新的局部保持鉴别分析算法

提出了一种新的局部保持鉴别分析算法：基于迹比准则与自适应近邻图嵌入的局部保持鉴别分析算法。根据样本分布特性自适应构建类内和类间近邻图,保持数据的局部结构并且利用数据的鉴别信息,定义局部类内离差矩阵以及局部类间离差矩阵,采用迹比Fisher判别函数作为目标函数,通过迭代的方法最大化局部类间离差矩阵与类内离差矩阵的迹比值,解得最优子空间。在ORL和Yale人脸数据库上的实验表明该方法是有效的。     

基于大间距准则的不相关保局投影分析

局部保持投影(Locality preserving projections,LPP)算法只保持了目标在投影后的邻域局部信息,为了更好地刻画数据的流形结构, 引入了类内和类间局部散度矩阵,给出了一种基于有效且稳定的大间距准则(Maximum margin criterion,MMC)的不相关保局投影分析方法.该方法在最大化散度矩阵迹差时,引入尺度因子α,对类内和类间局部散度矩阵进行加权,以便找到更适合分类的子空间并且可避免小样本问题; 更重要的是,大间距准则下提取的判别特征集一般情况下是统计相关的,造成了特征信息的冗余, 因此,通过增加一个不相关约束条件,利用推导出的公式提取不相关判别特征集, 这样做, 对正确识别更为有利.在Yale人脸库、PIE人脸库和MNIST手写数字库上的测试结果表明,本文方法有效且稳定, 与LPP、LDA (Linear discriminant analysis)和LPMIP(Locality-preserved maximum information projection)方法等相比,具有更高的正确识别率.     

中心线邻域鉴别嵌入算法及其在人脸识别中的应用*

针对边界费舍尔分析在特征提取过程中存在的不足,提出中心线邻域鉴别嵌入(CLNDE)算法,并应用于人脸识别中.CLNDE首先利用样本到类中心线的距离分别构造类内相似矩阵与类间相似矩阵;然后利用构造的相似矩阵计算样本的类间局部散度与类内局部散度;最后在最大化样本的类间局部散度的同时最小化类内局部散度,寻求最优投影矩阵.在人脸数据库上实验验证算法的优越性.     

基于二维邻域保持判别嵌入的人脸识别

提出二维邻域保持判别嵌入(2DNPDE)算法,该算法是一种有监督的基于二维图像矩阵的特征提取算法.为表示样本的类内邻域结构和类间距离关系,分别构建类内邻接矩阵和类间相似度矩阵.2DNPDE所获得的投影空间不但使不同类数据点的低维嵌入相互分离,而且保留同类样本的邻域结构和不同类样本的距离关系.在ORL和AR人脸数据库上的实验表明,该算法具有更好的识别效果.     

Learning in multimodal and mixmodal data: locality preserving discriminant analysis with kernel and sparse representation techniques

We consider the problem of feature extraction for “multimodal” and “mixmodal” data. A new supervised learning method called locality preserving discriminant analysis (LPDA) is presented, which aims to maximize the weighted between-class distances and minimize the locality-preserved within-class distances. By introducing a specific affinity matrix for each class, LPDA can better preserve the local geometric structure of the samples within it, and thus efficiently derive nonlinear characters of the data structure. Meanwhile, by using the defined between-class weight matrix, LPDA also preserves the interrelation information of data from different classes. This facilitates the separation of between-class data. We further extend LPDA to kernel-LPDA and sparse-LPDA by taking advantage of theories of kernel technique and sparse representation. Experiments for data classification, handwriting and face recognition are carried out to verify the feasibility and effectiveness of the proposed approaches.     

Local discriminant non-negative matrix factorization feature extraction for hyperspectral image classification

Non-negative matrix factorization (NMF) ignores both the local geometric structure of and the discriminative information contained in a data set. A manifold geometry-based NMF dimension reduction method called local discriminant NMF (LDNMF) is proposed in this paper. LDNMF preserves not only the non-negativity but also the local geometric structure and discriminative information of the data. The local geometric and discriminant structure of the data manifold can be characterized by a within-class graph and a between-class graph. An efficient multiplicative updating procedure is produced, and its global convergence is guaranteed theoretically. Experimental results on two hyperspectral image data sets show that the proposed LDNMF is a powerful and promising tool for extracting hyperspectral image features.     

适用于小样本问题的具有类内保持的正交特征提取算法

在人脸识别中, 具有正交性的特征提取算法是一类有效的特征提取算法, 但受到小样本问题的制约. 本文在正交判别保局投影的基础上, 提出了一种适用于小样本问题的具有类内保持的正交特征提取算法. 算法根据同类样本之间的空间结构信息, 重新定义了类内散度矩阵与类间散度矩阵, 进而给出了一个新的目标函数. 然而新的目标函数对于人脸识别问题, 同样存在着小样本问题. 为此本文将原始数据空间降到一个低维的子空间, 从而避免了总体散度矩阵奇异, 并在理论上证明了在该子空间中求解判别矢量集, 等价于在原空间中求解判别矢量集. 人脸库上的实验结果表明本文算法的有效性.     

