SELF-DEPENDENT LOCALITY PRESERVING PROJECTION WITH TRANSFORMED SPACE-ORIENTED NEIGHBORHOOD GRAPH

Locality preserving projection （LPP） is a typical and popular dimensionality reduction （DR） method,and it can potentially find discriminative projection directions by preserving the local geometric structure in data. However,LPP is based on the neighborhood graph artificially constructed from the original data,and the performance of LPP relies on how well the nearest neighbor criterion work in the original space. To address this issue,a novel DR algorithm,called the self-dependent LPP （sdLPP） is proposed. And it is based on the fact that the nearest neighbor criterion usually achieves better performance in LPP transformed space than that in the original space. Firstly,LPP is performed based on the typical neighborhood graph; then,a new neighborhood graph is constructed in LPP transformed space and repeats LPP. Furthermore,a new criterion,called the improved Laplacian score,is developed as an empirical reference for the discriminative power and the iterative termination. Finally,the feasibility and the effectiveness of the method are verified by several publicly available UCI and face data sets with promising results.

Sparse Kernel Locality Preserving Projection and Its Application in Nonlinear Process Fault Detection

Locality preserving projection (LPP) is a newly emerging fault detection method which can discover local manifold structure of a data set to be analyzed, but its linear assumption may lead to monitoring performance degradation for complicated nonlinear industrial processes. In this paper, an improved LPP method, referred to as sparse kernel locality preserving projection (SKLPP) is proposed for nonlinear process fault detection. Based on the LPP model, kernel trick is applied to construct nonlinear kernel model. Furthermore, for reducing the computational complexity of kernel model, feature samples selection technique is adopted to make the kernel LPP model sparse. Lastly, two monitoring statistics of SKLPP model are built to detect process faults. Simulations on a continuous stirred tank reactor (CSTR) system show that SKLPP is more effective than LPP in terms of fault detection performance.

Fault Diagnosis Model Based on Feature Compression with Orthogonal Locality Preserving Projection

Based on feature compression with orthogonal locality preserving projection（OLPP）,a novel fault diagnosis model is proposed in this paper to achieve automation and high-precision of fault diagnosis of rotating machinery.With this model,the original vibration signals of training and test samples are first decomposed through the empirical mode decomposition（EMD）,and Shannon entropy is constructed to achieve high-dimensional eigenvectors.In order to replace the traditional feature extraction way which does the selection manually,OLPP is introduced to automatically compress the high-dimensional eigenvectors of training and test samples into the low-dimensional eigenvectors which have better discrimination.After that,the low-dimensional eigenvectors of training samples are input into Morlet wavelet support vector machine（MWSVM） and a trained MWSVM is obtained.Finally,the low-dimensional eigenvectors of test samples are input into the trained MWSVM to carry out fault diagnosis.To evaluate our proposed model,the experiment of fault diagnosis of deep groove ball bearings is made,and the experiment results indicate that the recognition accuracy rate of the proposed diagnosis model for outer race crack、inner race crack and ball crack is more than 90%.Compared to the existing approaches,the proposed diagnosis model combines the strengths of EMD in fault feature extraction,OLPP in feature compression and MWSVM in pattern recognition,and realizes the automation and high-precision of fault diagnosis.

Multimode Process Monitoring Based on Fuzzy C-means in Locality Preserving Projection Subspace

For complex industrial processes with multiple operational conditions, it is important to develop effective monitoring algorithms to ensure the safety of production processes. This paper proposes a novel monitoring strategy based on fuzzy C-means. The high dimensional historical data are transferred to a low dimensional subspace spanned by locality preserving projection. Then the scores in the novel subspace are classified into several overlapped clusters, each representing an operational mode. The distance statistics of each cluster are integrated though the membership values into a novel BID (Bayesian inference distance) monitoring index. The efficiency and effectiveness of the proposed method are validated though the Tennessee Eastman benchmark process.

Local projection stabilized finite element method for Navier-Stokes equations

This paper extends the results of Matthies, Skrzypacz, and Tubiska for the Oseen problem to the Navier-Stokes problem. For the stationary incompressible Navier- Stokes equations, a local projection stabilized finite element scheme is proposed. The scheme overcomes convection domination and improves the restrictive inf-sup condition. It not only is a two-level approach but also is adaptive for pairs of spaces defined on the same mesh. Using the approximation and projection spaces defined on the same mesh, the scheme leads to much more compact stencils than other two-level approaches. On the same mesh, besides the class of local projection stabilization by enriching the approximation spaces, two new classes of local projection stabilization of the approximation spaces are derived, which do not need to be enriched by bubble functions. Based on a special interpolation, the stability and optimal prior error estimates are shown. Numerical results agree with some benchmark solutions and theoretical analysis very well.

