Linear Representation Method Research Articles

On the solution of the interpretation tomography problem within the framework of the linear integral representation method and discrete gravity and magnetic potential theories

A new of principle approach to solving inverse problems of geophysics on the background of the linear integral representation method and discrete gravity and magnetic potential theories is proposed. This approach makes it possible to restore the continuously distributed masses with relatively high accuracy from the heterogeneous data in some network points.

Solution of the Interpretation Tomography Problem in Geophysics under the Linear Integral Representation Method and Theories of Discrete Gravity and the Magnetic Potential

Solution of the Interpretation Tomography Problem in Geophysics under the Linear Integral Representation Method and Theories of Discrete Gravity and the Magnetic Potential

Hypergraph modeling and hypergraph multi-view attention neural network for link prediction

Hypergraph neural networks are widely used in link prediction because of their ability to learn the high-order structure relationship. However, most existing hypergraph modeling relies on the attribute information of nodes. And as for the link prediction, missing links are not utilized when training link predictors, so conventional transductive hypergraph learning are generally not consistent with link prediction tasks. To address these limitations, we propose the Network Structure Linear Representation (NSLR) method to model hypergraph for general networks without node attribute information and the inductive hypergraph learning method Hypergraph Multi-view Attention Neural Network (HMANN) that learns the rich high-order structure information from node-level and hyperedge-level. Also, this paper put forwards a novel NSLR-HMANN link prediction algorithm based on NSLR and HMANN methods. Extensive comparison and ablation experiments show that the NSLR-HMANN link prediction algorithm achieves state-of-the-art performance on link prediction and has better performance on robustness.

On Constructing Analytical Models of the Magnetic Field of Mercury from Satellite Data

Abstract—A new method is proposed for analytical description of the magnetic field of the Mercury from the data of satellite missions based on the local and regional versions of the linear integral representation method. The inverse problem on finding the sources of the field is reduced to solving ill-conditioned systems of linear algebraic equations with an approximately set right-hand part. The charts of the isolines of the z-component of the magnetic inductance vector in the Cartesian coordinate system rigidly connected with the planet, as well as the regional S-approximation of the field radial component are plotted. The results of the mathematical experiment on analytic continuation of the magnetic field towards the sources are presented.

Equilibrium space and a pseudo linearization of nonlinear systems

This paper attempts to extend the concept of the equilibrium point to what is called equilibrium space, which can adapt to a system in which there exists an infinite number of equilibrium points. In the context of Lyapunov’s linearization method extended for the equilibrium space, this paper proposes a pseudo linearization, from which we can derive a linear representation for a nonlinear system. The equilibrium state of this pseudo linearization and its stability are shown to be the same as that of the original nonlinear system. As an example of the applicability, the proposed pseudo linearization is applied to derive a discrete-time model for a control moment gyroscope system from a nonlinear continuous-time model. Simulation results show that the discrete-time model derived using the proposed pseudo linearization yields responses that are closer to that of the continuous-time model than the discrete-time model derived by the well-known forward-difference method and the conventional pseudo linear representation method, even with a large sampling interval.

Fault Diagnosis Method of Electromagnetic Launch and Recovery Systems Based on Large-Scale Time Series Similarity Search

Rapid fault diagnosis of electromagnetic launch and recovery (EMLR) Systems is of great significance. It is an important research direction to diagnose the system fault by mining the event data collected during the operation of a certain type of arresting gear controller. While event data have the characteristics of high sampling rate, multidimensional coupling, and nonperiodic transient, which belongs to complex large-scale time series, the existing steady-state time series diagnosis methods are not applicable. In order to solve this problem, this article proposes a large-scale time series similarity search method based on Transformer and M-Tree index to realize fault diagnosis. First, the dimension of event data was preliminarily reduced by the proposed piecewise linear representation method integrating important points and piecewise aggregation approximation (PAA). Second, referring to Transformer and its variant models, a feature extraction model was constructed to further extract temporal features, and index was organized through M-Tree to improve search efficiency. Finally, an improved dynamic time warping (DTW) early abandon algorithm was proposed to further optimize the accurate calculation of DTW to quickly match and locate faults. Experimental results show that the proposed method can match working conditions, identify, and locate system abnormalities quickly and accurately, which proves the effectiveness of the algorithm.

