the classical Fisher criterion, is a Rayleigh quotient in form, and the optimal linear projections are obtained by solving a generalized Eigen equation. Furthermore, the framework can be directly used in semi-supervised learning, and the semi-supervised LPE and semi-supervised kernel LPE are given. The proposed LPE is applied to face recognition (on the ORL and Yale face databases) and handwriting digital recognition (on the USPS database). The experimental results show that LPE consistently outperforms classical linear methods, e.g., principal component analysis and linear discriminant analysis, and the recent manifold learning-based methods, e.g., marginal Fisher analysis and constrained maximum variance mapping.     

一种基于极大熵的快速无监督线性降维方法

现实世界中高维数据无处不在,然而在高维数据中往往存在大量的冗余和噪声信息,这导致很多传统聚类算法在对高维数据聚类时不能获得很好的性能.实践中发现高维数据的类簇结构往往嵌入在较低维的子空间中.因而,降维成为挖掘高维数据类簇结构的关键技术.在众多降维方法中,基于图的降维方法是研究的热点.然而,大部分基于图的降维算法存在以下两个问题:(1)需要计算或者学习邻接图,计算复杂度高;(2)降维的过程中没有考虑降维后的用途.针对这两个问题,提出一种基于极大熵的快速无监督降维算法MEDR. MEDR算法融合线性投影和极大熵聚类模型,通过一种有效的迭代优化算法寻找高维数据嵌入在低维子空间的潜在最优类簇结构. MEDR算法不需事先输入邻接图,具有样本个数的线性时间复杂度.在真实数据集上的实验结果表明,与传统的降维方法相比, MEDR算法能够找到更好地将高维数据投影到低维子空间的投影矩阵,使投影后的数据有利于聚类.     

基于马氏距离度量的局部线性嵌入算法

局部线性嵌入算法(LLE)中常用欧氏距离度量样本间相似度。而对于图像等高维数据,欧氏距离不能准确体现样本间的相似程度。文中提出基于马氏距离度量的局部线性嵌入算法(MLLE)。算法首先从现有样本中学习到一个马氏度量,然后在LLE算法的近邻选择、现有样本及新样本降维过程中用马氏度量作为相似性度量。将MLLE算法及其它典型的流形学习算法在ORL和USPS数据库上进行对比实验,结果表明MLLE算法具有良好的识别性能。     

基于随机游走扩散映射的降维算法

传统数据降维算法分为线性或流形学习降维算法,但在实际应用中很难确定需要哪一类算法.设计一种综合的数据降维算法,以保证它的线性降维效果下限为主成分分析方法且在流形学习降维方面能揭示流形的数据结构.通过对高维数据构造马尔可夫转移矩阵,使越相似的节点转移概率越大,从而发现高维数据降维到低维流形的映射关系.实验结果表明,在人造...     

基于最近邻的随机非线性降维

针对线性降维技术应用于具有非线性结构的数据时无法得到令人满意的结果的问题,提出一种新的着重于保持高维空间局部最近邻信息的非线性随机降维算法(NNSE)。该算法首先在高维空间中通过计算样本点之间的欧氏距离找出每个样本点的最近邻点,接着在低维空间中产生一个随机的初始分布;然后通过将低维空间中的样本点不断向其最近邻点的平均位置移动,直到产生稳定的低维嵌入结果。与一种先进的非线性随机降维算法——t分布随机邻域嵌入(t-SNE)相比,NNSE算法得到的低维结果在可视化方面与t-SNE算法相差不大,但通过比较两者的量化指标可以发现,NNSE算法在保持最近邻信息方面上明显优于t-SNE算法。     

一种邻域竞争线性嵌入的降维方法

针对局部线性嵌入算法处理稀疏数据失效的问题,提出一种基于邻域竞争线性嵌入的降维方法。利用数据的统计信息动态确定局部线性化范围,并采用cam分布寻找数据点的近邻,避免了近邻选取方向的缺失。在数据集稀疏的情况下,通过对数据点近邻做局部结构的提取,该算法能够很好地把握数据的局部信息和整体信息。为了验证算法的有效性,将该算法应用于手工流形降维和对Corel数据库进行图像检索等,结果表明该算法不仅有较好的降维效果,而且具有很好的实用价值。     