Supervised local and non-local structure preserving projections with application to just-in-time learning for adaptive soft sensor

In soft sensor field, just-in-time learning(JITL) is an effective approach to model nonlinear and time varying processes. However, most similarity criterions in JITL are computed in the input space only while ignoring important output information, which may lead to inaccurate construction of relevant sample set. To solve this problem, we propose a novel supervised feature extraction method suitable for the regression problem called supervised local and non-local structure preserving projections(SLNSPP), in which both input and output information can be easily and effectively incorporated through a newly defined similarity index. The SLNSPP can not only retain the virtue of locality preserving projections but also prevent faraway points from nearing after projection,which endues SLNSPP with powerful discriminating ability. Such two good properties of SLNSPP are desirable for JITL as they are expected to enhance the accuracy of similar sample selection. Consequently, we present a SLNSPP-JITL framework for developing adaptive soft sensor, including a sparse learning strategy to limit the scale and update the frequency of database. Finally, two case studies are conducted with benchmark datasets to evaluate the performance of the proposed schemes. The results demonstrate the effectiveness of LNSPP and SLNSPP.

Locality Preserving Discriminant Projection for Speaker Verification

In this paper, a manifold subspace learning algorithm based on locality preserving discriminant projection (LPDP) is used for speaker verification. LPDP can overcome the deficiency of the total variability factor analysis and locality preserving projection (LPP). LPDP can effectively use the speaker label information of speech data. Through optimization, LPDP can maintain the inherent manifold local structure of the speech data samples of the same speaker by reducing the distance between them. At the same time, LPDP can enhance the discriminability of the embedding space by expanding the distance between the speech data samples of different speakers. The proposed method is compared with LPP and total variability factor analysis on the NIST SRE 2010 telephone-telephone core condition. The experimental results indicate that the proposed LPDP can overcome the deficiency of LPP and total variability factor analysis and can further improve the system performance.

Face recognition using illuminant locality preserving projections

A novel supervised manifold learning method was proposed to realize high accuracy face recognition under varying illuminant conditions. The proposed method, named illuminant locality preserving projections （ILPP）, exploited illuminant directions to alleviate the effect of illumination variations on face recognition. The face images were first projected into low dimensional subspace, Then the ILPP translated the face images along specific direction to reduce lighting variations in the face. The ILPP reduced the distance between face images of the same class, while increase the dis tance between face images of different classes. This proposed method was derived from the locality preserving projections （LPP） methods, and was designed to handle face images with various illumi nations. It preserved the face image＇ s local structure in low dimensional subspace. The ILPP meth od was compared with LPP and discriminant locality preserving projections （DLPP）, based on the YaleB face database. Experimental results showed the effectiveness of the proposed algorithm on the face recognition with various illuminations.

Nonconforming local projection stabilization for generalized Oseen equations

A new method of nonconforming local projection stabilization for the gen- eralized Oseen equations is proposed by a nonconforming inf-sup stable element pair for approximating the velocity and the pressure. The method has several attractive features. It adds a local projection term only on the sub-scale （H ≥ h）. The stabilized term is simple compared with the residual-free bubble element method. The method can handle the influence of strong convection. The numerical results agree with the theoretical expectations very well.

An object tracking and global localization method using the cylindrical projection of omnidirectional image

We present an omnidirectional vision system we have implemented to provide our mobile robot with a fast tracking and robust localization capability. An algorithm is proposed to do reconstruction of the environment from the omnidirectional image and global localization of the robot in the context of the Middle Size League RoboCup field. This is accomplished by learning a set of visual landmarks such as the goals and the corner posts. Due to the dynamic changing environment and the partially observable landmarks, four localization cases are discussed in order to get robust localization performance. Localization is performed using a method that matches the observed landmarks, i.e. color blobs, which are extracted from the environment. The advantages of the cylindrical projection are discussed giving special consideration to the characteristics of the visual landmark and the meaning of the blob extraction. The analysis is established based on real time experiments with our omnidirectional vision system and the actual mobile robot. The comparative studies are presented and the feasibility of the method is shown.

