Locally Linear Embedding Algorithm Research Articles

A novel local linear embedding algorithm via local mutual representation for bearing fault diagnosis

The locally linear embedding algorithm (LLE) mainly extracts significant features by mining the local neighborhood structure of the data. However, when the data exhibit strong nonlinearity in high-dimensional space, the single neighborhood structure of the LLE algorithm may not accurately capture the local linear relationships between instances, which degrades the performances of the LLE. Therefore, we propose a multi-structure neighborhood locally linear embedding algorithm via local mutual representation (LMR-LLE). Firstly, in each neighborhood, multiple local neighborhood structures of one instance are mined via local mutual representation to enhance the interconnectivity between the instances. Furthermore, the multiple neighborhood structures are fused in the low-dimensional space to construct a global reconstruction model, and the ultimate significant features are acquired by determining the model’s optimal solution. Finally, the extracted features are fed into a classifier for bearing fault diagnosis. Extensive experiments on two rolling bearing datasets illustrate that the LMR-LLE based diagnosis method has better performance accuracy than conventional LLE-based algorithms.

Robust locally linear embedding and its application in analogue circuit fault diagnosis

During long-term operation of analogue circuits, fault diagnosis is important for preventing the occurrence of hazards. However, noise often accompanies sampled signals and makes the task of fault diagnosis more difficult. Therefore, developing a robust feature extraction technique is an indispensable part of fault diagnosis. The locally linear embedding (LLE) algorithm has recently emerged as a promising technique for dimensional reduction and feature extraction because it preserves linear neighborhoods, and it is quite effective when there is a locally linear dependent structure embedded in fault data. However, LLE is sensitive to noise. Therefore, the maximum correntropy criterion is adopted to resist non-Gaussian noise by seeking the optimal weight coefficient, and a half-quadratic optimization procedure is introduced to address the objective function. Moreover, softmax regression is applied to locate faults. Finally, two typical analogue circuit systems are used to demonstrate the robustness of the modified algorithm to non-Gaussian noise. The experimental results show that the robust LLE algorithm can outperform LLE in the extraction of fault features when there is non-Gaussian noise in the fault signals, and the proposed fault diagnosis method has a better effect in locating faults compared with other feature extraction methods.

Texture feature dimensionality reduction-based mammography classification using Random Forest

Breast cancer is the most frequent cancer and the leading cause of death among females. Diagnosis mass from mammogram correctly can reduce the unnecessary biopsy to a large extent. In this paper, we present a novel mammogram classification method combining the Random Forest and the Locally Linear Embedding (LLE) dimensionality reduction algorithm for texture features. The proposed method consists of three stages. In the first stage, preprocessing is performed to enhance the contrast and suppress the noise of the ROI images. Then, the sixteen-dimensional texture features are extracted from Grey Level Co-occurrence Matrix (GLCM) as the input dataset of LLE and being mapped into a five-dimensional subspace. Finally, a Random Forest classifier is investigated for the mammogram classification and compared with the other four classifiers (SVM, KNN, Logistic Regression, MLPC). The experimental results show that the Random Forest classifier outperforms than the others, with an average accuracy of 92.87% and the AUC value of 0.99, that indicates that the combination of LLE algorithm and Random Forest classifier is a promising method for the mammogram classification.

Quantitative evaluation of structural complexity in Shengquan minefield based on improved local linear embedding algorithm

Mine water disaster is closely related to the geological structure of the mine. A scientific evaluation of the complexity of the minefield structure can greatly contribute to mining safety. In this study, we optimized the fault impact index in the study area and proposed an improved local linear embedding (LLE) algorithm by investigating the Shengquan coal mine. We analyzed the fault formation age and connectivity between faults in the study area, combined with topology theory, and based on previous studies. The mechanical properties of faults and the influence of small faults on the strata can be combined to derive a quantitative evaluation model of the structural complexity of mines. Based on the evaluation model, the study area was divided into a simple structural area, a medium structural area, and a complex structural area. By comparing the location of water inrush points in recent years with the three-dimensional high-density electrical exploration of the 21,304 working face, the effectiveness and rationality of structural complexity zoning were determined.

