Locality preserving and global discriminant projection with prior information

Existing supervised and semi-supervised dimensionality reduction methods utilize training data only with class labels being associated to the data samples for classification. In this paper, we present a new algorithm called locality preserving and global discriminant projection with prior information (LPGDP) for dimensionality reduction and classification, by considering both the manifold structure and the prior information, where the prior information includes not only the class label but also the misclassification of marginal samples. In the LPGDP algorithm, the overlap among the class-specific manifolds is discriminated by a global class graph, and a locality preserving criterion is employed to obtain the projections that best preserve the within-class local structures. The feasibility of the LPGDP algorithm has been evaluated in face recognition, object categorization and handwritten Chinese character recognition experiments. Experiment results show the superior performance of data modeling and classification to other techniques, such as linear discriminant analysis, locality preserving projection, discriminant locality preserving projection and marginal Fisher analysis.     

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.     

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。     

基于QR分解的扩展监督局部保留映射

针对局部保留映射(LPP)算法不能提供数据集的差异信息问题,提出一种基于QR分解的扩展有监督LPP算法。该方法对训练数据矩阵进行QR分解,采用有监督的LPP算法进行降维,利用类别信息对降维后的数据进行Fisher线性判别式分析,得到最终的映射矩阵以提高判别性能。实验结果表明,该方法较主成分分析法和LPP方法有更好的判别性能。     

一种用于特征提取的保局判别分析算法

针对保局投影(LPP)为无监督算法的局限,提出了一种新的监督版的LPP,即保局判别分析(LPDA)算法。LPDA吸收了流形学习算法与最大边界准则(MMC)的共同特点,可以将高维的人脸数据投影到低维子空间,具有能处理新样本与无小样本问题的优点。与现有的多种经典相关方法相比,从Yale, UMIST及MIT 3个人脸数据库的实验结果表明,提出的LPDA算法在降维的同时提取了用于人脸识别的更有效的特征,人脸图像识别性能较好,具有较强的判别分析能力。     

Local structure based supervised feature extraction

In the past few years, the computer vision and pattern recognition community has witnessed the rapid growth of a new kind of feature extraction method, the manifold learning methods, which attempt to project the original data into a lower dimensional feature space by preserving the local neighborhood structure. Among them, locality preserving projection (LPP) is one of the most promising feature extraction techniques. However, when LPP is applied to the classification tasks, it shows some limitations, such as the ignorance of the label information. In this paper, we propose a novel feature extraction method, called locally discriminating projection (LDP). LDP utilizes class information to guide the procedure of feature extraction. In LDP, the local structure of the original data is constructed according to a certain kind of similarity between data points, which takes special consideration of both the local information and the class information. The similarity has several good properties which help to discover the true intrinsic structure of the data, and make LDP a robust technique for the classification tasks. We compare the proposed LDP approach with LPP, as well as other feature extraction methods, such as PCA and LDA, on the public available data sets, FERET and AR. Experimental results suggest that LDP provides a better representation of the class information and achieves much higher recognition accuracies.     

基于自适应邻域选择的正交局部敏感判别分析

维数灾难是机器学习算法在高维数据上学习经常遇到的难题,基于局部敏感判别分析(locality sensitive discriminant analysis,LSDA),可以很好地解决维数灾难问题.且LSDA构建邻域时不能充分反映流形学习对邻域要求和克服测度扭曲问题,利用自适应邻域选择方法来度量邻域,同时,引入施密特正交化获得正交投影矩阵,提出一种自适应邻域选择的正交局部敏感判别分析算法.在ORL和YALE人脸数据库上进行实验,实验结果表明了该算法的有效性.     

无关性判别保局算法及其在人脸识别中的应用

特征提取是人脸识别过程中的一个重要步骤,是人脸识别算法有效性的关键。提出了一种基于无关性判别保局的特征提取算法,并应用于人脸识别。基于保局投影算法的人 脸识别是一种有效的人脸识别算法,但它只考虑了数据的局部性,没有考虑类别信息,也没有考虑所提特征之间的相关性,现有的改进算法虽然考虑了类别信息,但是没有考虑到 类间信息。本文算法使得所提特征之间相互无关,这样降低了数据冗余,同时考虑到类别信息,使得投影后的类间区分度加强了。实验结果验证了算法的正确性和有效性,比传统 算法有较好的识别性能。     