A representation coefficient-based k-nearest centroid neighbor classifier

K-nearest neighbor rule (KNN) has been regarded as one of the top 10 methods in the field of data mining. Due to its simplicity and effectiveness, it has been widely studied and applied to various classification tasks. In this article, we develop a novel representation coefficient-based k-nearest centroid neighbor method (RCKNCN), which aims to further improve the classification performance and reduce the method’s sensitivity to the neighborhood size k, especially in the cases of small sample size. Different from existing KNN-based methods, RCKNCN is able to capture both the proximity and the geometry of k-nearest neighbors, and learn to differentiate the contribution of each neighbor to the classification of a testing sample through a linear representation method. Moreover, under the RCKNCN framework, we also propose a novel weighted majority voting algorithm using the representation coefficients associated with individual nearest centroid neighbors, which are deemed to hold more discriminative information of the neighbors. To fully study the classification performance of RCKNCN, we compare it with the state-of-the-art KNN-based methods on many data sets that are widely used in the literature. The extensive experiments demonstrate the effectiveness and robustness of our method in various classification tasks.

A New Approach to Analytical Modeling of Mars’s Magnetic Field

ABSTRACT A new three-staged technique based on various versions of the linear integral representation method (S-, F- and R-approximations) is applied to solve the problem of analytical modelling of the magnetic field on the surface of Mars. At the first step, we build an analytical approximation from the given data set (in local or regional cases). In the second step, we analyze the previous stage results and solve an ordinary differential equation system to find the integral curve of the gravity or magnetic field. The points of this curve are included in an extended data set, and we repeat the procedure described above for the first stage. The final approximation of the anomalous field elements or the topographic data allows us to find various linear transformations of the field under investigation, e.g. higher derivatives of the potential or Fourier-spectra of the field elements. Analytical downward continuations of the magnetic field of Mars at various distances, including the planet's surface is presented.

A Shapelet Transform Classification over Uncertain Time Series

A shapelet is a time-series subsequence that can represent local, phase-independent similarity in shape. Time series classification with subsequences can save computing cost, improve computing speed and improve algorithm accuracy. The shapelet-based approaches for time series classification have an advantage of interpretability. Concentrating on uncertain time series, this paper tries to apply the shapelet-based method to classify uncertain time series. Due to the high dimensions of time series, the number of the generated candidate shapelets is generally huge. As a result, the calculation amount is large too. To deal with this problem, in this paper, we introduce a piecewise linear representation (PLR) method for uncertain time series based on key points so that the traditional shapelet discovery algorithm can be improved efficiently. We verify our approach with experiments. The experimental results show that the proposed shapelet algorithm can be used for uncertain time series and it can provide classification accuracy well while reducing time cost.

A root-cause analysis methodfor faultdiagnosisin condenser

Condenser is an important part of thermal power units. When the condenser fails, the quick determination of the root-cause fault can effectively avoid major safety accidents in thermal power units. Most existing methods are based on the assumption of stationary relationships among the variables. However, the relationships among the variables are non-stationary in the real industrial process. These methods are not suitable for real industries. According to the process knowledge, the condenser is a typical system of non-stationary. Aiming atthe non-stationary relationships, a root-cause analysis method based on multiple regression modelsis proposed in this paper.Firstly, the bottom-up piecewise linear representation method is applied to yield qualitative trends of historical data for each variable. Secondly, qualitative trend combinations of multiple variables are obtained based on amplitudes for each variable. Finally, the contributionsof the related variables in qualitative trend combinations to the main variableare calculatedbased on multiple regression models, and the root-cause variable can be determined according to the size of the contribution. Anindustrial example is provided to illustrate the effectiveness of the proposed method.

LNRLMI: Linear neighbour representation for predicting lncRNA-miRNA interactions.

LncRNA and miRNA are key molecules in mechanism of competing endogenous RNAs(ceRNA), and their interactions have been discovered with important roles in gene regulation. As supplementary to the identification of lncRNA‐miRNA interactions from CLIP‐seq experiments, in silico prediction can select the most potential candidates for experimental validation. Although developing computational tool for predicting lncRNA‐miRNA interaction is of great importance for deciphering the ceRNA mechanism, little effort has been made towards this direction. In this paper, we propose an approach based on linear neighbour representation to predict lncRNA‐miRNA interactions (LNRLMI). Specifically, we first constructed a bipartite network by combining the known interaction network and similarities based on expression profiles of lncRNAs and miRNAs. Based on such a data integration, linear neighbour representation method was introduced to construct a prediction model. To evaluate the prediction performance of the proposed model, k‐fold cross validations were implemented. As a result, LNRLMI yielded the average AUCs of 0.8475 ± 0.0032, 0.8960 ± 0.0015 and 0.9069 ± 0.0014 on 2‐fold, 5‐fold and 10‐fold cross validation, respectively. A series of comparison experiments with other methods were also conducted, and the results showed that our method was feasible and effective to predict lncRNA‐miRNA interactions via a combination of different types of useful side information. It is anticipated that LNRLMI could be a useful tool for predicting non‐coding RNA regulation network that lncRNA and miRNA are involved in.

