具有统计不相关性的核化图嵌入算法

提出统计不相关的核化图嵌入算法,为求解各种统计不相关的核化降维算法提供了一种统一方法。与已有核化降维算法相比,新的特征提取方法降低甚至消除了最佳鉴别矢量间的统计相关性,提高了识别率。通过在ORL,YALE和FERET人脸库上的实验结果表明,提出的具有统计不相关的核化图嵌入算法在识别率方面好于已有的核算法。另外,揭示了统计不相关的核化图嵌入与已有的核化图嵌入的内在关系。     

高效求解方法的核典型相关分析算法

针对高维小样本数据在核化图嵌入过程中出现的复杂度问题,引入基于核化图嵌入(kernel extension of graph embedding)的快速求解模型,提出了一种新的KGE/CCA算法(KGE/CCA-S_t)。首先将样本数据投影到维数远低于原样本空间维数的总体散度矩阵对应的秩空间,然后采用核典型相关分析进行特征提取,整个过程减少了核矩阵的计算量。在Yale人脸库和JAFFE人脸库上进行仿真实验,结果表明这种KGE/CCA算法的识别率明显优于KFD、KLPP和KNPE算法的识别率;和传统的KGE/CCA算法相比,在不影响识别率的情况下,KGE/CCA-S_t算法有效减少了计算时间。     

基于核函数的谱嵌入聚类算法

谱嵌入聚类(SEC)算法要求样本满足流形假设,样本标签总是可以嵌入到一个线性空间中去,这为线性可分数据的谱嵌入聚类问题提供了新的思路,但该算法使用的线性映射函数不适用于处理高维非线性数据。针对这一问题,通过核化线性映射函数,建立了基于核函数的谱嵌入聚类(KSEC)模型,该模型既能解决线性映射函数不能处理非线性数据的问题,又实现了对高维数据的核降维。在真实数据集上的实验分析结果表明,使用所提算法后聚类正确率平均提高了13.11%,最高可提高31.62%,特别在高维数据上平均提高了16.53%,而且在算法关于参数的敏感度实验中发现算法的稳定性更好。所以改进后的算法对高维非线性数据具有很好的聚类效果,获得了比传统谱嵌入聚类算法更高的聚类准确率和更好的聚类性能。所提方法可以用于诸如遥感影像这类复杂图像的处理领域。     

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.     

针对恶意JavaScript识别的降维方法

针对将JavaScript代码N-gram处理后识别算法特征维度较高的问题,提出一种高效的降维方法。该方法利用TF-IDF-like模型分别计算特征在正常样本和恶意样本中的权重,基于特征权重在两类样本中的差异度进行降维。基于多个识别算法,将提出的降维方法与基于主成分分析（Principal Component Analysis,PCA）的降维方法进行比较,实验结果表明：当识别算法维度相同时,基于本文所给降维方法的识别算法在识别效果方面优于基于PCA的识别算法;当降维后识别算法的维度超过某个阈值时,随着识别算法维度的增长,本降维方法的时间开销增长速率远低于PCA方法。     

新的局部线性嵌入下的人脸识别方法

针对LLE算法无法对后续采集的测试样本单独进行降维处理和未能利用样本点分类信息的两点不足之处,提出了一种有监督的增量式局部线性嵌入算法（SILLE）,并采取小波变换对图像进行预处理。通过对ORL数据库实验证明,SILLE算法与LLE算法相比大大降低了处理新增样本点的计算时间,并且提高了识别精度。     

基于图嵌入和最大互信息组合的降维

在特征降维方面,图嵌入框架统一了PCA,LDA等一系列特征降维算法,方便求解,但相似度矩阵计算有赖于人为假设.而最大互信息(MMI)从信息论的角度得到有效的特征降维变换,但是求解复杂.针对这种情况,本文指出了图嵌入和最大互信息的联系,给出了基于两者组合的新算法GE-MMI.该算法继承了两者的优点,是一种有效的特征降维方法.     