Feature extraction using constrained maximum variance mapping

In this paper, an efficient feature extraction method named as constrained maximum variance mapping (CMVM) is developed. The proposed algorithm can be viewed as a linear approximation of multi-manifolds learning based approach, which takes the local geometry and manifold labels into account. The CMVM and the original manifold learning based approaches have a point in common that the locality is preserved. Moreover, the CMVM is globally maximizing the distances between different manifolds. After the local scatters have been characterized, the proposed method focuses on developing a linear transformation that can maximize the dissimilarities between all the manifolds under the constraint of locality preserving. Compared to most of the up-to-date manifold learning based methods, this trick makes contribution to pattern classification from two aspects. On the one hand, the local structure in each manifold is still kept; on the other hand, the discriminant information between manifolds can be explored. Finally, FERET face database, CMU PIE face database and USPS handwriting data are all taken to examine the effectiveness and efficiency of the proposed method. Experimental results validate that the proposed approach is superior to other feature extraction methods, such as linear discriminant analysis (LDA), locality preserving projection (LPP), unsupervised discriminant projection (UDP) and maximum variance projection (MVP).     

图最优化线性鉴别投影及其在图像识别中的应用

在图最优化局部保持投影(GoLPP)算法的基础上,本文充分利用数据的类别信息,提出一种新的特征抽取算法——图最优化线性鉴别投影(GoLDP)。与GoLPP类似,GoLDP的邻接图是通过最优化一个目标函数创建的;与GoLPP不同,GoLDP利用数据的类别信息创建两幅最优邻接图——最优内在图和最优惩罚图,由这两幅最优邻接图求得最优投影矩阵。FERET与YALE人脸数据库以及PolyU掌纹数据库上的实验结果证明了GoLDP算法的有效性。     

Orthogonal sparse linear discriminant analysis

Linear discriminant analysis (LDA) is a linear feature extraction approach, and it has received much attention. On the basis of LDA, researchers have done a lot of research work on it, and many variant versions of LDA were proposed. However, the inherent problem of LDA cannot be solved very well by the variant methods. The major disadvantages of the classical LDA are as follows. First, it is sensitive to outliers and noises. Second, only the global discriminant structure is preserved, while the local discriminant information is ignored. In this paper, we present a new orthogonal sparse linear discriminant analysis (OSLDA) algorithm. The k nearest neighbour graph is first constructed to preserve the locality discriminant information of sample points. Then, L_2,1-norm constraint on the projection matrix is used to act as loss function, which can make the proposed method robust to outliers in data points. Extensive experiments have been performed on several standard public image databases, and the experiment results demonstrate the performance of the proposed OSLDA algorithm.     

加权自适应CS-LBP与局部判别映射相结合的掌纹识别方法

提取掌纹的最佳低维分类特征一直是掌纹识别研究领域的一个重要方向。针对掌纹图像具有丰富的纹理特征特点,提出一种基于加权自适应中心对称局部二值模式(WACS-LBP)与局部判别映射(LDP)相结合的掌纹识别方法。首先将掌纹感兴趣(ROI)图像分成大小均匀的小区域,利用自适应中心对称局部二值模式(ACS-LBP)算法获取不同区域的纹理特征直方图和权值,经过加权连接得到ROI的加权纹理特征直方图向量;再利用LDP算法对得到的特征向量进行维数约简;最后利用K-最近邻分类器进行掌纹识别。在掌纹公开数据库上进行实验,正确识别率高达97%以上。实验结果表明,该方法不仅是有效、可行的,而且研究思路比较明确。     

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.     

无参数无相关最大化判别边界算法

在人脸识别算法中,无参数局部保持投影(PFLPP)是一种有效的特征提取算法, 但忽略了异类近邻样本在分类中所起的作用,并且对于近邻的处理仅利用样本与总体均值的 距离关系来判断,因此并不能有效地确定近邻关系。基于此,提出一种无参数无相关最大化 判别边界算法,有效地利用了样本的类别信息,定义了无参数同类近邻样本的相似权值与异 类近邻样本的惩罚权值,样本邻域大小可根据类内平均余弦距离和类间余弦距离自适应确定, 为了进一步增强算法的性能,给出了具有不相关性的目标函数。UMIST 和 AR 人脸库上的实 验结果表明,该算法相对于不相关保局投影分析算法和 PFLPP 算法,具有运算量低、识别性 能高的优势。     

