浅谈基于PCA的网络流量分析

网络流量的特性分析一直是通信网络性能分析的一个极其重要的问题。本文主要采用主成分分析(PCA)的方法对采样到的网络流量数据进行分析,发现这些流量数据呈现低维特性,仿真结果证明该方法可行。     

Iterative kernel principal component analysis for image modeling

In recent years, Kernel Principal Component Analysis (KPCA) has been suggested for various image processing tasks requiring an image model such as, e.g., denoising or compression. The original form of KPCA, however, can be only applied to strongly restricted image classes due to the limited number of training examples that can be processed. We therefore propose a new iterative method for performing KPCA, the Kernel Hebbian Algorithm which iteratively estimates the Kernel Principal Components with only linear order memory complexity. In our experiments, we compute models for complex image classes such as faces and natural images which require a large number of training examples. The resulting image models are tested in single-frame super-resolution and denoising applications. The KPCA model is not specifically tailored to these tasks; in fact, the same model can be used in super-resolution with variable input resolution, or denoising with unknown noise characteristics. In spite of this, both super-resolution and denoising performance are comparable to existing methods.     

Kernel PCA for Feature Extraction and De-Noising in Nonlinear Regression

In this paper, we propose the application of the Kernel Principal Component Analysis (PCA) technique for feature selection in a high-dimensional feature space, where input variables are mapped by a Gaussian kernel. The extracted features are employed in the regression problems of chaotic Mackey–Glass time-series prediction in a noisy environment and estimating human signal detection performance from brain event-related potentials elicited by task relevant signals. We compared results obtained using either Kernel PCA or linear PCA as data preprocessing steps. On the human signal detection task, we report the superiority of Kernel PCA feature extraction over linear PCA. Similar to linear PCA, we demonstrate de-noising of the original data by the appropriate selection of various nonlinear principal components. The theoretical relation and experimental comparison of Kernel Principal Components Regression, Kernel Ridge Regression and ε-insensitive Support Vector Regression is also provided.     

Structural analysis of network traffic matrix via relaxed principal component pursuit

The network traffic matrix is widely used in network operation and management. It is therefore of crucial importance to analyze the components and the structure of the network traffic matrix, for which several mathematical approaches such as Principal Component Analysis (PCA) were proposed. In this paper, we first argue that PCA performs poorly for analyzing traffic matrix that is polluted by large volume anomalies, and then propose a new decomposition model for the network traffic matrix. According to this model, we carry out the structural analysis by decomposing the network traffic matrix into three sub-matrices, namely, the deterministic traffic, the anomaly traffic and the noise traffic matrix, which is similar to the Robust Principal Component Analysis (RPCA) problem previously studied in [13]. Based on the Relaxed Principal Component Pursuit (Relaxed PCP) method and the Accelerated Proximal Gradient (APG) algorithm, we present an iterative approach for decomposing a traffic matrix, and demonstrate its efficiency and flexibility by experimental results. Finally, we further discuss several features of the deterministic and noise traffic. Our study develops a novel method for the problem of structural analysis of the traffic matrix, which is robust against pollution of large volume anomalies.     

Maximum and Minimum Likelihood Hebbian Learning for Exploratory Projection Pursuit

In this paper, we review an extension of the learning rules in a Principal Component Analysis network which has been derived to be optimal for a specific probability density function. We note that this probability density function is one of a family of pdfs and investigate the learning rules formed in order to be optimal for several members of this family. We show that, whereas we have previously (Lai et al., 2000; Fyfe and MacDonald, 2002) viewed the single member of the family as an extension of PCA, it is more appropriate to view the whole family of learning rules as methods of performing Exploratory Projection Pursuit. We illustrate this on both artificial and real data sets.     