DBSCAN-Based Automatic De-Duplication for Software Quality Inspection Data

Software quality inspection will generate too much data, and removing duplicate data can improve the efficiency of software quality inspection. This paper studies the automatic de-duplication method of software quality inspection data based on density-based spatial clustering of applications with noise (DBSCAN) clustering. Intelligent optimization algorithm is used to generate software quality inspection data by initializing individuals, calculating fitness function value, improving individuals and splitting individuals that meet the conditions. Local linear embedding algorithm is selected to extract software quality inspection data features by searching neighborhood points, calculating reconstruction weight and projection vector. The extracted features are used to select DBSCAN multi-density clustering algorithm of regional division, and the automatic de-duplication of software quality inspection data is realized by grid division, data bin dividing and grid merging. The experimental results show that the precision and recall of this method are higher than 99%, and the resource consumption rate is low, which can effectively improve the efficiency of software quality inspection.

Dual-weight local linear embedding algorithm based on adaptive neighborhood

Local linear embedding (LLE) algorithm mainly depends on local structures to extract significant features; however, the local structures are sensitive to the selection of neighborhood parameters. To solve this problem, the dual-weight local linear embedding algorithm based on adaptive neighborhood (AN-DWLLE) is proposed. First, the neighborhood parameter is adaptively estimated by computing the distances between the inquiry point and the centers of the inquiry point’s candidate neighborhoods. Then, the neighbor sequence and the local linear structures are integrated to construct the robust local structure that can be used to extract the significant features. A large number of experiments are performed on two bearing data sets. The experimental results illustrate that, compared with other related methods, the AN-DWLLE algorithm can extract more salient features and has greater dimensionality reduction effect.

Allying topology and shape optimization through machine learning algorithms

Structural optimization is part of the mechanical engineering field and, in most cases, tries to minimize the overall weight of a given design domain, subjected to functionality constraints given in terms of stresses or displacements. The most relevant techniques are topology and shape optimization. Topology optimization provides the optimal material distribution layout into a given, static, design domain. On the other hand, shape optimization provides the optimal combination of the parameters that define the required parametrization of the domain's boundary. Both techniques have strengths and weaknesses, thus a hybrid optimization approach that combines the former techniques will define a more general structural optimization framework that will take advantage of their synergistic combination. The difficulty arises when communicating both techniques for which, in this paper, we propose a machine learning-based methodology. • We proposed a methodology that allies topology and parametrized shape optimization algorithms, obtaining an hybrid optimization algorithm. • We studied the strengths and weaknesses of topology and shape optimization algorithms, which justified its combination to obtain a synergetic effect. • The use of manifold learning techniques, such as the Locally Linear Embedding (LLE), to extract the principal geometrical modes from a set of material distributions that topology optimization algorithm provides. • In order to properly use the LLE technique, the quasi-boolean material distribution provided by the topology optimization algorithm must be transformed into a richer level-set with the distance information. • The geometrical modes, extracted with the LLE algorithm, may be used to generate brand new geometries, as they define a parametric geometrical model. • The parametric space of geometrical modes may be considered by a shape optimization algorithm as its design space.

Fuzzy Applications in Demonstration of Chinese Teaching Research Based on Machine Learning

In order to improve the effect of Chinese teaching, this paper combines machine learning to conduct Chinese teaching research, constructs an intelligent Chinese teaching system, and conducts online monitoring of the Chinese teaching process. Moreover, this paper uses the general histogram matching algorithm to transfer the color style of the source image to the original image. The image’s local color information will be lost as a consequence of this procedure, according to the processing findings. This paper proposes a multi-directional cutting algorithm to partition the image, then uses the local linear embedding algorithm to realize the color style transfer method, and builds an intelligent Chinese teaching system based on machine learning to achieve a more realistic and natural color style transfer effect. The experimental research shows that the Chinese teaching method based on machine learning proposed in this paper can effectively improve the quality of Chinese teaching.