完备鉴别保局投影人脸识别算法

为了充分利用保局总体散布主元空间内的鉴别信息进行人脸识别,提出了一种完备鉴别保局投影(complete discriminant locality preserving projections,简称CDLPP)人脸识别算法.鉴于Fisher鉴别分析和保局投影已经被广泛的应用于人脸识别,完备鉴别保局投影(locality preserving projections,简称LPP)算法将这两者结合起来,分析了保局类内散布、类间散布和总体散布的主元空间和零空间内包含的鉴别信息.该算法采用奇异值分解(singular value decomposition,简称SVD),去除了不含任何鉴别信息的保局总体散布的零空间;分别在保局类内散布的主元空间和零空间提取规则鉴别特征和不规则鉴别特征;用串联的方式在特征层融合规则鉴别特征和不规则鉴别特征形成完备的鉴别特征进行人脸识别.在ORL库、FERET子库和PIE子库上的大量识别实验充分表明了完备鉴别保局投影算法的性能优于线性鉴别分析、保局投影和鉴别保局投影等现有的子空间人脸识别算法,验证了算法的有 效性.     

基于张量局部保持投影算法的图像检索

针对局部保持投影算法是无监督的学习,无法区别类别信息的缺点,本文通过加入鉴别信息的方式对局部保持投影算法进行改进,并将改进的算法推广到张量空间。通过在标准数据集上的对比实验得出,张量改进的局部保持投影算法的检索效果要比原有算法的效果好。     

正则化保局鉴别分析方法

提出一种正则化保局鉴别分析方法(RLPDA)并将其应用于人脸识别。受样本有限制约和大量噪声干扰,保局类内散布矩阵的零特征值及小特征值估计不准确,进而影响鉴别保局投影算法的性能。结合倒数谱模型对保局类内散布矩阵的特征值进行正则化,并利用正则化后的特征值对相应的特征空间加权,使人脸空间被保留,噪声空间被削弱,而零空间则被加强。通过分析鉴别信息在数据空间的分布可发现,RLPDA方法有效利用整个特征空间的鉴别信息,有利于提高算法的识别精度,同时从原理上回避小样本问题。在FERET和UMIST人脸数据库上的识别结果表明,RLPDA是一种有效的人脸特征提取方法。     

Artificial neural networks for feature extraction and multivariatedata projection

Classical feature extraction and data projection methods have been well studied in the pattern recognition and exploratory data analysis literature. We propose a number of networks and learning algorithms which provide new or alternative tools for feature extraction and data projection. These networks include a network (SAMANN) for J.W. Sammon's (1969) nonlinear projection, a linear discriminant analysis (LDA) network, a nonlinear discriminant analysis (NDA) network, and a network for nonlinear projection (NP-SOM) based on Kohonen's self-organizing map. A common attribute of these networks is that they all employ adaptive learning algorithms which makes them suitable in some environments where the distribution of patterns in feature space changes with respect to time. The availability of these networks also facilitates hardware implementation of well-known classical feature extraction and projection approaches. Moreover, the SAMANN network offers the generalization ability of projecting new data, which is not present in the original Sammon's projection algorithm; the NDA method and NP-SOM network provide new powerful approaches for visualizing high dimensional data. We evaluate five representative neural networks for feature extraction and data projection based on a visual judgement of the two-dimensional projection maps and three quantitative criteria on eight data sets with various properties.     

面向酉子空间的二维判别保局投影的人脸识别*

保局投影算法（LPP）在人脸识别中具有较好的识别性能,但它是一种非监督学习,并且在具体实现时需要把图像转换为向量,破坏了图像的像素结构,这显然不利于模式识别。针对这些问题,提出基于酉子空间的二维判别保局算法,不仅在判别保局算法的基础上增加了类别信息,而且直接在灰度矩阵上进行水平和垂直方向上的二维保局投影。该方法构造酉空间上的复向量后再运用线性判别分析提取特征。在ORL、Yale和XJTU人脸库中验证了算法的正确性和有效性,其识别率比传统的2DLDA和2DLPP等方法提高4～5个百分点。     

局部敏感的半监督鉴别分析方法

为解决图像处理中的高维特征在模式分类中带来的问题,提出一种基于半监督学习理论的数据降维方法,称为局部敏感的半监督鉴别分析算法.为能够发现局部的流形结构,算法寻找一个能够最小化类内距离的同时最大化类间距离的投影,并且在最优化过程中充分利用无标签数据,控制局部邻域的散度.在人脸识别数据库和行为数据库中的测试结果表明了该算法是有效的.