3-D Reconstruction and Visualization of Laser-Scanned Trees by Weighted Locally Optimal Projection and Accurate Modeling Method

This paper presents a method to reconstruct 3-D models of trees from terrestrial laser scan(TLS)point clouds.This method uses the weighted locally optimal projection(WLOP)and the AdTree method to reconstruct detailed 3-D tree models.To improve its representation accuracy,the WLOP algorithm is introduced to consolidate the point cloud.Its reconstruction accuracy is tested using a dataset of ten trees,and the one-sided Hausdorff distances between the input point clouds and the resulting 3-D models are measured.The experimental results show that the optimal projection modeling method has an average one-sided Hausdorff distance(mean)lower by 30.74%and 6.43%compared with AdTree and AdQSM methods,respectively.Furthermore,it has an average one-sided Hausdorff distance(RMS)lower by 29.95%and 12.28%compared with AdTree and AdQSM methods.Results show that the 3-D model generated fits closely to the input point cloud data and ensures a high geometrical accuracy.

A Comparative Study of Locality Preserving Projection and Principle Component Analysis on Classification Performance Using Logistic Regression

There are a variety of classification techniques such as neural network, decision tree, support vector machine and logistic regression. The problem of dimensionality is pertinent to many learning algorithms, and it denotes the drastic raise of computational complexity, however, we need to use dimensionality reduction methods. These methods include principal component analysis (PCA) and locality preserving projection (LPP). In many real-world classification problems, the local structure is more important than the global structure and dimensionality reduction techniques ignore the local structure and preserve the global structure. The objectives is to compare PCA and LPP in terms of accuracy, to develop appropriate representations of complex data by reducing the dimensions of the data and to explain the importance of using LPP with logistic regression. The results of this paper find that the proposed LPP approach provides a better representation and high accuracy than the PCA approach.

基于KLPP-K-means-BiLSTM的台区短期电力负荷预测

随着智能电网的发展,各场景的用电更加多元化,而准确的台区负荷预测是确保相关电力部门制定合适检修任务的关键,同时为有序用电、电网经济运行提供重要参考。为了挖掘台区负荷的特征以提高台区负荷预测的精度,提出了一种基于核主元分析与局部保持投影降维、K均值聚类算法(K-means)以及双向长短时记忆网络(BiLSTM)的台区电力负荷预测方法。首先利用核局部保持投影(KLPP)对台区多特征负荷数据进行降维以提取主要特征信息;然后采取K-means聚类算法将相似特征的数据归类成各自的簇集;最后针对聚类后的各典型类型,有针对性地训练BiLSTM,并选取中国某高校低压台区负荷作为算例与其他经典预测方法进行对比分析,结果表明所提方法更拟合实际负荷走向,有效提升了预测效果。

基于RMDLPP的雷达空中目标分类

针对鉴别局部保持投影(discriminant locality preserving projections, DLPP)在窄带雷达目标数据降维时出现的类内离散度矩阵奇异和对孤立点敏感进而导致类别之间可分性弱的问题,提出了基于鲁棒性边界DLPP(robust margin DLPP, RMDLPP)的窄带雷达空中目标分类方法。首先,在计算样本之间距离时将两样本点的欧氏距离与同类样本均值相关联。然后,挑选一定数量的边界样本点进行处理并对优化DLPP目标函数进行降维。最后,使用高性能分类器对降维后的数据进行区分,实现对空中目标的分类。通过对X波段对空警戒雷达实测数据的对比实验表明,所提方法具有更好的分类准确率和对孤立点的鲁棒性。

