A malware propagation prediction model based on representation learning and graph convolutional networks

The traditional malware research is mainly based on its recognition and detection as a breakthrough point,without focusing on its propagation trends or predicting the subsequently infected nodes.The complexity of network structure,diversity of network nodes,and sparsity of data all pose difficulties in predicting propagation.This paper proposes a malware propagation prediction model based on representation learning and Graph Convolutional Networks(GCN)to address the aforementioned problems.First,to solve the problem of the inaccuracy of infection intensity calculation caused by the sparsity of node interaction behavior data in the malware propagation network,a mechanism based on a tensor to mine the infection intensity among nodes is proposed to retain the network structure information.The influence of the relationship between nodes on the infection intensity is also analyzed.Second,given the diversity and complexity of the content and structure of infected and normal nodes in the network,considering the advantages of representation learning in data feature extraction,the corresponding representation learning method is adopted for the characteristics of infection intensity among nodes.This can efficiently calculate the relationship between entities and relationships in low dimensional space to achieve the goal of low dimensional,dense,and real-valued representation learning for the characteristics of propagation spatial data.We also design a new method,Tensor2vec,to learn the potential structural features of malware propagation.Finally,considering the convolution ability of GCN for non-Euclidean data,we propose a dynamic prediction model of malware propagation based on representation learning and GCN to solve the time effectiveness problem of the malware propagation carrier.The experimental results show that the proposed model can effectively predict the behaviors of the nodes in the network and discover the influence of different characteristics of nodes on the malware propagation situation.

An elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor

Based on the Cayley-Hamilton theorem and fixed-point method,we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional(3D)inner-product space,which avoids introducing the generating function and Taylor series expansion.The proof is also extended to any finite-dimensional inner-product space.

CANONICAL REPRESENTATIONS AND DEGREE OF FREEDOM FORMULAE OF ORTHOGONAL TENSORS IN N-DIMENSIONAL EUCLIDEAN SPACE

In this paper, with the help of the eigenvalue properties of orthogonal tensors in n-dimensional Euclidean space and the representations of the orthogonal tensors in 2-dimensional space, the canonical representations of orthogonal tensors in n-dimensional Euclidean space are easily gotten. The paper also gives all the constraint relationships among the principal invariants of arbitrarily given orthogonal tensor by use of Cayley-Hamilton theorem; these results make it possible to solve all the eigenvalues of any orthogonal tensor based on a quite reduced equation of m-th order, where m is the integer part ofn \2. Finally, the formulae of the degree of freedom of orthogonal tensors are given.

Explicit Algebraic Stress Model for Three-Dimensional Turbulent Buoyant Flows Derived Using Tensor Representation

An explicit algebraic stress model (EASM) has been formulated for two-dimensional turbulent buoyant flows using a five-term tensor representation in a prior study. The derivation was based on partitioning the buoyant flux tensor into a two-dimensional and a three-dimensional component. The five-term basis was formed with the two-dimensional component of the buoyant flux tensor. As such, the derived EASM is limited to two-dimensional flows only. In this paper, a more general approach using a seven-term representation without partitioning the buoyant flux tensor is used to derive an EASM valid for two- and three-dimensional turbulent buoyant flows. Consequently, the basis tensors are formed with the fully three-dimensional buoyant flux tensor. The derived EASM has the two-dimensional flow as a special case. The matrices and the representation coefficients are further simplified using a four-term representation. When this four-term representation model is applied to calculate two-dimensional homogeneous buoyant flows, the results are essentially identical with those obtained previously using the two-dimensional component of the buoyant flux tensor. Therefore, the present approach leads to a more general EASM formulation that is equally valid for two- and three-dimensional turbulent buoyant flows.

Tensor-Product Representation for Switched Linear Systems

This paper presents the method for the construction of tensor-product representation for multivariate switched linear systems, based on a suitable tensor-product representation of vectors and matrices. We obtain a representation theorem for multivariate switched linear systems. The stability properties of the tensor-product representation are investigated in depth, achieving the important result that any stable switched systems can be constructed a stable tensor-product representation of finite dimension. It is shown that the tensor-product representation provides a high level framework for describing the dynamic behavior. The interpretation of expressions within the tensor-product representation framework leads to enhanced conceptual and physical understanding of switched linear systems dynamic behavior.

张量学习诱导的多视图谱聚类

现有的方法将通过张量奇异值分解(t-SVD)正则化的低秩表示应用到多视图子空间聚类中,取得了令人印象深刻的聚类性能.然而,它们都具有以下两个共同的缺点:(1)他们专注于探索样本之间的关系以构建表征,然后将其堆叠为张量,其计算复杂度至少为O(n2logn);(2)他们总是直接在整合的表征上运行标准的谱聚类算法,而忽略了不同表征对最终聚类结果的先验知识.为了解决这些问题,本文提出了一种新颖的张量学习诱导的多视图谱聚类(TLIMSC)方法,其中同时探索了空间聚类结构和互补信息.具体来说,该方法将关联样本和簇关系的多视图谱嵌入表示堆叠成张量,计算复杂度最终变为O(n logn).然后,将学习到的带有不同自适应置信度的表征与最终的一致聚类结果联系起来.在五个数据集上的广泛实验证明了TLIMSC所具有的有效性和高效性.