Pipeline signal feature extraction method based on multi-feature entropy fusion and local linear embedding

This paper considers the problem of effective feature extraction of acoustic signals from oil and gas pipelines under different working conditions. A feature extraction of pipeline leakage detection method is proposed based on multi-feature entropy fusion and local linear embedding (LLE). First, seven kinds of commonly used entropy which can reflect the characteristics of the signal better are extracted from the pipeline signal through experiments, including permutation entropy, envelope entropy, approximate entropy, fuzzy entropy, energy entropy, sample entropy and dispersion entropy. The seven-dimensional feature vectors are obtained by feature fusion. Second, the LLE algorithm is used to reduce the dimension of the feature vector to complete the secondary feature extraction. Finally, the support vector machine (SVM) is used to identify the working conditions of the pipeline. The experimental results show that, compared with other dimensionality reduction methods, single-feature entropy method and multi-feature entropy fusion method, the proposed method can identify the types of pipeline working conditions effectively and reduce the problems of false negatives and false positives in pipeline leakage detection.

State degradation evaluation and early fault identification of wind turbine bearings

To solve the shortage of state degradation characteristic and evaluation parameters in the monitoring of the running state of wind turbine bearings, and the low accuracy of early fault identification, a state degradation characteristic index, which combines multi-scale weighted permutation entropy (MWPE) and local linear embedding algorithm (LLE), is proposed for performance degradation monitoring and early fault identification of wind turbine bearings. The degradation index is quantitatively evaluated by four evaluation parameters: the initial time of state degradation, the sensitivity of initial degradation, the failure mutability and the consistency of degradation trend. Through the full cycle acceleration life monitoring data of the bearings, the result show that the proposed MWPE LLE degradation index can effectively characterize the whole process of bearing life cycle from stable operation to degradation to failure. Compared with the quantitative evaluation result of the kernel principal component analysis (KPCA), weighted permutation entropy (WPE), the root mean square (RMS) and kurtosis index, the comprehensive expression ability of MWPE-LLE degradation index is better. It can not only accurately capture the mutation time of state degradation, but also detect the initial degradation time in advance of the four kinds of characteristic indexes, and accurately judge the failure type of the early failure of the test bearing, and the judgment result is consistent with the inspection result after the experiment.

Local linear embedding algorithm of mutual neighborhood based on multi-information fusion metric

Local linear embedding (LLE) algorithm is an effective tool, which mines low-dimensional features in high-dimensional space. However, the local region and inner structure directly affect the performance of the LLE algorithm. To address this problem, the LLE algorithm of mutual neighborhood by employing multi-information fusion metric (MIFM-MNLLE) is proposed. First, the Euclidean distance and cosine similarity method are combined to evaluate the similary among samples, by which the accuracy of selected neighbors can be improved. Subsequently, the idea of mutual neighbor structure is utilized to construct the neighbor and the mutual neighbor graph of the sample to describe the internal structure of the data set. Finally, the coefficient of LLE is rectified according to the mutual neighborhood relationship between the sample and its neighbors, so as to extract significant features effectively. Extensive experimental results show that the proposed method has better performance compared with the existing methods on bearing datasets.

Dimensionality reduction of tensor data based on local linear embedding and mode product

There are three contributions in this paper. (1) A tensor version of LLE (short for Local Linear Embedding algorithm) is deduced and presented. LLE is the most famous manifold learning algorithm. Since its proposal, various improvements to LLE have kept emerging without interruption. However, all these achievements are only suitable for vector data, not tensor data. The proposed tensor LLE can also be used a bridge for various improvements to LLE to transfer from vector data to tensor data. (2) A framework of tensor dimensionality reduction based on tensor mode product is proposed, in which the mode matrices can be determined according to specific criteria. (3) A novel dimensionality reduction algorithm for tensor data based on LLE and mode product (LLEMP-TDR) is proposed, in which LLE is used as a criterion to determine the mode matrices. Benefiting from local LLE and global mode product, the proposed LLEMP-TDR can preserve both local and global features of high-dimensional tenser data during dimensionality reduction. The experimental results on data clustering and classification tasks demonstrate that our method performs better than 5 other related algorithms published recently in top academic journals.

Generative locally linear embedding: A module for manifold unfolding and visualization

<h2>Abstract</h2> Data often have nonlinear patterns in machine learning. One can unfold the nonlinear manifold of a dataset for low-dimensional visualization and feature extraction. Locally Linear Embedding (LLE) is a nonlinear spectral method for dimensionality reduction and manifold unfolding. It embeds data using the same linear reconstruction weights as in the input space. In this paper, we propose an open source module which not only implements LLE, but also includes implementations of two generative LLE algorithms whose linear reconstruction phases are stochastic. Using this module, one can generate as many manifold unfoldings as desired for data visualization or feature extraction.