Discriminant Analysis with Local Gaussian Similarity Preserving for Feature Extraction

In this paper, we propose a novel discriminant analysis with local Gaussian similarity preserving (DA-LGSP) method for feature extraction. DA-LGSP can be viewed as a linear approximation of manifold learning based approach which seeks to find a linear projection that maximizes the between-class dissimilarities under the constraint of locality preserving. The local geometry of each point is preserved by the Gaussian coefficients of its neighbors, meanwhile the between-class dissimilarities are represented by Euclidean distances. Experiments are conducted on USPA data, COIL-20 dataset, ORL dataset and FERET dataset. The performance of the proposed method demonstrates that DA-LGSP is effective in feature extraction.     

局部非参数子空间分析在人脸识别中的应用

提出了一种局部非参数子空间分析算法（Local Nonparametric Subspace Analysis,LNSA）,将其应用在人脸识别中。LNSA算法结合了非参数子空间算法（Nonparametric Subspace Analysis,NSA）与局部保留投影算法（Locality Preserving Projection,LPP）。它利用LPP算法中的相似度矩阵重构NSA的类内散度矩阵,使得在最大化类间散度矩阵的同时保留了类的局部结构。在ORL人脸库和XM2VTS人脸库上作了实验并证明LNSA方法要优于其他方法。     

最小距离鉴别投影及其在人脸识别中的应用

针对人脸识别问题,提出了最小距离鉴别投影算法,其与经典的线性鉴别分析不同,它是一种流形学习降维算法。该算法首先定义样本的类内相似度与类间相似度:前者能够度量样本与类内中心的距离关系,后者不仅能够反映样本与类间中心的距离关系而且能够反映样本类间距与类内距的大小关系;然后将高维数据映射到低维特征空间,使得样本到类内中心距离最小同时到类间中心距离最大。最后,在ORL、FERET及AR人脸库上的实验结果表明所提算法识别性能要优于其他算法。     

Feature extraction based on Laplacian bidirectional maximum margin criterion

Maximum margin criterion (MMC) based feature extraction is more efficient than linear discriminant analysis (LDA) for calculating the discriminant vectors since it does not need to calculate the inverse within-class scatter matrix. However, MMC ignores the discriminative information within the local structures of samples and the structural information embedding in the images. In this paper, we develop a novel criterion, namely Laplacian bidirectional maximum margin criterion (LBMMC), to address the issue. We formulate the image total Laplacian matrix, image within-class Laplacian matrix and image between-class Laplacian matrix using the sample similar weight that is widely used in machine learning. The proposed LBMMC based feature extraction computes the discriminant vectors by maximizing the difference between image between-class Laplacian matrix and image within-class Laplacian matrix in both row and column directions. Experiments on the FERET and Yale face databases show the effectiveness of the proposed LBMMC based feature extraction method.     

基于竞争性协同表示的局部判别投影特征提取

特征提取算法中利用样本间的协同表示关系构造邻接图只考虑所有训练样本的协同能力,而忽视了每一类训练样本的内在竞争能力。为此,本文提出一种基于竞争性协同表示的局部判别投影特征提取算法（competitive collaborative repesentation-based local discrininant projection for feature extraction,CCRLDP）,该算法利用基于具有竞争性协同表示的方法构造类间图和类内图,考虑到邻接图中各类型系数的影响,引入保留正表示系数的思想稀疏化邻接图,通过计算类内散度矩阵和类间散度矩阵来刻画图像的局部结构并得其最优投影矩阵。在一些数据集上的实验结果表明,相比同类基于局部判别投影的特征提取算法,该算法具有很高的识别率,并在噪声和遮挡上具有良好的鲁棒性,该算法能有效地提高图像的识别效率。     

Face Recognition and Micro-expression Recognition Based on Discriminant Tensor Subspace Analysis Plus Extreme Learning Machine

In this paper, a novel recognition algorithm based on discriminant tensor subspace analysis (DTSA) and extreme learning machine (ELM) is introduced. DTSA treats a gray facial image as a second order tensor and adopts two-sided transformations to reduce dimensionality. One of the many advantages of DTSA is its ability to preserve the spatial structure information of the images. In order to deal with micro-expression video clips, we extend DTSA to a high-order tensor. Discriminative features are generated using DTSA to further enhance the classification performance of ELM classifier. Another notable contribution of the proposed method includes significant improvements in face and micro-expression recognition accuracy. The experimental results on the ORL, Yale, YaleB facial databases and CASME micro-expression database show the effectiveness of the proposed method.     

