非线性特征提取和LSSVM在化工过程故障诊断中应用

提出利用非线性特征提取（核主成分分析（KPCA）和核独立成分分析）消除数据的不相关性,降低维数。核主成分分析利用核函数把输入数据映射到特征空间,进行线性主成分分析计算提取特征;核独立成分分析在KPCA白化空间进行线性独立成分分析（ICA）变换提取独立成分。提取的特征作为最小二乘支持向量机分类器的输入,构建融合非线性特征提取和最小二乘支持向量机的智能故障分类方法。研究了该方法应用到某石化企业润滑油生产过程的故障诊断中的有效性和可行性。     

Modified non-Gaussian multivariate statistical process monitoring based on the Gaussian distribution transformation

Independent component analysis (ICA) has been applied for non-Gaussian multivariate statistical process monitoring (MSPM) for several years. As the independent components do not satisfy the multivariate Gaussian distribution, a missed alarm occurs when monitoring with traditional statistics. In this paper, we propose a Gaussian distribution transformation (GDT)-based monitoring method. Independent components are first transformed into approximate Gaussian distributions through the proposed nonlinear mapping. Then, we propose new statistics and their control limits to reduce missed alarms. The proposed method is particularly suitable for slight magnitude fault and early-stage fault detection. The ratio part of the area above the curve (RPAAC) is developed to evaluate the performance in fault detection. The experimental results from a synthetic example show the effectiveness of our proposed method. We also apply our method to monitor an electrical fused magnesia furnace (EFMF), and eruption and furnace wall melt faults can be detected in time.     

Kernel ICA: An alternative formulation and its application to face recognition

This paper formulates independent component analysis (ICA) in the kernel-inducing feature space and develops a two-phase kernel ICA algorithm: whitened kernel principal component analysis (KPCA) plus ICA. KPCA spheres data and makes the data structure become as linearly separable as possible by virtue of an implicit nonlinear mapping determined by kernel. ICA seeks the projection directions in the KPCA whitened space, making the distribution of the projected data as non-gaussian as possible. The experiment using a subset of FERET database indicates that the proposed kernel ICA method significantly outperform ICA, PCA and KPCA in terms of the total recognition rate.     

基于KPCA和CPSO的故障检测方法

提出一种基于核主元分析(KPCA)和混沌粒子优化群(CPSO)算法的非线性故障检测方法。通过核函数完成非线性变换,将变量由非线性的输入空间转换到线性的特征空间来计算主元,构造平方预测误差统计量检测故障是否发生。为避免粒子群算法的早熟现象,利用混沌优化的搜索特性,将CPSO算法应用到KPCA核参数的优化中。变压器故障检测结果表明,与基于PCA、KPCA和 PSO-KPCA的故障检测方法相比,该方法的检测正确率较高。     

一种新的核线性鉴别分析算法及其在人脸识别上的应用

基于核策略的核Fisher鉴别分析（KFD）算法已成为非线性特征抽取的最有效方法之一。但是先前的基于核Fisher鉴别分析算法的特征抽取过程都是基于2值分类问题而言的。如何从重叠（离群）样本中抽取有效的分类特征没有得到有效的解决。本文在结合模糊集理论的基础上,利用模糊隶属度函数的概念,在特征提取过程中融入了样本的分布信息,提出了一种新的核Fisher鉴别分析方法——模糊核鉴别分析算法。在ORL人脸数据库上的实验结果验证了该算法的有效性。     

Kernel discriminant analysis for regression problems

In this paper, we propose a nonlinear feature extraction method for regression problems to reduce the dimensionality of the input space. Previously, a feature extraction method LDAr, a regressional version of the linear discriminant analysis, was proposed. In this paper, LDAr is generalized to a nonlinear discriminant analysis by using the so-called kernel trick. The basic idea is to map the input space into a high-dimensional feature space where the variables are nonlinear transformations of input variables. Then we try to maximize the ratio of distances of samples with large differences in the target value and those with small differences in the target value in the feature space. It is well known that the distribution of face images, under a perceivable variation in translation, rotation, and scaling, is highly nonlinear and the face alignment problem is a complex regression problem. We have applied the proposed method to various regression problems including face alignment problems and achieved better performances than those of conventional linear feature extraction methods.     

Combination of independent component analysis and support vector machines for intelligent faults diagnosis of induction motors

This paper studies the application of independent component analysis (ICA) and support vector machines (SVMs) to detect and diagnose of induction motor faults. The ICA is used for feature extraction and data reduction from original features. The principal components analysis is also applied in feature extraction process for comparison with ICA does. In this paper, the training of the SVMs is carried out using the sequential minimal optimization algorithm and the strategy of multi-class SVMs-based classification is applied to perform the faults identification. Also, the performance of classification process due to the choice of kernel function is presented to show the excellent of characteristic of kernel function. Various scenarios are examined using data sets of vibration and stator current signals from experiments, and the results are compared to get the best performance of classification process.     

