LOCAL STRUCTURE-PRESERVING ALGORITHMS FOR THE KLEIN-GORDON-ZAKHAROV EQUATION

In this paper, using the concatenating method, a series of local structure-preserving algorithms are obtained for the Klein-Gordon-Zakharov equation, including four multisymplectic algorithms, four local energy-preserving algorithms, four local momentumpreserving algorithms;of these, local energy-preserving and momentum-preserving algorithms have not been studied before. The local structure-preserving algorithms mentioned above are more widely used than the global structure-preserving algorithms, since local preservation algorithms can be preserved in any time and space domains, which overcomes the defect that global preservation algorithms are limited to boundary conditions. In particular, under appropriate boundary conditions, local preservation laws are global preservation laws.Numerical experiments conducted can support the theoretical analysis well.

Loop Closure Detection via Locality Preserving Matching With Global Consensus

A critical component of visual simultaneous localization and mapping is loop closure detection(LCD),an operation judging whether a robot has come to a pre-visited area.Concretely,given a query image(i.e.,the latest view observed by the robot),it proceeds by first exploring images with similar semantic information,followed by solving the relative relationship between candidate pairs in the 3D space.In this work,a novel appearance-based LCD system is proposed.Specifically,candidate frame selection is conducted via the combination of Superfeatures and aggregated selective match kernel(ASMK).We incorporate an incremental strategy into the vanilla ASMK to make it applied in the LCD task.It is demonstrated that this setting is memory-wise efficient and can achieve remarkable performance.To dig up consistent geometry between image pairs during loop closure verification,we propose a simple yet surprisingly effective feature matching algorithm,termed locality preserving matching with global consensus(LPM-GC).The major objective of LPM-GC is to retain the local neighborhood information of true feature correspondences between candidate pairs,where a global constraint is further designed to effectively remove false correspondences in challenging sceneries,e.g.,containing numerous repetitive structures.Meanwhile,we derive a closed-form solution that enables our approach to provide reliable correspondences within only a few milliseconds.The performance of the proposed approach has been experimentally evaluated on ten publicly available and challenging datasets.Results show that our method can achieve better performance over the state-of-the-art in both feature matching and LCD tasks.We have released our code of LPM-GC at https://github.com/jiayi-ma/LPM-GC.

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.

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.

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.

3D Face Reconstruction from a Single Image Using a Combined PCA-LPP Method

In this paper, we proposed a combined PCA-LPP algorithm toimprove 3D face reconstruction performance. Principal component analysis(PCA) is commonly used to compress images and extract features. Onedisadvantage of PCA is local feature loss. To address this, various studies haveproposed combining a PCA-LPP-based algorithm with a locality preservingprojection (LPP). However, the existing PCA-LPP method is unsuitable for3D face reconstruction because it focuses on data classification and clustering.In the existing PCA-LPP, the adjacency graph, which primarily shows the connectionrelationships between data, is composed of the e-or k-nearest neighbortechniques. By contrast, in this study, complex and detailed parts, such aswrinkles around the eyes and mouth, can be reconstructed by composing thetopology of the 3D face model as an adjacency graph and extracting localfeatures from the connection relationship between the 3D model vertices.Experiments verified the effectiveness of the proposed method. When theproposed method was applied to the 3D face reconstruction evaluation set,a performance improvement of 10% to 20% was observed compared with theexisting PCA-based method.

Preservation of local linearity by neighborhood subspace scaling for solving the pre-image problem

An important issue involved in kernel methods is the pre-image problem. However, it is an ill-posed problem, as the solution is usually nonexistent or not unique. In contrast to direct methods aimed at minimizing the distance in feature space, indirect methods aimed at constructing approximate equivalent models have shown outstanding performance. In this paper, an indirect method for solving the pre-image problem is proposed. In the proposed algorithm, an inverse mapping process is constructed based on a novel framework that preserves local linearity. In this framework, a local nonlinear transformation is implicitly conducted by neighborhood subspace scaling transformation to preserve the local linearity between feature space and input space. By extending the inverse mapping process to test samples, we can obtain pre-images in input space. The proposed method is non-iterative,and can be used for any kernel functions. Experimental results based on image denoising using kernel principal component analysis(PCA) show that the proposed method outperforms the state-of-the-art methods for solving the pre-image problem.

