基于稀疏重构的判别分析

为了解决现有判别分析算法对残缺和遮挡等外部干扰比较敏感的问题,从局部稀疏表示的角度,提出一种基于稀疏重构的判别分析(SDA)降维算法。该算法首先利用稀疏表示完成各个类内局部稀疏重构,然后通过非所在类内的样本均值完成各样本的类间局部稀疏重构,最后在降维过程中保持类间和类内的稀疏重构信息之比。在AR和UMIST人脸库人脸数据集上的实验结果表明,与基于图优化的Fisher分析(GbFA)算法和基于重构判别分析(RDA)算法相比,该算法提高了基于近邻分类的最高识别准确率2%~10%。     

基于稀疏张量判别分析的人体行为识别

在模式识别中,如何在提取关键特征的同时对样本进行降维与识别是研究的热点之一。在局部Fisher判别分析（LFDA）的基础上,结合张量表示和稀疏分析,本文提出一种基于稀疏张量的特征提取方法：稀疏张量局部Fisher判别分析（STLFDA）。该方法把张量局部Fisher判别分析（TLFDA）算法中特征分解问题转化为线性回归问题,并用弹性网络解决线性回归中的特征选择问题,既满足了张量局部Fisher判别分析的目标,又保证了得到的投影矩阵的稀疏性。通过在Weizmann人体行为数据库上的实验,表明了稀疏张量局部Fisher判别分析（STLFDA）算法的有效性。     

稀疏判别分析

针对流形嵌入降维方法中在高维空间构建近邻图无益于后续工作,以及不容易给近邻大小和热核参数赋合适值的问题,提出一种稀疏判别分析算法（SEDA）。首先使用稀疏表示构建稀疏图保持数据的全局信息和几何结构,以克服流形嵌入方法的不足;其次,将稀疏保持作为正则化项使用Fisher判别准则,能够得到最优的投影。在一组高维数据集上的实验结果表明,SEDA是非常有效的半监督降维方法。     

一种邻域自适应半监督局部Fisher判别分析算法

针对利用局部化思想解决多模数据的判别分析问题时,根据经验对局部邻域大小进行全局统一设定无法体现局部几何结构的差异性的不足,提出一种邻域自适应半监督局部Fisher判别分析（neighborhood adaptive semi-supervised local Fisher discriminant analysis,NA-SELF）算法。该算法在半监督局部Fisher判别分析算法的基础上,结合马氏距离和余弦相似度确定初始近邻数,并根据样本空间概率密度估计调整近邻数。通过人工数据集和5组UCI标准数据集对该算法的特征降维性能进行验证,并与典型的维数约简算法和采用传统k近邻方法的判别分析算法进行比较,实验结果表明该算法具备更高的有效性。     

用于人脸识别的正则正交化的局部判别分析

非线性结构保持能力的不足是正则正交化的线性判别分析ROLDA(Regularized Orthogonal Linear Discriminant Analysis)在人脸识别中的主要问题。提出一个用于人脸识别的正则正交化的局部Fisher判别分析ROLFDA(Regularized Orthogonal LocalFisher Discriminant Analysis)降维算法。该算法在ROLDA基础上引入局部结构保持,继承ROLDA的特性,克服了ROLDA的非线性能力的不足的问题。在YaleB和AR人脸数据集上的实验验证了该算法的有效性。     

监督型稀疏保持投影

稀疏保持投影（SPP）是最近提出的一种无监督降维方法,因此无法利用标号数据提供的监督信息。为此,对SPP进行了扩展,给出了两种监督型稀疏保持投影算法：基于稀疏保持的判别分析（SPP+LDA）和监督稀疏保持投影（S2PP）。前者通过在SPP变换的子空间内进行线性判别分析（LDA）达到利用数据间稀疏重建关系和监督信息的目的;后者借助数据标号直接修正SPP构建的稀疏重建图在SPP中自然地融入监督信息。分析了两种算法的优缺点,在两个常用的人脸数据集（Yale和AR）上验证了两者的可行性及有效性。     

融合稀疏保持的成对约束投影

提出一种融合稀疏保持的成对约束投影(Pairwise Constraint Projections inosculating Sparsity Preserving, SPPCP)。该算法在成对约束指导的降维过程中,通过平衡参数引入稀疏保持投影(Sparsity Preserving Projections, SPP),在保持成对约束特征的同时,也继承了稀疏保持所蕴含的几何结构保持和近部保持特性。在UCI数据集和 AR人脸库上的实验表明,该算法有效地融合了稀疏保持投影的优点,与典型的成对约束的半监督降维算法相比,提 高了基于最短欧氏距离的分类算法的精度和稳定性。     

多流形判别分析在人脸识别中的研究

局部保持投影LPP(Locality Preserving Projection)是一种有效的非线性降维方法,能够使投影降维后的数据与原输入空间中的相似局部结构保持一致,但是该方法没有充分利用类间样本点的权重等重要信息。为了解决这个问题,提出基于Fisher准则的多流形判别分析FMMDA(Fisher Multi-Manifold Discriminant Analysis)方法。结合Fisher准则训练样本类内拉普拉斯图和样本均值类间拉普拉斯图,既保持了原样本的相似局部结构,又充分地利用了不同类别之间的权重。在ORL及Yale人脸库上验证了该方法的有效性。与其他几种最先进的方法相比,FMMDA方法取得了更好的识别效果。     