一种核最大散度差判别分析人脸识别方法

提出一种有效的非线性子空间学习方法--核最大散度差判别分析(KMSD),并将其用于人脸识别.核最大散度差判别分析首先把输入空间的样本非线性映射到特征空间,然后通过核方法的技巧,采用最大散度差判别分析(MSD)方法在特征空间里求解.在Yale和ORL人脸数据库上的实验结果表明,提出的核最大散度差判别分析方法用于人脸识别具有较高的识别率.     

基于核规范变量分析的非线性故障诊断方法

提出一种基于核规范变量分析（KCVA）的非线性过程故障诊断方法．该方法使用核函数完成非线性空间到高维线性空间的映射,避免了高维空间中的数据处理和非线性映射函数的使用．在线性空间中使用规范变量分析（CVA）来辨识状态空闻模型,从数据中提取状态信息．3个监测量（Tr^2,Ts^2,Q）用来进行故障检测,同时使用贡献图分离故障变量,并判断故障原因．在CSTR系统上的仿真结果表明,KCVA方法比主元分析法（PCA）和CVA方法能更灵敏地检测到故障的发生,更有效地监控过程变化．     

On feature extraction via kernels.

Using the kernel trick idea and the kernels-as-features idea, we can construct two kinds of nonlinear feature spaces, where linear feature extraction algorithms can be employed to extract nonlinear features. In this correspondence, we study the relationship between the two kernel ideas applied to certain feature extraction algorithms such as linear discriminant analysis, principal component analysis, and canonical correlation analysis. We provide a rigorous theoretical analysis and show that they are equivalent up to different scalings on each feature. These results provide a better understanding of the kernel method.     

核正交判别局部正切空间对齐算法

针对现有的局部正切空间算法中存在的问题,文中提出一种基于核变换的特征提取方法——核正交判别局部正切空间对齐算法(KOTSDA)。该算法首先利用核方法将人脸图像投影到一个高维非线性空间,提取其非线性信息;然后在目标函数中利用正切空间判别分析算法在保持样本的类内局部几何结构的同时最大化类间差异;最后添加正交约束,得到核正交判别局部正切空间对齐算法。该算法不需要经过PCA降维,有效避免判别信息的丢失,在ORL和Yale人脸库上的实验验证算法有效性。     

Kernel class-wise locality preserving projection

In the recent years, the pattern recognition community paid more attention to a new kind of feature extraction method, the manifold learning methods, which attempt to project the original data into a lower dimensional feature space by preserving the local neighborhood structure. Among them, locality preserving projection (LPP) is one of the most promising feature extraction techniques. However, when LPP is applied to the classification tasks, it shows some limitations, such as the ignorance of the label information. In this paper, we propose a novel local structure based feature extraction method, called class-wise locality preserving projection (CLPP). CLPP utilizes class information to guide the procedure of feature extraction. In CLPP, the local structure of the original data is constructed according to a certain kind of similarity between data points, which takes special consideration of both the local information and the class information. The kernelized (nonlinear) counterpart of this linear feature extractor is also established in the paper. Moreover, a kernel version of CLPP namely Kernel CLPP (KCLPP) is developed through applying the kernel trick to CLPP to increase its performance on nonlinear feature extraction. Experiments on ORL face database and YALE face database are performed to test and evaluate the proposed algorithm.     

基于特征样本的KPCA在故障诊断中的应用

核函数主元分析（KPCA）可用于非线性过程监控.建立KPCA模型首先要计算核矩阵K,K的维数等于训练样本的数量,对于大样本集,计算K很困难.对此提出一种基于特征样本的KPCA（SKPCA）,其基本思想是,首先利用非线性映射函数将输入空间映射到特征子空间,然后在特征子空间中计算主元.将SKPCA应用于监控Tennessee Eastman过程,并与基于全体样本的KPCA作比较,仿真结果显示,二者诊断结果基本相同,然而特征样本只是训练样本中的一小部分,因此减少了K的维数,解决了K的计算问题.     