基于自适应LPP特征降维和改进VPMCD的滚动轴承故障诊断

针对机械系统状态监测与故障诊断中存在的故障特征维数较高及模式识别导致的耗时较高问题,提出了一种基于自适应局部保持投影(Locality Preserving Projection,LPP)特征降维和改进多变量预测模型(Variable Predictive Model based Class Discriminate,VPMCD)的故障诊断方法。首先,从滚动轴承振动信号中提取时频域特征、能量特征,以及复杂度特征组成高维故障特征数据集;其次,利用自适应LPP方法对高维故障特征数据集进行降维处理,得到低维敏感故障特征;最后,采用改进VPMCD方法对低维敏感故障特征进行分类识别,进而判断故障类型。通过滚动轴承故障诊断试验分析表明,自适应LPP方法克服了传统LPP方法需要人工选取参数的缺陷,在获得低维敏感故障特征的基础上具有较少计算时间,相比主成分分析(Principal Component Analysis,PCA)、局部切空间排列(Local Tangent Space Alignment,LTSA)、线性局部切空间排列(Linear Local Tangent Space Alignment,LLTSA)、等距特征映射(Isometric Mapping,Isomap),以及局部线性嵌入(Locally Linear Embedding,LLE)等算法具有明显的优势;改进VPMCD方法可克服人工选择模型的偶然性和片面性,在滚动轴承10种故障状态的识别中获得了99.4%的诊断精度,相比优化参数支持向量机方法提高了故障诊断效率,大大降低了识别时间,具有一定的优越性。

基于LP与小波包的复杂机电系统监测序列混沌降噪方法

针对流程工业生产系统监测数据存在强噪声和混沌性的特点,提出了一种局部投影方法(Local Projection Method)与小波包方法相结合的信号降噪方法。该方法先利用局部投影方法从动力学系统嵌入流形的角度进行多次迭代降噪,并根据关联维数来判定迭代终止;再利用小波包方法从频率的角度进行降噪,抑制高频噪声的干扰,取得了较好的降噪效果。用Lorenz时间序列进行仿真验证,对仿真时间序列加入不同程度的噪声,对比分析小波包、局部投影与该方法降噪后的相空间、SNR值和最大Lyapunov指数,证明了该方法对于中高强度噪声具有更好的降噪效果。并将该方法用于某压缩机组的实际监测数据降噪,评估三种方法的降噪效果,进一步验证了该方法的优越性。

一种有监督的LPP算法及其在人脸识别中的应用

为了提高局部保持投影算法(Locality Preserving Projections,LPP)对光照、姿态等外部因素的鲁棒性,该文对传统的LPP算法进行改进,提出了一种有监督的LPP(SLPP)方法。首先对LPP子空间进行判别分析,然后选择主要反应类内差异的基向量来构造子空间,最后在子空间上进行识别。通过Havard人脸库和Umist人脸库上的实验,结果表明该方法能够对光照和姿态的变化具有一定的鲁棒性和较高的识别率,比传统的LPP方法和其它子空间分析法识别率提高了10%以上。

Lp-投影体的均质积分和对偶均质积分的Brunn-Minkowski不等式

在Lutwak,Yang和Zhang提出的L_p-投影体概念的基础上结合凸体的Blaschke L_p-组合,分别得到了L_p-投影体的均质积分和对偶均质积分的Brunn-Minkowski不等式.另外,还给出了关于L_p-投影体的均质积分和对偶均质积分的单调性不等式.

基于DMOLPP的间歇过程在线故障检测

为了保持过程数据集的局部结构,确保数据投影后的投影向量正交,降低数据误差重构方面的难度,提出了一种基于动态多向正交局部保持投影(DMOLPP)进行间歇过程故障检测的方法。该方法将滑动窗口技术和正交局部保持投影(OLPP)相结合用于间歇过程在线检测。首先,将批次数据展开成二维数据,利用滑动窗口技术分别在时间片内运用OLPP算法提取能表征过程正常数据内在局部近邻结构的特征;然后,对于新来批次数据标准化处理后分别在相应窗口内投影,提取特征向量;最后利用核密度估计(KDE)确定控制限进行过程检测。通过仿真结果表明,运用DMOLPP算法检测到故障发生的时刻早于动态多向局部保持投影(DMLPP)、动态多向邻域保持嵌入(DMNPE)方法。与动态多向主元分析(DMPCA)相比,具有较低或者无误报时刻,验证了该方法的有效性。

基于多尺度正交PCA-LPP流形学习算法的故障特征增强方法

针对齿轮箱故障声发射信号特征增强问题,提出一种多尺度正交PCA-LPP非线性流形学习特征增强方法,兼顾PCA的全局方差增大变换特性以及LPP的局部非线性特征保持特性,并通过正交化消除投影分量间的冗余信息,使处理之后的齿轮箱故障信号内含的故障特征得到增强,一方面增强后信号包络谱中的故障谱线清晰明显,另一方面增强后信号以小波包能量熵为特征量,故障类型的辨识率显著提高,可以达到93.75%。