一种深度自监督聚类集成算法

针对聚类集成中一致性函数设计问题,本文提出一种深度自监督聚类集成算法。该算法首先根据基聚类划分结果采用加权连通三元组算法计算样本之间的相似度矩阵,基于相似度矩阵表达邻接关系,将基聚类由特征空间中的数据表示变换至图数据表示;在此基础上,基聚类的一致性集成问题被转化为对基聚类图数据表示的图聚类问题。为此,本文利用图神经网络构造自监督聚类集成模型,一方面采用图自动编码器学习图的低维嵌入,依据低维嵌入似然分布估计聚类集成的目标分布;另一方面利用聚类集成目标对低维嵌入过程进行指导,确保模型获得的图低维嵌入与聚类集成结果是一致最优的。在大量数据集上进行了仿真实验,结果表明本文算法相比HGPA、CSPA和MCLA等算法可以进一步提高聚类集成结果的准确性。     

基于局部线性嵌入的免疫检测器优化生成算法

网络安全已上升到国家安全战略层面,入侵检测技术是其重要的组成部分,已得到广泛关注.在基于免疫的入侵检测研究中,针对传统实值否定选择算法不利于高效分析数据而造成的检测器生成速度慢、检测效率低等问题,引入局部线性嵌入算法,借鉴其能对高维数据进行映射降维的特点,提出一种基于局部线性嵌入的免疫检测器优化生成算法,利用局部线性嵌入对高维数据预处理优化降维,并结合实值否定选择算法生成检测器.将该算法用于检测模型,从而提升检测器的生成速率,并可保证生成的检测器高效地处理高维数据.该算法在降维前后可保证样本的局部线性结构不变,具有可变参数少、计算时间短的特点.实验结果表明,所提出算法在显著提高检测器生成速率和对数据检测效率的基础上,检测性能也表现出很好的水平.     

基于核化图嵌入的最佳鉴别分析与人脸识别

将压缩映射和同构映射引入核化图嵌入框架(kernel extension of graph embedding,简称KGE),从理论上证明了KGE框架内的各种核算法其实质是KPCA(kernel principal component analysis)+LGE(linear extension of graph embedding,简称LGE)框架内的线性降维算法,并且基于所给出的理论框架提出了一种综合利用零空间和非零空间鉴别信息的组合方法.任何一种可以用核化图嵌入框架描述的核算法,都可以有相应的组合方法.在ORL,Yale,FERET和PIE人脸数据库上验证了所提出的理论和方法的有效性.     

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     

基于Beta分布和半监督学习的非确定性知识图谱嵌入模型

近年来,面向确定性知识图谱的嵌入模型在知识图谱补全等任务中取得了长足的进展,但如何设计和训练面向非确定性知识图谱的嵌入模型仍然是一个重要挑战。不同于确定性知识图谱,非确定性知识图谱的每个事实三元组都有着对应的置信度,因此,非确定性知识图谱嵌入模型需要准确地计算出每个三元组的置信度。现有的非确定性知识图谱嵌入模型结构较为简单,只能处理对称关系,并且无法很好地处理假负(false-negative)样本问题。为了解决上述问题,该文首先提出了一个用于训练非确定性知识图谱嵌入模型的统一框架,该框架使用基于多模型的半监督学习方法训练非确定性知识图谱嵌入模型。为了解决半监督学习中半监督样本噪声过高的问题,我们还使用蒙特卡洛Dropout计算出模型对输出结果的不确定度,并根据该不确定度有效地过滤了半监督样本中的噪声数据。此外,为了更好地表示非确定性知识图谱中实体和关系的不确定性以处理更复杂的关系,该文还提出了基于Beta分布的非确定性知识图谱嵌入模型UBetaE,该模型将实体、关系均表示为一组相互独立的Beta分布。在公开数据集上的实验结果表明,结合该文所提出的半监督学习方法和UBetaE模型,不仅极大地缓解了假负样本问题,还在多个任务中明显优于UKGE等当前最优的非确定性知识图谱嵌入模型。     

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.     