Modeling of unsupervised knowledge graph of events based on mutual information among neighbor domains and sparse representation

Text event mining, as an indispensable method of text mining processing, has attracted the extensive attention of researchers. A modeling method for knowledge graph of events based on mutual information among neighbor domains and sparse representation is proposed in this paper, i.e. UKGE-MS. Specifically, UKGE-MS can improve the existing text mining technology's ability of understanding and discovering high-dimensional unmarked information, and solves the problems of traditional unsupervised feature selection methods, which only focus on selecting features from a global perspective and ignoring the impact of local connection of samples. Firstly, considering the influence of local information of samples in feature correlation evaluation, a feature clustering algorithm based on average neighborhood mutual information is proposed, and the feature clusters with certain event correlation are obtained; Secondly, an unsupervised feature selection method based on the high-order correlation of multi-dimensional statistical data is designed by combining the dimension reduction advantage of local linear embedding algorithm and the feature selection ability of sparse representation, so as to enhance the generalization ability of the selected feature items. Finally, the events knowledge graph is constructed by means of sparse representation and l1 norm. Extensive experiments are carried out on five real datasets and synthetic datasets, and the UKGE-MS are compared with five corresponding algorithms. The experimental results show that UKGE-MS is better than the traditional method in event clustering and feature selection, and has some advantages over other methods in text event recognition and discovery.

Predicting the bending rigidity and shearing stiffness of fabric based on three-dimensional drape model

In this paper, the problem of inferring fabric mechanical properties based on three-dimensional (3D) fabric drape model and fabric weight was studied. Firstly, the three-dimensional point cloud of draped fabric was scanned via a self-built three-dimensional scanning device followed with triangulation. Then the local linear embedding (LLE) algorithm was used to resample the three-dimensional draped models (triangular meshes). Besides, all meshes resampled with the same uniform discrete points have the same triangular topology (vertex number and triangle index). Thirdly, the distribution function of curvature (DFC) of resampled 3 D mesh was extracted. At last, four neural networks with the combination of fabric weight and DFC as input were constructed to predict the bending rigidity and shearing stiffness separately. The result shows that the correlation coefficient between true warp bending rigidity and predicted result could reach 0.925. The correlation coefficient between true warp shearing stiffness and the predicted result is 0.7953. The correlation coefficient between true weft bending rigidity and the predicted result is 0.857. The correlation coefficient between true weft shearing stiffness and the predicted result is 0.605.

A novel approach to discriminate transgenic soybean seeds based on terahertz spectroscopy

In qualitative and quantitative terahertz(THz)spectroscopic analyses, reduction and feature extraction of original spectral data are important steps. Due to the parameters, sample preparation, and experimental conditions used in THz time-domain spectroscopy (THz-TDS), the sample absorption lines present different degrees of oscillation and contain certain background noise; therefore spectral data dimension reduction is necessary. Since the existing traditional algorithms, such as principal component analysis, cannot extract useful information from signals, an improved spectral feature extraction method is proposed based on geodesic distance nonlinear reduction and partial least squares regression. Three kinds of transmission spectra of transgenic soybeans are obtained in this experiment. To extract the useful information from the spectral data, principal component analysis (PCA), a locally linear embedding (LLE) algorithm and Floyd's improved LLE algorithm (FLLE) are applied. Multiple linear regression analysis (MLR) and partial least squares regression analysis (PLSR) are performed on the reduced dimensional spectral data. The root mean square error (RMSE) of the FLLE-PLSR algorithm is 0.0079, and the determination coefficient(R) is 0.9966, which are obviously better than those of the PCA-MLR, LLE-MLR, FLLE-MLR, PCA-PLSR and LLE-PLSR algorithms. The proposed method can effectively extract characteristic quantities from the THz spectrum data of transgenic soybeans that have broad application value in agricultural security and food supervision.

