基于Fisher判别分析的增量式非负矩阵分解算法

增量式非负矩阵分解算法是基于子空间降维技术的无监督增量学习方法.文中将Fisher判别分析思想引入增量式非负矩阵分解中,提出基于Fisher判别分析的增量式非负矩阵分解算法.首先,利用初始样本训练的先验信息,通过索引矩阵对新增系数矩阵进行初始化赋值.然后,将增量式非负矩阵分解算法的目标函数改进为批量式的增量学习算法,在此基础上施加类间散度最大和类内散度最小的约束.最后,采用乘性迭代的方法计算分解后的因子矩阵.在ORL、Yale B和PIE等3个不同规模人脸数据库上的实验验证文中算法的有效性.     

基于概率类和不相关判别的半监督局部Fisher 方法

Fisher 判别分析是统计模式识别中经典的有监督维数约简方法, 可以在最大化类间散度的同时最小化类内散度, 但存在分析过程中仅使用有标记数据而忽略无标记数据的问题. 鉴于此, 提出基于概率类和不相关判别的半监督局部Fisher (SLFisher) 方法, 以实现半监督学习的高维映射到低维的类间数据对尽可能地分离, 且类内邻近数据尽可能地紧凑. 采用2 组标准数据集进行实验, 结果表明了SLFisher 方法能够有效提高识别率.     

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.     

基于核正交半监督鉴别分析的人脸识别算法

针对人脸识别中的非线性特征提取和有标记样本不足问题,提出了在核空间具有正交性半监督鉴别矢量的计算方法。算法利用核函数将人脸数据映射到高维非线性空间,在该空间采用边界Fisher判别分析（Marginal Fisher Analysis,MFA）算法将少量有类别标签样本进行降维,同时采用无监督鉴别投影（Unsupervised Discriminant Projection,UDP）对大量无标签样本进行学习,以半监督的方法构造算法的目标函数,在特征值求解时以正交方式找出最优投影向量,进行人脸识别。通过实验,在ORL和YALE人脸数据库上验证了该算法的有效性。     

基于张量的半监督判别分析算法

边界Fisher判别分析算法因采用一维向量表示而无法很好保持图像的空间几何结构,且无法利用大量未标记样本信息.为此,提出一种基于张量的半监督判别分析算法.采用二维张量表示人脸空间中的样本图像,揭示流形的内在几何结构,利用有判别信息的标记样本和大量未标记样本,使数据在投影空间的类间分离度最大,同时保证高维空间中不相邻的点在低维空间中也不相邻.在PIE和FERET人脸库上的实验结果表明,该算法能够获得较高的识别率.     

一种自适应邻域选择半监督判别分析算法

为克服边界Fisher判别分析(MFA)只利用少量有标记样本和构建邻域不能充分反映流形学习对邻域要求的缺点,提出一种基于局部线性结构的自适应邻域选择半监督判别分析的算法。采用自适应算法扩大或者缩小近邻系数k来构建邻域以保持局部线性结构。MFA通过少量有类别标签样本进行降维的同时UDP对大量无标签样本进行学习,以半监督的方法对高维人脸数据进行维数约减。最后,在ORL和YALE人脸数据库通过实验结果验证了该算法的有效性。     

一种基于离散度平衡的降维算法

已有的监督维数约简算法大都通过最大化类间离散度总和等相关手段选取判别能力较强的子空间,使得原始空间中距离较小的一些类易被忽略而在子空间中出现不同类的融合现象.为此,提出一种基于离散度平衡的降维算法——离散度平衡投影.该算法利用对称相对熵来衡量样本间的离散度,将对称相对熵与离散度平衡的概念结合,使得算法在降维过程中保持较大类间离散度的同时更加注重较小的类间离散度,以实现类间散度平衡的目的;为了充分使用现实生活中大量无标签样本,通过保持所有样本间拉普拉斯图结构进一步提出了半监督离散度平衡投影.对Soybean,Isolet,COIL20等标准数据集进行维数约简的实验结果表明,文中算法具有较好的降维效果.     