人脸识别中基于核的子空间鉴别分析

尽管基于Fisher准则的线性鉴别分析被公认为特征抽取的有效方法之一，并被成功地用于人脸识别，但是由于光照变化、人脸表情和姿势变化，实际上的人脸图像分布是十分复杂的，因此，抽取非线性鉴别特征显得十分必要。为了能利用非线性鉴别特征进行人脸识别，提出了一种基于核的子空间鉴别分析方法。该方法首先利用核函数技术将原始样本隐式地映射到高维（甚至无穷维）特征空间；然后在高维特征空间里，利用再生核理论来建立基于广义Fisher准则的两个等价模型；最后利用正交补空间方法求得最优鉴别矢量来进行人脸识别。在ORL和NUST603两个人脸数据库上，对该方法进行了鉴别性能实验，得到了识别率分别为94％和99．58％的实验结果，这表明该方法与核组合方法的识别结果相当，且明显优于KPCA和Kernel fisherfaces方法的识别结果。     

Face recognition using a kernel fractional-step discriminant analysis algorithm

Feature extraction is among the most important problems in face recognition systems. In this paper, we propose an enhanced kernel discriminant analysis (KDA) algorithm called kernel fractional-step discriminant analysis (KFDA) for nonlinear feature extraction and dimensionality reduction. Not only can this new algorithm, like other kernel methods, deal with nonlinearity required for many face recognition tasks, it can also outperform traditional KDA algorithms in resisting the adverse effects due to outlier classes. Moreover, to further strengthen the overall performance of KDA algorithms for face recognition, we propose two new kernel functions: cosine fractional-power polynomial kernel and non-normal Gaussian RBF kernel. We perform extensive comparative studies based on the YaleB and FERET face databases. Experimental results show that our KFDA algorithm outperforms traditional kernel principal component analysis (KPCA) and KDA algorithms. Moreover, further improvement can be obtained when the two new kernel functions are used.     

Monitoring of quality-relevant and quality-irrelevant blocks with characteristic-similar variables based on self-organizing map and kernel approaches

Variables in quality-related process monitoring can be divided into quality-relevant and quality-irrelevant groups depending on the correlation with the quality indicator. These variables can also be separated into multiple sets in which variables are closely relevant to one another because of the interdependence of the process. Block monitoring with reasonable variable partition and reliable model can distinguish quality-related and quality-unrelated faults and improve monitoring performance. A block monitoring method based on self-organizing map (SOM) and kernel approaches is proposed. After collecting and normalizing the sample data including process variables and quality ones, the data matrix is transposed. The inverted samples are used as the input of SOM, and variables with the same behavioral characteristic and a close correlation are topologically mapped in a similar area. Accordingly, samples can be visually blocked into quality-relevant and independent subspaces. Given the nonlinearity of industrial process, kernel partial least squares (KPLS) and kernel principal component analysis (KPCA) are employed to monitor the two types of blocks. The information provided by fault detection can reveal the effects on quality indicators and the location of faults. Finally, the effectiveness of SOM-KPLS/KPCA is evaluated using a numerical example and the Tennessee–Eastman process.     

基于核的慢特征分析算法

提出一种基于核的慢特征分析算法。通过引入核技巧,既充分扩充特征空间,又避免直接在高维空间中运算的困难。由于充分利用数据所隐含的非线性信息,所得到的解是稳定的。同时基于对慢特征分析算法目标函数的分析,给出一个对算法结果的评价准则,并用以指导核参数的选择。实验结果验证算法的有效性。     

极小化类内散布度的大间距非线性鉴别分析

提出了一种新的非线性鉴别分析算法——极小化类内散布的大间距非线性鉴别分析。该算法的主要思想是将原始样本映射到更高维的空间中,利用核技术对传统的大间距分类算法进行改进,在新的高维空间中利用再生核技术寻找核鉴别矢量,使得在这个新的空间中核类内散度尽可能的小。在ORL人脸数据库上进行实验,分析了识别率及识别时间,结果表明该方法具有一定优势。     

Kernel-based nonlinear discriminant analysis for face recognition

Linear subspace analysis methods have been successfully applied to extract features for face recognition.But they are inadequate to represent the complex and nonlinear variations of real face images,such as illumination,facial expression and pose variations,because of their linear properties.In this paper,a nonlinear subspace analysis method,Kernel-based Nonlinear Discriminant Analysis (KNDA),is presented for face recognition,which combines the nonlinear kernel trick with the linear subspace analysis method-Fisher Linear Discriminant Analysis (FLDA).First,the kernel trick is used to project the input data into an implicit feature space,then FLDA is performed in this feature space.Thus nonlinear discriminant features of the input data are yielded.In addition,in order to reduce the computational complexity,a geometry-based feature vectors selection scheme is adopted.Another similar nonlinear subspace analysis is Kernel-based Principal Component Analysis (KPCA),which combines the kernel trick with linear Principal Component Analysis (PCA).Experiments are performed with the polynomial kernel,and KNDA is compared with KPCA and FLDA.Extensive experimental results show that KNDA can give a higher recognition rate than KPCA and FLDA.