四元数矩阵方程(A_(1)XB_(1),…,A_(k)XB_(k))=(C_(1),…,C_(k))的极小范数最小二乘Toeplitz解

基于四元数矩阵实表示,结合矩阵H-表示和矩阵半张量积提出一种求解四元数矩阵方程(A_(1)XB_(1),…,A_(k)XB_(k))=(C_(1),…,C_(k))的极小范数最小二乘Toeplitz解的有效方法,给出该四元数矩阵方程存在Toeplitz解的充要条件及通解表达式.给出数值算法并通过算例分别从误差与计算时间两个方面验证该方法的有效性.

基于张量Tucker分解的高光谱图像异常目标识别

高光谱图像每个像素点的光谱信息包含数百甚至数千个波段,使得高光谱图像在维度上具有高度的复杂性,且由于光谱波段众多,其中存在大量的冗余信息,加大了异常目标识别计算的负担。为此,文中提出基于张量Tucker分解的高光谱图像异常目标识别方法。通过张量Tucker分解压缩高光谱图像后,采用依据高光谱图像数据样本学习的构造方法,构建压缩后高光谱图像的字典,获取高光谱图像数据的稀疏表示形式后,通过RX异常检测方法检测出高光谱图像中的异常目标。实验结果表明:所提方法张量分解重构高光谱图像后,可以缩短压缩时间,减少算法复杂度;重构后的高光谱图像清晰度高,且高光谱图像异常目标检测虚警率低。

基于张量分解嵌入的时序知识图谱推理

针对现有时序知识图谱推理中外推方法没有充分利用时间信息的问题,受张量分解模型的启发,提出将关系嵌入分为静态和动态(时序)2个部分,并通过头实体嵌入、关系嵌入和所有实体嵌入之间的双线性评分函数,计算得到对象实体的概率,从而预测对象实体。最后,在3个数据集上的实验结果验证了该方法的有效性。

An irreducible polynomial functional basis of two-dimensional Eshelby tensors

The two-dimensional (2D) Eshelby tensors are discussed. Based upon the complex variable method, an integrity basis of ten isotropic invariants of the 2D Eshelby tensors is obtained. Since an integrity basis is always a polynomial functional basis, these ten isotropic invariants are further proven to form an irreducible polynomial functional basis of the 2D Eshelby tensors.

FIfth-ORDER ISOTROPIC DESCARTES TENSOR

Fifth-order isotropic descartes tensor and its existence theorem and representation problems are researched, then a general representation formula of fifth-order isotropic descartes tensor is got.

PRINCIPAL AXIS INTRINSIC METHOD AND THE HIGH DIMENSIONAL TENSOR EQUATION AX－XA＝C

The present paper spreads the principal axis intrinsic method to the highdimensional case and discusses the solution of the tensor equation AX --XA = C

F范数度量下的鲁棒张量低维表征

张量主成分分析(Tensor principal component analysis, TPCA)在彩色图像低维表征领域得到广泛深入研究,采用F范数平方作为低维投影的距离度量方式,表征含离群数据和噪声图像的鲁棒性较弱.L1范数能够抑制噪声的影响,但所获的低维投影数据缺乏重构误差约束,其局部表征能力也较弱.针对上述问题,利用F范数作为目标函数的距离度量方式,提出一种基于F范数的分块张量主成分分析算法(Block TPCA withF-norm,BlockTPCA-F),提高张量低维表征的鲁棒性.考虑到同时约束投影距离与重构误差,提出一种基于比例F范数的分块张量主成分分析算法(Block TPCA with proportional F-norm, BlockTPCA-PF),其最大化投影距离与最小化重构误差均得到了优化.然后,给出其贪婪的求解算法,并对其收敛性进行理论证明.最后,对包含不同噪声块和具有实际遮挡的彩色人脸数据集进行实验,结果表明,所提算法在平均重构误差、图像重构与分类率等方面均得到明显提升,在张量低维表征中具有较强的鲁棒性.