人脸识别中适合于小样本情况下的监督化拉普拉斯判别分析

提取有效特征对高维数据的模式分类起着关键的作用.无监督判别投影,通过最大化非局部散度和局部散度之比,在数据降维和特征提取上表现出较好的性能,但是它是一种非监督学习算法,并且存在小样本问题.针对这些问题,提出了监督化拉普拉斯判别分析,算法在考虑非局部散度和局部散度时考虑了样本的类别信息;通过丢弃总体拉普拉斯散度矩阵的零空间,并将类内拉普拉斯散度矩阵投影到总体拉普拉斯散度矩阵的主空间中,然后在该空间中进行特征问题的求解,从而避免了小样本问题.通过理论分析,该算法没有任何判别信息损失,同时在计算上效率也较高.在人脸识别上的实验验证了算法的正确性和有效性.     

基于矩阵指数变换的边界Fisher分析

边界Fisher分析是一种经典的有监督线性降维方法,被广泛用于高维数据的模式分类.由于边界Fisher分析算法中涉及到矩阵求逆的运算,在数值计算中会产生矩阵的奇异性问题,尤其当样本的个数小于样本的维数时,导致所谓的"小样本问题".采用主成分分析方法对样本数据进行预处理可以克服奇异性问题,然而可能会损失样本的某些判别信息.针对此不足之处,根据矩阵指数的非奇异性,对边界Fisher分析中的散度矩阵进行矩阵指数变换,从而克服了矩阵求逆中的奇异性问题.理论分析表明,该方法等价于零空间上的边界Fisher分析,有效利用了类内散度矩阵的零空间上的信息,因此其判别能力得到了增强.数据可视化和人脸识别实验表明,该方法可以有效挖掘样本中潜在的判别特性,提高分类性能.     

正交及不相关边界邻域保持嵌入的人脸识别

邻域保持嵌入(NPE)算法本质上仍是一种无监督方法,并没有有效利用已有的类别信息提高分类效率。为此提出两种有监督流形学习方法：正交边界邻域保持嵌入(OMNPE)和不相关边界邻域保持嵌入(UMNPE)。首先构造类内和类间邻接图,并定义类内和类间重构误差;然后分别在正交和不相关约束条件下寻找最小化类内重构误差同时最大化类间重构误差的投影向量;将训练样本和测试样本分别投影到低维子空间中,再利用最近邻分类器进行分类识别。在ORL和Yale人脸库上的实验结果表明,与线性判别分析(LDA)、边界Fisher分析(MFA)等子空间人脸识别算法相比,所提算法的平均识别率提高了0.5%~3%,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.     

Semi-supervised local Fisher discriminant analysis for dimensionality reduction

When only a small number of labeled samples are available, supervised dimensionality reduction methods tend to perform poorly because of overfitting. In such cases, unlabeled samples could be useful in improving the performance. In this paper, we propose a semi-supervised dimensionality reduction method which preserves the global structure of unlabeled samples in addition to separating labeled samples in different classes from each other. The proposed method, which we call SEmi-supervised Local Fisher discriminant analysis (SELF), has an analytic form of the globally optimal solution and it can be computed based on eigen-decomposition. We show the usefulness of SELF through experiments with benchmark and real-world document classification datasets.     

Enhanced semi-supervised local Fisher discriminant analysis for face recognition

An improved manifold learning method, called enhanced semi-supervised local Fisher discriminant analysis (ESELF), for face recognition is proposed. Motivated by the fact that statistically uncorrelated and parameter-free are two desirable and promising characteristics for dimension reduction, a new difference-based optimization objective function with unlabeled samples has been designed. The proposed method preserves the manifold structure of labeled and unlabeled samples in addition to separating labeled samples in different classes from each other. The semi-supervised method has an analytic form of the globally optimal solution and it can be computed based on eigen decomposition. Experiments on synthetic data and AT&T, Yale and CMU PIE face databases are performed to test and evaluate the proposed algorithm. The experimental results and comparisons demonstrate the effectiveness of the proposed method.     