局部结构保持的鉴别分析方法

局部投影保持LPP(Locality Preserving Projections)是一种局部特征提取算法,它能够有效地保留数据集的局部结构。不相关保局投影鉴别UDLPP(Uncorrelated Discriminant Locality Preserving Projections)在LPP的基础上考虑了类别信息,通过保留类内几何结构并最大化类间距离获得了良好的鉴别性能。结合UDLPP的思想,在UDLPP的基础上提出了一种局部结构保持的鉴别分析方法PCLSP(Pattern Classification based on Local Structure Preserving)。该方法结合了数据集的类别信息以及数据集的局部结构信息,通过最小化类内近邻分离度以及最大化类间近邻分离度来提高鉴别性能,从而进一步反映了数据的局部结构,提高了识别率。通过在ORL(Olivetti-Oracle Research Lab)和YALE两个标准人脸库上实验验证了该算法的有效性。     

相异度导引的有监督鉴别分析方法

提出了相异度导引的有监督鉴别分析方法（D-SDA）。结合模式局部信息和全局信息,定义了类内散度权重矩阵[RW]和类间散度权重矩阵[RB],分别表示类内样本的相异度、类间样本的相异度。由[RW]、[RB]导出类内散度矩阵[SW]和类间散度矩阵[SB],根据Fisher鉴别准则函数确定最优变换矩阵。在YALE和AR人脸图像库上的实验验证了这一算法的有效性。     

Learning a locality discriminating projection for classification

This paper introduces a new algorithm called locality discriminating projection (LDP) for subspace learning, which provides a new scheme for discriminant analysis by considering both the manifold structure and the prior class information. In the LDP algorithm, the overlap among the class-specific manifolds is approximated by an invader graph, and a locality discriminant criterion is proposed to find the projections that best preserve the within-class local structures while decrease the between-class overlap. The feasibility of the LDP algorithm has been successfully tested in text data and visual recognition experiments. Experiment results show it is an effective technique for data modeling and classification comparing to linear discriminant analysis, locality preserving projection, and marginal Fisher analysis.     

Kernel analysis on Grassmann manifolds for action recognition

Modelling video sequences by subspaces has recently shown promise for recognising human actions. Subspaces are able to accommodate the effects of various image variations and can capture the dynamic properties of actions. Subspaces form a non-Euclidean and curved Riemannian manifold known as a Grassmann manifold. Inference on manifold spaces usually is achieved by embedding the manifolds in higher dimensional Euclidean spaces. In this paper, we instead propose to embed the Grassmann manifolds into reproducing kernel Hilbert spaces and then tackle the problem of discriminant analysis on such manifolds. To achieve efficient machinery, we propose graph-based local discriminant analysis that utilises within-class and between-class similarity graphs to characterise intra-class compactness and inter-class separability, respectively. Experiments on KTH, UCF Sports, and Ballet datasets show that the proposed approach obtains marked improvements in discrimination accuracy in comparison to several state-of-the-art methods, such as the kernel version of affine hull image-set distance, tensor canonical correlation analysis, spatial-temporal words and hierarchy of discriminative space-time neighbourhood features.     

动态加权非参数判别分析

线性判别分析(LDA)是最经典的子空间学习和有监督判别特征提取方法之一.受到流形学习的启发,近年来众多基于LDA的改进方法被提出.尽管出发点不同,但这些算法本质上都是基于欧氏距离来度量样本的空间散布度.欧氏距离的非线性特性带来了如下两个问题:1)算法对噪声和异常样本点敏感;2)算法对流形或者是多模态数据集中局部散布度较大的样本点过度强调,导致特征提取过程中数据的本质结构特征被破坏.为了解决这些问题,提出一种新的基于非参数判别分析(NDA)的维数约减方法,称作动态加权非参数判别分析(DWNDA).DWNDA采用动态加权距离来计算类间散布度和类内散布度,不仅能够保留多模态数据集的本质结构特征,还能有效地利用边界样本点对之间的判别信息.因此,DWNDA在噪声实验中展现出对噪声和异常样本的强鲁棒性.此外,在人脸和手写体数据库上进行实验,DWNDA方法均取得了优异的实验结果.     

Feature extraction by learning Lorentzian metric tensor and its extensions

We develop a supervised dimensionality reduction method, called Lorentzian discriminant projection (LDP), for feature extraction and classification. Our method represents the structures of sample data by a manifold, which is furnished with a Lorentzian metric tensor. Different from classic discriminant analysis techniques, LDP uses distances from points to their within-class neighbors and global geometric centroid to model a new manifold to detect the intrinsic local and global geometric structures of data set. In this way, both the geometry of a group of classes and global data structures can be learnt from the Lorentzian metric tensor. Thus discriminant analysis in the original sample space reduces to metric learning on a Lorentzian manifold. We also establish the kernel, tensor and regularization extensions of LDP in this paper. The experimental results on benchmark databases demonstrate the effectiveness of our proposed method and the corresponding extensions.     

Feature Extraction Using Laplacian Maximum Margin Criterion

Feature extraction by Maximum Margin Criterion (MMC) can more efficiently calculate the discriminant vectors than LDA, by avoiding calculation of the inverse within-class scatter matrix. But MMC ignores the local structures of samples. In this paper, we develop a novel criterion to address this issue, namely Laplacian Maximum Margin Criterion (Laplacian MMC). We define the total Laplacian matrix, within-class Laplacian matrix and between-class Laplacian matrix by using the similar weight of samples to capture the scatter information. Laplacian MMC based feature extraction gets the discriminant vectors by maximizing the difference between between-class laplacian matrix and within-class laplacian matrix. Experiments on FERET and AR face databases show that Laplacian MMC works well.