Block-Extraction and Haar Transform Based Linear Singularity Representation for Image Enhancement

In this paper, we develop a novel linear singularity representation method using spatial K-neighbor block-extraction and Haar transform (BEH). Block-extraction provides a group of image blocks with similar (generally smooth) backgrounds but different image edge locations. An interblock Haar transform is then used to represent these differences, thus achieving a linear singularity representation. Next, we magnify the weak detailed coefficients of BEH to allow for image enhancement. Experimental results show that the proposed method achieves better image enhancement, compared to block-matching and 3D filtering (BM3D), nonsubsampled contourlet transform (NSCT), and guided image filtering.

Locality-constrained least squares regression for subspace clustering

Low-rank representation (LRR) is a typical data representation method that has been developed in recent years. Based on the main idea of LRR, least squares regression (LSR) constructs a new optimization problem to group the highly correlated data together. Compared with other LRR algorithms that are sophisticated, LSR is simpler and more efficient. It is a linear representation method that captures the global structure of data with a low-rank constraint. Research has shown that locality constraints typically improve the discrimination of the representation and demonstrate better performance than those “non-local” methods for image recognition tasks. To combine LSR and the locality constraints, we propose a novel data representation method called locality-constrained LSR (LCLSR) for subspace clustering. LCLSR forces the representation to prefer the selection of neighborhood points. The locality constraint is calculated based on the Euclidean distances between data points. Under the locality constraint, the obtained affinity matrix captures the locally linear relationship for data points lie on a nonlinear manifold. We propose three approaches to obtain the locality constraint and compare their performance with other related work on subspace clustering. We conducted extensive experiments on several datasets for subspace clustering. The results demonstrated that the proposed DCLSR, LCLSR ε, and LCLSRk substantially outperformed state-of-the-art subspace clustering methods.

Subspace clustering using a low-rank constrained autoencoder

The performance of subspace clustering is affected by data representation. Data representation for subspace clustering maps data from the original space into another space with the property of better separability. Many data representation methods have been developed in recent years. Typical among them are low-rank representation (LRR) and an autoencoder. LRR is a linear representation method that captures the global structure of data with low-rank constraint. Alternatively, an autoencoder nonlinearly maps data into a latent space using a neural network by minimizing the difference between the reconstruction and input. To combine the advantages of an LRR (globality) and autoencoder (self-supervision based locality), we propose a novel data representation method for subspace clustering. The proposed method, called low-rank constrained autoencoder (LRAE), forces the latent representation of the neural network to be of low rank, and the low-rank constraint is computed as a prior from the input space. One major advantage of the LRAE is that the learned data representation not only maintains the local features of the data, but also preserves the underlying low-rank global structure. Extensive experiments on several datasets for subspace clustering were conducted. They demonstrated that the proposed LRAE substantially outperformed state-of-the-art subspace clustering methods.

Robust face recognition via sparse boosting representation

Recently linear representation provides an effective way for robust face recognition. However, the existing linear representation methods cannot make an adaptive adjustment in responding to the variations on facial image, so the generalization ability of these methods is limited. In this paper, we propose a sparse boosting representation classification (SBRC) for robust face recognition. To improve the effectiveness of representation coding, an error detection machine (EDM) with multiple error detectors (ED) in SBRC, is proposed to detect and remove destroyed features (i.e. pixels) on a testing image. SBRC has three advantages: First, it has good generalization ability, since the EDM can self-adjust the number of ED according to different variations; Second, EDM would boost the sparsity of coding vector; Third, its implementation is simple and efficient as the EDM is based on l2−norm. In addition, five popular face image databases including AR database, Extended Yale B database, ORL database, FERET database and LFW database were applied to validate the performance of SBRC. The superiority of SBRC is confirmed by comparing it with the state-of-the-art face recognition methods.