A Survey and Experimental Review on Data Distribution Strategies for Parallel Spatial Clustering Algorithms

The advent of Big Data has led to the rapid growth in the usage of parallel clustering algorithms that work over distributed computing frameworks such as MPI,MapReduce,and Spark.An important step for any parallel clustering algorithm is the distribution of data amongst the cluster nodes.This step governs the methodology and performance of the entire algorithm.Researchers typically use random,or a spatial/geometric distribution strategy like kd-tree based partitioning and grid-based partitioning,as per the requirements of the algorithm.However,these strategies are generic and are not tailor-made for any specific parallel clustering algorithm.In this paper,we give a very comprehensive literature survey of MPI-based parallel clustering algorithms with special reference to the specific data distribution strategies they employ.We also propose three new data distribution strategies namely Parameterized Dimensional Split for parallel density-based clustering algorithms like DBSCAN and OPTICS,Cell-Based Dimensional Split for dGridSLINK,which is a grid-based hierarchical clustering algorithm that exhibits efficiency for disjoint spatial distribution,and Projection-Based Split,which is a generic distribution strategy.All of these preserve spatial locality,achieve disjoint partitioning,and ensure good data load balancing.The experimental analysis shows the benefits of using the proposed data distribution strategies for algorithms they are designed for,based on which we give appropriate recommendations for their usage.

Surface Detection of Continuous Casting Slabs Based on Curvelet Transform and Kernel Locality Preserving Projections

Longitudinal cracks are common defects of continuous casting slabs and may lead to serious quality accidents. Image capturing and recognition of hot slabs is an effective way for on-line detection of cracks, and recognition of cracks is essential because the surface of hot slabs is very complicated. In order to detect the surface longitudinal cracks of the slabs, a new feature extraction method based on Curvelet transform and kernel locality preserving projections （KLPP） is proposed. First, sample images are decomposed into three levels by Curvelet transform. Second, Fourier transform is applied to all sub-band images and the Fourier amplitude spectrum of each sub-band is computed to get features with translational invariance. Third, five kinds of statistical features of the Fourier amplitude spectrum are computed and combined in different forms. Then, KLPP is employed for dimensionality reduction of the obtained 62 types of high-dimensional combined features. Finally, a support vector machine （SVM） is used for sample set classification. Experiments with samples from a real production line of continuous casting slabs show that the algorithm is effective to detect longitudinal cracks, and the classification rate is 91.89%.

Performance monitoring of non-gaussian chemical processes with modes-switching using globality-locality preserving projection

In this paper, we propose a novel performance monitoring and fault detection method, which is based on modified structure analysis and globality and locality preserving （MSAGL） projection, for non-Gaussian processes with multiple operation conditions. By using locality preserving projection to analyze the embedding geometrical manifold and extracting the non-Gaussian features by independent component analysis, MSAGL preserves both the global and local structures of the data simultaneously. Furthermore, the tradeoff parameter of MSAGL is tuned adaptively in order to find the projection direction optimal for revealing the hidden structural information. The validity and effectiveness of this approach are illustrated by applying the proposed technique to the Tennessee Eastman process simulation under multiple operation conditions. The results demonstrate the advantages of the proposed method over conventional eigendecomposition-based monitoring methotis.

基于核局部保留映射的全视点三维空间目标识别(英文)

Space object recognition plays an important role in spatial exploitation and surveillance, followed by two main problems： lacking of data and drastic changes in viewpoints. In this article, firstly, we build a three-dimensional （3D） satellites dataset named BUAA Satellite Image Dataset （BUAA-SID 1.0） to supply data for 3D space object research. Then, based on the dataset, we propose to recognize full-viewpoint 3D space objects based on kernel locality preserving projections （KLPP）. To obtain more accurate and separable description of the objects, firstly, we build feature vectors employing moment invariants, Fourier descriptors, region covariance and histogram of oriented gradients. Then, we map the features into kernel space followed by dimensionality reduction using KLPP to obtain the submanifold of the features. At last, k-nearest neighbor （kNN） is used to accomplish the classification. Experimental results show that the proposed approach is more appropriate for space object recognition mainly considering changes of viewpoints. Encouraging recognition rate could be obtained based on images in BUAA-SID 1.0, and the highest recognition result could achieve 95.87%.

KDLPCCA-Based Projection for Feature Extraction in SSVEP-Based Brain-Computer Interfaces

An electroencephalogram(EEG)signal projection using kernel discriminative locality preserving canonical correlation analysis(KDLPCCA)-based correlation with steady-state visual evoked potential(SSVEP)templates for frequency recognition is presented in this paper.With KDLPCCA,not only a non-linear correlation but also local properties and discriminative information of each class sample are considered to extract temporal and frequency features of SSVEP signals.The new projected EEG features are classified with classical machine learning algorithms,namely,K-nearest neighbors(KNNs),naive Bayes,and random forest classifiers.To demonstrate the effectiveness of the proposed method,16-channel SSVEP data corresponding to 4 frequencies collected from 5 subjects were used to evaluate the performance.Compared with the state of the art canonical correlation analysis(CCA),experimental results show significant improvements in classification accuracy and information transfer rate(ITR),achieving 100%and 240 bits/min with 0.5 s sample block.The superior performance demonstrates that this method holds the promising potential to achieve satisfactory performance for high-accuracy SSVEP-based brain-computer interfaces.