基于成对约束的非线性维数约减框架

半监督维数约简是指借助于辅助信息与大量无标记样本信息从高维数据空间找到一个最优低维判别空间,便于后续的分类或聚类操作,它被看作是理解基因序列、文本与人脸图像等高维数据的有效方法。提出一个基于成对约束的半监督维数约简一般框架（SSPC）。该方法首先通过使用成对约束和无标号样本的内在几何结构学习一个判别邻接矩阵;其次,新方法应用学到的投影将原来高维空间中的数据映射到低维空间中,以至于聚类内的样本之间距离变得更加紧凑,而不同聚类间的样本之间距离变得尽可能得远。所提出的算法不仅能找到一个最佳的线性判别子空间,还可以揭示流形数据的非线性结构。在一些真实数据集上的实验结果表明,新方法的性能优于当前主流基于成对约束的维数约简算法的性能。     

A unified dimensionality reduction framework for semi-paired and semi-supervised multi-view data

Canonical correlation analysis (CCA) is a popular and powerful dimensionality reduction method to analyze paired multi-view data. However, when facing semi-paired and semi-supervised multi-view data which widely exist in real-world problems, CCA usually performs poorly due to its requirement of data pairing between different views and un-supervision in nature. Recently, several extensions of CCA have been proposed, however, they just handle the semi-paired scenario by utilizing structure information in each view or just deal with semi-supervised scenario by incorporating the discriminant information. In this paper, we present a general dimensionality reduction framework for semi-paired and semi-supervised multi-view data which naturally generalizes existing related works by using different kinds of prior information. Based on the framework, we develop a novel dimensionality reduction method, termed as semi-paired and semi-supervised generalized correlation analysis (S²GCA). S²GCA exploits a small amount of paired data to perform CCA and at the same time, utilizes both the global structural information captured from the unlabeled data and the local discriminative information captured from the limited labeled data to compensate the limited pairedness. Consequently, S²GCA can find the directions which make not only maximal correlation between the paired data but also maximal separability of the labeled data. Experimental results on artificial and four real-world datasets show its effectiveness compared to the existing related dimensionality reduction methods.     

Semi-supervised orthogonal discriminant analysis via label propagation

Trace ratio is a natural criterion in discriminant analysis as it directly connects to the Euclidean distances between training data points. This criterion is re-analyzed in this paper and a fast algorithm is developed to find the global optimum for the orthogonal constrained trace ratio problem. Based on this problem, we propose a novel semi-supervised orthogonal discriminant analysis via label propagation. Differing from the existing semi-supervised dimensionality reduction algorithms, our algorithm propagates the label information from the labeled data to the unlabeled data through a specially designed label propagation, and thus the distribution of the unlabeled data can be explored more effectively to learn a better subspace. Extensive experiments on toy examples and real-world applications verify the effectiveness of our algorithm, and demonstrate much improvement over the state-of-the-art algorithms.     

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。     

Semi-supervised locally discriminant projection for classification and recognition

Semi-supervised dimensional reduction methods play an important role in pattern recognition, which are likely to be more suitable for plant leaf and palmprint classification, since labeling plant leaf and palmprint often requires expensive human labor, whereas unlabeled plant leaf and palmprint is far easier to obtain at very low cost. In this paper, we attempt to utilize the unlabeled data to aid plant leaf and palmprint classification task with the limited number of the labeled plant leaf or palmprint data, and propose a semi-supervised locally discriminant projection (SSLDP) algorithm for plant leaf and palmprint classification. By making use of both labeled and unlabeled data in learning a transformation for dimensionality reduction, the proposed method can overcome the small-sample-size (SSS) problem under the situation where labeled data are scant. In SSLDP, the labeled data points, combined with the unlabeled data ones, are used to construct the within-class and between-class weight matrices incorporating the neighborhood information of the data set. The experiments on plant leaf and palmprint databases demonstrate that SSLDP is effective and feasible for plant leaf and palmprint classification.     

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．