基于BP神经网络的景象匹配算法

针对以可见光图像为基准、红外图像为实测的景象匹配问题,提出了一种基于BP神经网络的景象匹配方法。该方法首先抽取满足平移、旋转、尺度不变性的Krawtchouk不变矩作为红外目标的特征描述并构造特征向量,随后,基于主分量分析法消除特征向量各个分量间的相关性,去掉多个对目标匹配识别贡献不大的特征的影响,形成描述目标的有效特征向量。接下来,构造三层BP神经网络,以有效匹配特征作为输入,匹配位置作为输出,按照经验公式确定隐层节点个数,基于样本集对红外目标在可见光基准图像中的匹配过程进行训练,最终形成智能化景象匹配识别器。实验结果表明,与常用的景象匹配算法相比,提出方法不仅具有更高的匹配精度和速度,而且鲁棒性好,能抵抗实测图像的旋转几何畸变。     

一种基于张量PCA的人耳识别的改进方法

张量主成分分析是一种新的主元分析方法,可以解决传统PCA方法对图像进行降维时出现的问题。小波变换具有良好的时频分析特性,同时还能起到降维的作用。综合利用这两个方法的优点,提出了一种基于张量PCA的人耳识别新方法。该方法对人耳图像采用小波变换做预处理得到4个子带图像,对其中“LL”低频子带图像用张量PCA进行特征提取,用支持向量机的方法进行识别。实验结果表明,利用此方法与传统主成分分析识别相比,提高了识别率,缩短了识别时间。在USTB人耳库上实验,该方法的识别率比传统PCA方法提高了6%,识别时间为传统PCA方法的35.23%。     

Use of an artificial model of monitoring data to aid interpretation of principal component analysis

An artificial data matrix of element concentrations at sampling locations was created which included six simulated gradients of correlated variables (Ca+Mg, Ni+V, Pb+Cu+Zn, Cd, Fe and K), representing a simplified model of a National survey. The data matrix model was used to explore the efficiency with which Principal Components Analysis (PCA), without and with Varimax rotation, could derive the imposed gradients. The dependence of PCA on outliers was decreased by log-transformation of data. The Components derived from non-rotated PCA were confounded by bipolar clusters and oblique gradients, both resulting in superimposition of two independent gradients on one Component. Therefore, erroneous interpretation of results could result from assessment of variable loadings on Components, without assessment of coupled independent gradients. Varimax rotation greatly improved the results, by rotation of too few Components led to the same problems, and rotation of too many Components led to fragmentation of correlated variables onto single-element Components. The best configuration matching the original model could be selected after investigation of element concentrations superimposed on sample ordinations.     

Cloth and Skin Deformation with a Triangle Mesh Based Convolutional Neural Network

We introduce a triangle mesh based convolutional neural network. The proposed network structure can be used for problems where input and/or output are defined on a manifold triangle mesh with or without boundary. We demonstrate its applications in cloth upsampling, adding back details to Principal Component Analysis (PCA) compressed cloth, regressing clothing deformation from character poses, and regressing hand skin deformation from bones' joint angles. The data used for training in this work are generated from high resolution extended position based dynamics (XPBD) physics simulations with small time steps and high iteration counts and from an offline FEM simulator, but it can come from other sources. The inference time of our prototype implementation, depending on the mesh resolution and the network size, can provide between 4 to 134 times faster than a GPU based simulator. The inference also only needs to be done for meshes currently visible by the camera.     

非线性和非高斯性共存的序批次反应处理过程故障诊断

序批式反应器(SBR)的处理过程的数据具有非高斯分布和高度非线性的特点,传统特征提取方法在进行特征提取时仅仅考虑信息最大化而忽略数据的簇结构信息导致数据特征提取的不完整.由于多向核熵成分分析是一种新的监测方法,在监测过程中的应用表明能够克服传统监测方法的缺陷,减少误报警率.因此本文结合多向核熵成分分析的的优势,提出多向核熵独立成分分析方法用于SBR过程监测及故障诊断.首先,将三维SBR过程数据利用一种新的数据展开技术变为二维数据;其次,利用核熵成分分析将展开后的二维数据映射到高维空间用独立成分分析进行独立成分提取;最后提出一种基于多向核熵独立成分分析的故障诊断方法进行故障诊断.将该方法和传统方法应用于80升的SBR处理过程的监测结果表明,本文提出的方法优于传统的多向独立成分分析方法.     