WITHDRAWN: A data-driven prognostics method for explicit health index assessment and improved remaining useful life prediction of bearings

Although bearings offer a broad extent of applications and rank among the most-used elements in rotating machinery they also are the most vulnerable to failure. Consequently, "prognostics and health management (PHM)" of bearings has gained awareness in both academia and industry. As it aims to predict future failure events, "remaining useful life (RUL)" prediction is an important process to ensure a reliable and safe operation of bearings in the course of their degradation. However, accurate RUL prediction can hardly be carried out without an explicit health index that fully reflects the bearing's dynamic performance degradation process. Thus, obtaining an explicit health index is a major concern. This paper advocates a novel method to solve this issue. The "proposed method" is based on the ensemble of "deep autoencoder (DAE)" and "locally linear embedding (LLE)". To begin with, secondary features are extracted from the original unprocessed data obtained from sensors. These secondary features are used as inputs to the DAE where they become compressed to a more compact, lower-dimension form. Accordingly, the dimensionally reduced features are evaluated based on a trend factor with which higher-trend features are selected to enhance the accuracy and computational efficiency of the subsequent RUL prediction. The selected features are used as inputs for the LLE algorithm to determine a truly representative explicit health index which fully reflects the bearing's dynamic performance degradation. Having obtained the health index by the "proposed method", the RUL is finally predicted by employing the "long short-term memory (LSTM)" neural network. The obtained results from the experiment, authenticates the "effectiveness and superiority" of the "proposed method".

ANFIS Construction With Sparse Data via Group Rule Interpolation.

A major assumption for constructing an effective adaptive-network-based fuzzy inference system (ANFIS) is that sufficient training data are available. However, in many real-world applications, this assumption may not hold, thereby requiring alternative approaches. In light of this observation, this article focuses on automated construction of ANFISs in an effort to enhance the potential of the Takagi-Sugeno fuzzy regression models for situations where only limited training data are available. In particular, the proposed approach works by interpolating a group of fuzzy rules in a certain given domain with the assistance of existing ANFISs in its neighboring domains. The construction process involves a number of computational mechanisms, including a rule dictionary which is created by extracting the rules from the existing ANFISs; a group of rules which are interpolated by exploiting the local linear embedding algorithm to build an intermediate ANFIS; and a fine-tuning method which refines the resulting intermediate ANFIS. The experimental evaluation on both synthetic and real-world datasets is reported, demonstrating that when facing the data shortage situations, the proposed approach helps significantly improve the performance of the original ANFIS modeling mechanism.

Improved weighted local linear embedding algorithm based on Laplacian eigenmaps

To solve the shortcomings of local linear embedding (LLE), such as sensitive to noise and poor generalization ability for new samples, an improved weighted local linear embedding algorithm based on Laplacian eigenmaps (IWLLE-LE) is proposed in this paper. In the proposed algorithm, Laplacian eigenmaps are used to reconstruct the objective function of dimensionality reduction. The weights of it are introduced by combining the geodesic distance with Euclidean distance, which can effectively represent the manifold structure of nonlinear data. Compared the existing LLE algorithm, the proposed one better maintains the original manifold structure of the data. The merit of the proposal is enhanced by the theoretical analysis and numerical experiments, where the classification recognition rate is 2%–8% higher than LLE.

Stock price forecasting based on Hausdorff fractional grey model with convolution and neural network.

Forecast of stock prices can guide investors' investment decisions. Due to the high-dimensional and long-memory characteristics of stock data, it is difficult to predict. The fractional grey model with convolution (FGMC (1, m)) can be used to predict time series, because of its memory and ability to process high-dimensional data. However, the FGMC (1, m) model has some disadvantages, including complex calculation, loss of information, and approximate background values. In this paper, Hausdorff fractional derivative and Newton-Cotes formula are used to optimize these shortcomings and can get a Hausdorff fractional grey model with convolution (HFGMC (1, m)) model. The HFGMC (1, m)-LLE-BP model is proposed in this paper. HFGMC (1, m) provides a solution that can reduce the complexity of the cumulative generator matrix calculation and preserve the global information of the sequence. Newton-Cotes formula is used to calculate the background value, which can solve the shortcomings of approximate background values. The HFGMC (1, m) model is used to predict the linear component of the sequence, and the BP neural network is used to predict the nonlinear component of the sequence. In addition, because of the high-dimensional and nonlinear characteristics of stock data, a local linear embedding (LLE) algorithm is used to remove redundant information in high-dimensional non-linear data. The experimental results show that the HFGMC (1, m)-LLE-BP model is effective for predicting the stock price in different trends.