基于张量计算的卷积神经网络语义表示学习

卷积神经网络已在多个领域取得了优异的性能表现,然而由于其不透明的内部状态,其可解释性依然面临很大的挑战.其中一个原因是卷积神经网络以像素级特征为输入,逐层地抽取高级别特征,然而这些高层特征依然十分抽象,人类不能直观理解.为了解决这一问题,我们需要表征出网络中隐藏的人类可理解的语义概念.本文通过预先定义语义概念数据集(例如红色、条纹、斑点、狗),得到这些语义在网络某一层的特征图,将这些特征图作为数据,训练一个张量分类器.我们将与分界面正交的张量称为语义激活张量(Semantic Activation Tensors,SATs),每个SAT都指向对应的语义概念.相对于向量分类器,张量分类器可以保留张量数据的原始结构.在卷积网络中,每个特征图中都包含了位置信息和通道信息,如果将其简单地展开成向量形式,这会破坏其结构信息,导致最终分类精度的降低.本文使用SAT与网络梯度的内积来量化语义对分类结果的重要程度,此方法称为TSAT(Testing with SATs).例如,条纹对斑马的预测结果有多大影响.本文以图像分类网络作为解释对象,数据集选取ImageNet,在ResNet50和Inceptionv3两种网络架构上进行实验验证.最终实验结果表明,本文所采用的张量分类方法相较于传统的向量分类方法,在数据维度较大或数据不易区分的情况下,分类精度有显著的提高,且分类的稳定性也更加优秀.这从而保证了本文所推导出的语义激活张量更加准确,进一步确保了后续语义概念重要性量化的准确性.

基于子空间表示和加权低秩张量正则化的高光谱图像混合噪声去除方法

针对高光谱图像中存在混合噪声的问题,提出一种基于子空间表示和加权低秩张量正则化的方法去除高光谱图像中的混合噪声.子空间表示利用光谱频带之间的相关性,选取合适的正交矩阵,将高光谱图像投影到低维子空间中,使提出的算法具有较低的复杂度,简化去噪过程的同时去除图像中的部分噪声.去噪过程基于从简化图像中提取的低秩张量进行,引入加权低秩张量正则化项表征简化图像子空间的先验信息,基于Tucker分解中核范数的物理意义构建合理的加权机制,保留高光谱图像的内在结构相关性.并且设计了一种基于迭代最小化的方法,用于求解提出的非凸去噪模型.在模拟和真实数据集上的实验结果表明,该子空间表示和加权低秩张量正则化方法在定量和定性分析上都取得了较好的去噪效果.

联合低秩张量分解与稀疏表示的高光谱异常目标检测算法

异常目标检测是当前高光谱图像处理中的一个研究热点。针对当前异常目标检测算法存在的问题,从解决高光谱图像中含有的背景、异常目标和噪声等相关量出发,利用高光谱图像的空间谱和光谱特性,提出了联合低秩张量分解和稀疏表示的新的高光谱图像异常目标检测算法。该算法首先利用低秩张量分解模型对高光谱进行图像恢复,使图像质量得到提升,从而使得异常目标变得突出,易于进行目标检测;然后,再利用稀疏差异指数进行异常目标检测,得到需要的异常检测结果;最后,利用真实的高光谱图像进行仿真实验,结果表明,新的异常目标检测算法具有检测精度高、虚警率低和鲁棒性好的特点。

基于矩阵半张量积求解弱双四元数调节方程

基于矩阵半张量积及弱双四元数的实向量表示,将弱双四元数调节方程A_(1)X-A_(2)XB=C转化为无约束的实矩阵方程,利用实矩阵方程得到弱双四元数调节方程的(anti-)Hermitian解,通过数值实验检验了此方法的有效性,并将此方法应用于时变线性系统的连续归零动力学设计.

求解四元数矩阵方程X-AXB=CY+D的一种新方法

提出了四元数矩阵的一种实向量表示法,可以结合矩阵的半张量积研究四元数矩阵方程.给出了四元数矩阵方程X−AXB=CY+D的最小二乘Hermitian解的通解表达式,以及该方程具有Hermitian解的充要条件,通过数值实验,验证该方法的有效性.

Dynamic background modeling using tensor representation and ant colony optimization

Background modeling and subtraction is a fundamental problem in video analysis. Many algorithms have been developed to date, but there are still some challenges in complex environments, especially dynamic scenes in which backgrounds are themselves moving, such as rippling water and swaying trees. In this paper, a novel background modeling method is proposed for dynamic scenes by combining both tensor representation and swarm intelligence. We maintain several video patches, which are naturally represented as higher order tensors,to represent the patterns of background, and utilize tensor low-rank approximation to capture the dynamic nature. Furthermore, we introduce an ant colony algorithm to improve the performance. Experimental results show that the proposed method is robust and adaptive in dynamic environments, and moving objects can be perfectly separated from the complex dynamic background.

低秩张量填充及降噪模型的彩色图像复原方法

现有大多数彩色图像去噪方法分开处理输入图像的彩色通道,利用张量挖掘通道间的相关性,补全带有缺失的彩色图像以及图像去噪.从少部分观测项中恢复一个低秩张量,并且对存在于图像中的各类噪声针对性的去除.对广泛分布于多维成像数据中的非局部自相似性以及稀疏线性逼近中的相似斑块进行分组,通过使用即插即用框架将两者结合.文章提出一种适用于即插即用框架下用块对角表示的张量填充去噪方法,使用去噪算法作为基于模型反演的先验.将全局截断奇异值分解与局部鲁棒主成分分析结合,能够利用更多空间信息,附带不完整信息且含噪声的图像能够完整复原.实验显示使用块对角去噪方式比其他去噪方式在峰值信噪比及结构相似指数上皆有提升,证明该方法是一种精确度较高的方法.