基于PPI网络与机器学习的蛋白质功能预测方法

针对现有的基于蛋白质相互作用（PPI）网络的蛋白质功能预测方法预测精度不高、易受数据噪声影响的问题,提出一种基于机器学习（层次聚类、主成分分析和多层感知器）的蛋白质功能预测方法HPMM。该方法综合考虑蛋白质宏观和微观层面的信息,将蛋白质家族、结构域和重要位点信息作为顶点属性整合到PPI网络中以减轻网络中数据噪声的影响。首先,基于层次聚类和主成分分析进行特征提取,得到功能模块和属性主成分特征,然后训练多层感知器模型,建立多特征与多功能之间的映射关系以用于功能预测。在三个分别被分子功能（MF）、生物过程（BP）和细胞组件（CC）注释的人类PPI网络上进行测试,对HPMM、余弦迭代算法（CIA）和有向PPI网络基因本体术语传播（GoDIN）算法的功能预测效果进行比较分析。实验结果表明,相比CIA和GoDIN这两种完全基于PPI网络的方法,HPMM的精确度与F值更高。     

图像矩阵上的广义最大噪声分离算法

主成分分析（PCA）是模式识别中一种重要的变换工具,在图像处理的特征提取和降维方面有广泛的应用。然而,由于二维图像数据需要进行向量化处理,导致高维向量的产生和像素空间位置丢失。广义主成分分析（GPCA）则是基于图像矩阵的主成分分析推广算法,它不改变像素间的空间位置关系,而且计算量也显著降低。但主成分分析和广义主成分分析都没有考虑到实际图像中存在的噪声干扰。最大噪声分离（MNF）则是一种面向噪声干扰的变换方法,与主成分分析基于方差的最大化不同,最大噪声分离是基于信噪比的最大化。与GPCA的推广类似,在图像二维矩阵上推广最大噪声分离方法,提出一种广义最大噪声分离（GMNF）算法。该变换方法在保证重构时信噪比最大的同时,也具有不改变像素空间位置、计算量小的优点。在人脸和红外图像上的仿真实验结果验证了所提算法的有效性。     

Independent complexity patterns in single neuron activity induced by static magnetic field

We applied a combination of fractal analysis and Independent Component Analysis (ICA) method to detect the sources of fractal complexity in snail Br neuron activity induced by static magnetic field of 2.7 mT. The fractal complexity of Br neuron activity was analyzed before (Control), during (MF), and after (AMF) exposure to the static magnetic field in six experimental animals. We estimated the fractal dimension (FD) of electrophysiological signals using Higuchi's algorithm, and empirical FD distributions. By using the Principal Component Analysis (PCA) and FastICA algorithm we determined the number of components, and defined the statistically independent components (ICs) in the fractal complexity of signal waveforms. We have isolated two independent components of the empirical FD distributions for each of three groups of data by using FastICA algorithm. ICs represent the sources of fractal waveforms complexity of Br neuron activity in particular experimental conditions. Our main results have shown that there could be two opposite intrinsic mechanisms in single snail Br neuron response to static magnetic field stimulation. We named identified ICs that correspond to those mechanisms - the component of plasticity and the component of elasticity. We have shown that combination of fractal analysis with ICA method could be very useful for the decomposition and identification of the sources of fractal complexity of bursting neuronal activity waveforms.     

卷积鲁棒主成分分析

鲁棒主成分分析（RPCA）是一种经典的高维数据分析方法,可从带噪声的观测样本中恢复出原始数据。但是,RPCA能工作的前提是目标数据拥有低秩矩阵结构,不能有效处理实际应用中广泛存在的非低秩数据。研究发现,虽然图像、视频等数据矩阵本身可能不是低秩的,但它们的卷积矩阵通常是低秩的。根据这一原理,提出一种称为卷积鲁棒主成分分析（CRPCA）的新方法,利用卷积矩阵的低秩性对原始数据的结构进行约束,从而实现精确的数据恢复。CPRCA模型的计算过程是一个凸优化问题,通过乘子交替方向法（ADMM）来进行求解。通过对合成数据向量以及真实数据图片、视频序列进行实验,验证了该方法相较于其他算法如RPCA、广义鲁棒主成分分析（GRPCA）以及核鲁棒主成分分析（KRPCA）在处理数据非低秩问题上优越性。     

A comparison of three methods for principal component analysis of fuzzy interval data