Exploring supervised neighborhood preserving embedding (SNPE) as a nonlinear feature extraction method for vibrational spectroscopic discrimination of agricultural samples according to geographical origins

Supervised neighborhood preserving embedding (SNPE), a nonlinear dimensionality reduction method, was employed to represent near-infrared (NIR) and Raman spectral features of agricultural samples (Angelica gigas, sesame, and red pepper), and the newly constructed variables were used to discriminate their geographical origins. This study was done to evaluate the potential of SNPE for recognizing minute spectral differences between classes by preserving local relationships, in comparison with widely adopted linear feature representation methods such as principal component analysis (PCA) and partial least squares (PLS). For this purpose, diffuse reflectance NIR spectral datasets of Angelica gigas, sesame, and red pepper, and a Raman spectral dataset of the same red pepper were prepared. The spectra were represented into new variables in reduced dimensions by PCA, PLS, neighborhood preserving embedding (NPE), and SNPE, and the represented variables were used to determine the geographical origins of samples by using the k-nearest neighbor (k-NN) and support vector machine (SVM). The combination of SNPE and SVM differentiated the geographical origins with improved accuracy. Overall results demonstrate that SNPE is a valuable alternative feature representation method, especially when complex and highly overlapping vibrational spectra are used for analysis.

New method for multi-state system reliability analysis based on linear algebraic representation

Multi-state system is a certain complex system with failure criteria that are not limited to “normal or failure.” During the life cycle, both the system and each component inside have different states at any time point. State transition of the whole system depends on the structure function while that of any component has a certain mechanism. To directly express state transition processes of the whole system and all components, we develop a linear algebraic representation method. Based on this method, dynamic transition can be expressed by mathematic equations, in which information of both system structure function and components transition mechanism is embedded. Furthermore, the extended multi-state dynamic fault tree is introduced to multi-state system modeling. By means of the proposed linear algebraic representation, standard operating rules for both static and dynamic gates are generated by introducing two variables that are used to determine whether the transition occurs and which state the output would convert into, respectively. Then, a Monte Carlo simulation coupled with the multi-state dynamic fault tree method is proposed to calculate the reliability indices of a multi-state system. The proposed method is then validated with a dynamic fault tree problem from a literature. Finally, the servo turret system is taken as an example for the application of the proposed method.

L1-norm locally linear representation regularization multi-source adaptation learning

In most supervised domain adaptation learning (DAL) tasks, one has access only to a small number of labeled examples from target domain. Therefore the success of supervised DAL in this “small sample” regime needs the effective utilization of the large amounts of unlabeled data to extract information that is useful for generalization. Toward this end, we here use the geometric intuition of manifold assumption to extend the established frameworks in existing model-based DAL methods for function learning by incorporating additional information about the target geometric structure of the marginal distribution. We would like to ensure that the solution is smooth with respect to both the ambient space and the target marginal distribution. In doing this, we propose a novel L1-norm locally linear representation regularization multi-source adaptation learning framework which exploits the geometry of the probability distribution, which has two techniques. Firstly, an L1-norm locally linear representation method is presented for robust graph construction by replacing the L2-norm reconstruction measure in LLE with L1-norm one, which is termed as L1-LLR for short. Secondly, considering the robust graph regularization, we replace traditional graph Laplacian regularization with our new L1-LLR graph Laplacian regularization and therefore construct new graph-based semi-supervised learning framework with multi-source adaptation constraint, which is coined as L1-MSAL method. Moreover, to deal with the nonlinear learning problem, we also generalize the L1-MSAL method by mapping the input data points from the input space to a high-dimensional reproducing kernel Hilbert space (RKHS) via a nonlinear mapping. Promising experimental results have been obtained on several real-world datasets such as face, visual video and object.

A patent time series processing component for technology intelligence by trend identification functionality

Technology intelligence indicates the concept and applications that transform data hidden in patents or scientific literatures into technical insight for technology strategy-making support. The existing frameworks and applications of technology intelligence mainly focus on obtaining text-based knowledge with text mining components. However, what is the corresponding technological trend of the knowledge over time is seldom taken into consideration. In order to capture the hidden trend turning points and improve the framework of existing technology intelligence, this paper proposes a patent time series processing component with trend identification functionality. We use piecewise linear representation method to generate and quantify the trend of patent publication activities, then utilize the outcome to identify trend turning points and provide trend tags to the existing text mining component, thus making it possible to combine the text-based and time-based knowledge together to support technology strategy making more satisfactorily. A case study using Australia patents (year 1983---2012) in Information and Communications Technology industry is presented to demonstrate the feasibility of the component when dealing with real-world tasks. The result shows that the new component identifies the trend reasonably well, at the same time learns valuable trend turning points in historical patent time series.

Measurement and correction of coupling in BEPC II

The existing linear coupling theory and representation method are introduced briefly. The so-called local and global coupling is discussed in more detail. The vertical orbit distortion excited by a horizontal corrector is represented with the coupling parameters at the corrector and the observation point. The formula is used to measure the coupling in BEPCII. In order to correct the coupling, vertical correctors are used to change the vertical orbit through sextupoles by a least square method. We also introduce and review other frequently used coupling measurement/tuning methods used in our machine.