一种基于全局信息保持的局部线性嵌入算法及应用

局部线性嵌入（LLE）作为一种经典的流形学习算法，能够得到高维空间的低维流形，但对近邻样本数选择敏感，缺乏全局结构保持能力.为解决此问题，提出了一种改进的LLE算法.在综合考虑样本间差异和数据全局代表性的基础上，通过引入离散度保持项和全局权重指标，提高了算法在降维重构过程中的信息挖掘能力，并降低了对噪声的敏感度，克服了传统LLE算法只关注局部流形特征而忽略全局结构的缺陷.数值仿真和小麦籽粒蛋白质含量软测量的应用仿真验证了该算法的有效性和优越性.     

局部线性嵌入优化光谱回归的鲁棒人脸识别

针对高维小样本鲁棒人脸识别问题,提出了一种局部线性嵌入优化光谱回归算法。计算出训练样本的特征向量,然后用局部线性嵌入算法构建分类问题所需的嵌入,并学习每种分类的子流形所需的嵌入;利用光谱回归计算投影矩阵,最近邻分类器完成人脸的识别。在人脸数据库FERET、AR及扩展YaleB上的实验结果表明,相比其他几种光谱回归算法,该算法取得了更好的识别效果。     

Dimensionality reduction-based spoken emotion recognition

To improve effectively the performance on spoken emotion recognition, it is needed to perform nonlinear dimensionality reduction for speech data lying on a nonlinear manifold embedded in a high-dimensional acoustic space. In this paper, a new supervised manifold learning algorithm for nonlinear dimensionality reduction, called modified supervised locally linear embedding algorithm (MSLLE) is proposed for spoken emotion recognition. MSLLE aims at enlarging the interclass distance while shrinking the intraclass distance in an effort to promote the discriminating power and generalization ability of low-dimensional embedded data representations. To compare the performance of MSLLE, not only three unsupervised dimensionality reduction methods, i.e., principal component analysis (PCA), locally linear embedding (LLE) and isometric mapping (Isomap), but also five supervised dimensionality reduction methods, i.e., linear discriminant analysis (LDA), supervised locally linear embedding (SLLE), local Fisher discriminant analysis (LFDA), neighborhood component analysis (NCA) and maximally collapsing metric learning (MCML), are used to perform dimensionality reduction on spoken emotion recognition tasks. Experimental results on two emotional speech databases, i.e. the spontaneous Chinese database and the acted Berlin database, confirm the validity and promising performance of the proposed method.     

一种基于稀疏嵌入分析的降维方法

近几年局部流形学习算法研究得到了广泛的关注, 如局部线性嵌入以及局部切空间排列算法等.这些算法都是基于局部可线性化的假设而提出的, 但局部是否可线性化的问题没有得到很好有效的解决, 使得目前的降维算法对自然数据效果不佳. 自然数据中有很多是稀疏的,对稀疏数据的降维是局部线性嵌入算法所面临的一个问题. 基于对数据自然属性的考虑,利用数据的统计信息动态确定局部线性化范围, 依据数据的分布提出一种排列的稀疏局部线性嵌入算法(Sparse local linear embedding algorithm, SLLEA). 在数据集稀疏的情况下,该算法能够很好地把握数据的局部和整体信息. 将该算法应用于手工流形及图像检索等试验中,验证了该算法的有效性.     

结合优化MGFR与二维线性降维的特征提取算法

受限于人脸姿态、光照变化等因素,通过引入多通道Gaborface表征结合基于子空间的二维双向线性降维算法,提出了一种结合优化多通道Gaborface与二维线性降维的特征提取算法。首先,采用多通道Gaborface表征(MGFR)模型对样本集进行预处理,提取不同通道下的人脸Gabor特征表示并优化选取通道融合方式而组合成新特征;再引入样本间类别信息获得改进线性二维双向特征降维算法,从而对获得的人脸表示进行特征降维与提取;最终通过最近邻分类器得到分类结果。试验结果表明,通过在AR、ORL和YALE人脸库进行对比分析,改进算法对人脸姿态等变化具有较强的鲁棒性,且较其他算法表现出了较优的识别性能。