Vertices Principal Component Analysis (V-PCA), and Centers Principal Component Analysis (C-PCA) generalize Principal Component Analysis (PCA) in order to summarize interval valued data. Neural Network Principal Component Analysis (NN-PCA) represents an extension of PCA for fuzzy interval data. However, also the first two methods can be used for analyzing fuzzy interval data, but they then ignore the spread information. In the literature, the V-PCA method is usually considered computationally cumbersome because it requires the transformation of the interval valued data matrix into a single valued data matrix the number of rows of which depends exponentially on the number of variables and linearly on the number of observation units. However, it has been shown that this problem can be overcome by considering the cross-products matrix which is easy to compute. A review of C-PCA and V-PCA (which hence also includes the computational short-cut to V-PCA) and NN-PCA is provided. Furthermore, a comparison is given of the three methods by means of a simulation study and by an application to an empirical data set. In the simulation study, fuzzy interval data are generated according to various models, and it is reported in which conditions each method performs best.     

基于动态主元分析的空分过程异常工况在线诊断

空分过程异常工况的在线诊断对于保证空分产品质量、降低"氮塞"等故障的发生率和减小故障损失有着重要的实用价值。主元分析(PCA)是1种数据驱动的统计建模方法,已广泛应用于复杂工业过程的运行状态监控和故障诊断,然而,传统的PCA方法不能够反应数据的动态特性。动态主元分析(DPCA)作为1种将传统PCA推广到多变量动态过程的方法,其时滞长度的确定是DPCA的关键点。本文应用动态主元分析(DPCA)方法建立了空分过程异常工况的在线诊断系统,并结合空分过程的故障诊断特性,对DPCA中时滞长度提出了可行的确定方法。实际运行效果表明该系统对故障的报警率为100%,误报率约4%,证明了文中所建立的诊断系统的有效性及文中所提出的对于复杂连续生产系统确定DPCA时滞长度的方法的有效性及可行性。     

基于对称线性判别分析算法的人脸识别

小样本问题的存在使得类内离散度矩阵为奇异阵,因此求解线性判别分析(LDA)算法的广义特征方程存在病态奇异问题。为解决此问题,在已有算法的基础上,引入镜像图像来扩大样本容量,并采用零空间的方法求得Fisher准则函数的最优解。通过在ORL和Yale标准人脸库上的实验结果表明,人脸识别效果优于传统LDA方法、独立成分分析(ICA)方法以及二维对称主成分分析(2DSPCA)方法。     

Contrast and Change in the Idiolects of Ben Jonson Characters

The paper presents the results of a series of Principal Components Analyses of the frequencies of very common words in the dialogue of characters in plays by Ben Jonson. The first Principal Component in the data, the most important axis of differentiation, proves in each case to be a spectrum from elaborate, authoritative pronouncements to a dialogue style of reaction and interchange. Reference to other quantitative studies, literary and otherwise, suggests that a version of this axis may often be among the most important in stylistic difference generally. In Jonson it has a chronological aspect -- there is a shift over his career from one end to the other -- and there is often significant change within the idiolects of his characters as well. Successive segments of Volpone and Mosca's parts (they are protagonist and antagonist of Volpone, perhaps Jonson's best-known comedy) change markedly along this axis, beginning far apart but coming by the end of the play to resemble each other very closely on this measure. This revised version was published online in July 2006 with corrections to the Cover Date.     

Contrast and Change in the Idiolects of Ben Jonson Characters

The paper presents the results of a series of Principal Components Analyses of the frequencies of very common words in the dialogue of characters in plays by Ben Jonson. The first Principal Component in the data, the most important axis of differentiation, proves in each case to be a spectrum from elaborate, authoritative pronouncements to a dialogue style of reaction and interchange. Reference to other quantitative studies, literary and otherwise, suggests that a version of this axis may often be among the most important in stylistic difference generally. In Jonson it has a chronological aspect -- there is a shift over his career from one end to the other -- and there is often significant change within the idiolects of his characters as well. Successive segments of Volpone and Mosca's parts (they are protagonist and antagonist of Volpone, perhaps Jonson's best-known comedy) change markedly along this axis, beginning far apart but coming by the end of the play to resemble each other very closely on this measure. This revised version was published online in July 2006 with corrections to the Cover Date.