Geometric characterization and clustering of graphs using heat kernel embeddings

In this paper, we investigate the use of heat kernels as a means of embedding the individual nodes of a graph in a vector space. The reason for turning to the heat kernel is that it encapsulates information concerning the distribution of path lengths and hence node affinities on the graph. The heat kernel of the graph is found by exponentiating the Laplacian eigensystem over time. In this paper, we explore how graphs can be characterized in a geometric manner using embeddings into a vector space obtained from the heat kernel. We explore two different embedding strategies. The first of these is a direct method in which the matrix of embedding co-ordinates is obtained by performing a Young–Householder decomposition on the heat kernel. The second method is indirect and involves performing a low-distortion embedding by applying multidimensional scaling to the geodesic distances between nodes. We show how the required geodesic distances can be computed using parametrix expansion of the heat kernel. Once the nodes of the graph are embedded using one of the two alternative methods, we can characterize them in a geometric manner using the distribution of the node co-ordinates. We investigate several alternative methods of characterization, including spatial moments for the embedded points, the Laplacian spectrum for the Euclidean distance matrix and scalar curvatures computed from the difference in geodesic and Euclidean distances. We experiment with the resulting algorithms on the COIL database.     

Regularized locality preserving discriminant embedding for face recognition

For face recognition, graph embedding techniques attempt to produce a high data locality projection for better recognition performance. However, estimation of population data locality could be severely biased due to small number of training samples. The biased estimation triggers overfitting problem and hence poor generalization. In this paper, we propose a new linear graph embedding technique based upon an adaptive locality preserving regulation model (ALPRM), known as Regularized Locality Preserving Discriminant Embedding (RLPDE). In RLPDE, the projection features are regulated based on ALPRM to approach population data locality, which can directly enhance the locality preserving capability of the projection features. This paper also presents the relation between locality preserving capability and class discrimination. Specifically, we show that the optimization of the locality preserving function minimizes the within-class variability. Experiments on three face datasets such as PIE, FRGC and FERET show the promising performance of the proposed technique.     

基于高斯分布监督学习样本的Fisher核构造方法

结合实际应用背景, 针对各类样本服从高斯分布的监督学习情形, 提出了构造Fisher核的新方法. 由于利用了样本中的类别信息, 该方法用极大似然估计代替EM算法估计GMM参数, 有效降低了Fisher核构造的时间复杂度. 结合核Fisher分类法, 上述方法在标准人脸库上的仿真实验结果显示, 用所提方法所构造的Fisher核不仅时间复杂度低, 且识别率也优于传统的高斯核与多项式核. 本文的研究有利于将Fisher 核的应用从语音识别领域拓展到图像识别等领域.     

基于路径签名的改进时空图卷积网络

针对时空图卷积网络ST-GCN中GCN的关节邻接图不易学习远端关节之间的语义信息和TCN在描述时间信息方面存在不足的问题,引入了数字签名预处理来增强数据,提出了基于路径签名的改进时空图卷积网络SSIT-GCN。首先将关节位置坐标的时间序列输入签名层进行数据预处理,在该层时间序列通过嵌入算法被转换为多维路径,将其划分为多条路径并计算每条路径的签名特征;其次重新设计GCN的关节邻接矩阵,并用反卷积来代替补零,以保持TCN的尺寸不变,还引入1×1的卷积核增加非线性来改进ST-GCN,得到改进时空图卷积网络SIT-GCN;最后用签名特征代替原始数据输入SIT-GCN,得到最终的输出结果。实验结果表明,基于路径签名的改进时空图卷积网络大大提高了训练精度,缩短了训练时间,对动态手势识别有较好的识别能力和识别速度。