成对约束指导的稀疏保持投影

针对稀疏保持投影的稀疏重构过程中监督信息不足的问题,提出一种成对约束指导的稀疏保持投影算法。该算法在训练样本数据的稀疏重构的过程中,通过引入正约束和负约束监督信息指导稀疏重构,使得稀疏保持投影有效地融合了约束监督信息。在UMIST、YALE和AR人脸库人脸数据集上的实验结果表明,与无监督的稀疏保持投影相比,该方法提高了基于最近近邻分类算法的5%~15%识别准确率,有效地提高了降维分类性能。     

张量局部Fisher判别分析的人脸识别

子空间特征提取是人脸识别中的关键技术之一,结合局部Fisher判别分析技术和张量子空间分析技术的优点, 本文提出了一种新的张量局部Fisher判别分析(Tensor local Fisher discriminant analysis, TLFDA)子空间降维技术. 首先,通过对局部Fisher判别技术进行分析,调整了其类间散度目标泛函, 使算法的识别性能更高且时间复杂度更低;其次,引入张量型降维技术对输入数据进行双边投影变换而非单边投影, 获得了更高的数据压缩率;最后,采用迭代更新的方法计算最优的变换矩阵.通过ORL和PIE两个人脸库验证了所提算法的有效性.     

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.     

Local sparse representation projections for face recognition

How to define the sparse affinity weight matrices is still an open problem in existing manifold learning algorithm. In this paper, we propose a novel supervised learning method called local sparse representation projections (LSRP) for linear dimensionality reduction. Differing from sparsity preserving projections (SPP) and the recent manifold learning methods such as locality preserving projections (LPP), LSRP introduces the local sparse representation information into the objective function. Although there are no labels used in the local sparse representation, it still can provide better measure coefficients and significant discriminant abilities. By combining the local interclass neighborhood relationships and sparse representation information, LSRP aims to preserve the local sparse reconstructive relationships of the data and simultaneously maximize the interclass separability. Comprehensive comparison and extensive experiments show that LSRP achieves higher recognition rates than principle component analysis, linear discriminant analysis and the state-of-the-art techniques such as LPP, SPP and maximum variance projections.     

Discriminative learning by sparse representation for classification

Recently, sparsity preserving projections (SPP) algorithm has been proposed, which combines l₁-graph preserving the sparse reconstructive relationship of the data with the classical dimensionality reduction algorithm. However, when applied to classification problem, SPP only focuses on the sparse structure but ignores the label information of samples. To enhance the classification performance, a new algorithm termed discriminative learning by sparse representation projections or DLSP for short is proposed in this paper. DLSP algorithm incorporates the merits of both local interclass geometrical structure and sparsity property. That makes it possess the advantages of the sparse reconstruction, and more importantly, it has better capacity of discrimination, especially when the size of the training set is small. Extensive experimental results on serval publicly available data sets show the feasibility and effectiveness of the proposed algorithm.     

Effective multiplicative updates for non-negative discriminative learning in multimodal dimensionality reduction

Fisher discriminant analysis gives the unsatisfactory results if points in the same class have within-class multimodality and fails to produce the non-negativity of projection vectors. In this paper, we focus on the newly formulated within and between-class scatters based supervised locality preserving dimensionality reduction problem and propose an effective dimensionality reduction algorithm, namely, Multiplicative Updates based non-negative Discriminative Learning (MUNDL), which optimally seeks to obtain two non-negative embedding transformations with high preservation and discrimination powers for two data sets in different classes such that nearby sample pairs in the original space compact in the learned embedding space, under which the projections of the original data in different classes can be appropriately separated from each other. We also show that MUNDL can be easily extended to nonlinear dimensionality reduction scenarios by employing the standard kernel trick. We verify the feasibility and effectiveness of MUNDL by conducting extensive data visualization and classification experiments. Numerical results on some benchmark UCI and real-world datasets show the MUNDL method tends to capture the intrinsic local and multimodal structure characteristics of the given data and outperforms some established dimensionality reduction methods, while being much more efficient.     

基于成对约束和稀疏保留的数据降维算法

结合以成对约束形式给出的监督信息和无监督信息,提出一种基于成对约束和稀疏保留的数据降维算法。通过成对约束信息进行鉴别分析,利用稀疏表示方法保留数据集在变换空间中的全局稀疏结构。实验结果表明,与传统特征抽取算法相比,该算法的识别效果更好,需要调节的参数更少,且鲁棒性较高。     

结合成对约束的近邻稀疏保留投影算法

稀疏保持投影算法是一种无监督的全局线性降维方法,无法应对训练样本不足及类内样本间差异过大的情况。针对该问题,提出一种结合成对约束机制的近邻稀疏保留投影算法。利用近邻样本求取稀疏系数以保留局部结构信息,引入成对约束监督的思想,利用样本类别指导稀疏重构过程,最后定义能最大限度保留稀疏系数中蕴含的类别信息的低维子空间。将该算法用于人脸识别,实验结果证明了算法在识别率以及运行时间上的有效性和可行性。     

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.     

A unified framework for semi-supervised dimensionality reduction

In practice, many applications require a dimensionality reduction method to deal with the partially labeled problem. In this paper, we propose a semi-supervised dimensionality reduction framework, which can efficiently handle the unlabeled data. Under the framework, several classical methods, such as principal component analysis (PCA), linear discriminant analysis (LDA), maximum margin criterion (MMC), locality preserving projections (LPP) and their corresponding kernel versions can be seen as special cases. For high-dimensional data, we can give a low-dimensional embedding result for both discriminating multi-class sub-manifolds and preserving local manifold structure. Experiments show that our algorithms can significantly improve the accuracy rates of the corresponding supervised and unsupervised approaches.