Locally Linear Embedding Method Research Articles

State-of-health estimation for lithium-ion batteries based on Bi-LSTM-AM and LLE feature extraction

With the increasing demands for battery safety management, data-driven method becomes a promising solution for highly accurate battery state of health (SOH) estimation. However, the data-driven method faces problems of poor interpretability and high dependence on input features. This paper proposes a SOH estimation method that integrates data-driven model and signal analysis method. Specifically, the differential thermal voltammetry (DTV) analysis method is used to analyze aging characteristics to obtain features strongly related to battery aging and solve the problem of poor interpretability of data-driven methods. The use of local linear embedding method (LLE) for feature extraction has improved model efficiency. A data-driven model is constructed with the Bi-directional long short-term memory (Bi-LSTM) as the core, and the attention mechanism (AM) is added to focus on important parts of the sequence to further improve the accuracy of the model. The proposed method is validated based on the Oxford battery degradation dataset, and the results show that the proposed method achieves high accuracy and strong robustness in SOH estimation with a root mean square error (RMSE) maintained at about 0.4%. This method has the potential to be employed on cloud platforms or end-cloud collaboration systems for online implementation.

Locally linear embedding and plantar pressure–time graph selection in heel pain classification: An observational, case-control study

Plantar heel pain mainly manifests during the gait cycle when the whole foot is in contact with the floor, which corresponds to the second rocker of the gait. This moment can be studied through the analysis of pressure–time graphs obtained using plantar pressure plate systems. However, these graphs are complex, and a dimensionality reduction method, such as locally linear embedding (LLE), greatly assists in their comprehension. This observational, case-control pilot study included 45 subjects divided into case (n = 21) and control (n = 24) groups, depending on the presence/absence of plantar heel pain. The second rocker pressure–time graphs of the 45 subjects were obtained using the Footwork Pro® plantar pressure plate system. These graphs were analyzed and defined as the dynamic simultaneity surfaces (DSSs). This complex structure was composed of four dimensions: the dynamic simultaneity time (DST), slope upward grade (α), slope downward grade (β), and height (h), and were reduced into one dimension and classified into pathological and non-pathological subjects using the LLE method. All 45 DSSs were successfully reduced and classified to distinguish between the case (plantar heel pain) and control (non-plantar heel pain) subjects. This study is the first to use the LLE method for gait analysis. This method serves as a novel and promising tool for the study and classification of pathological and non-pathological gait cycles. This method opens the door for future research and analysis, with significant potential to assess diagnosis, treatment follow-up, and injury prevention in physical medicine consultations.

Analysis of Feasibility Modeling of Multimode Physical Fitness Training for Long-Distance Runners

Because the traditional multimode feasibility modeling analysis method of physical fitness training for long-distance runners has the problems of long modeling time and low modeling accuracy, a new multimode feasibility modeling analysis method for physical fitness training of long-distance runners is proposed. The improved LLE (local linear embedding) method is used to reduce the dimensionality of the training data for the physical fitness of long-distance runners. According to the processing results, the information theory is used to analyze the information content of the physical fitness training features of the long-distance runners, the information entropy of each feature is calculated, and the long-distance runners are extracted. Athlete’s physical fitness enhancement training characteristics, combined with quantitative regression analysis method to carry out the information regression analysis of the long-distance runners’ physical fitness training multimode statistical sequence, construct the feasibility evaluation model of the long-distance runners’ physical fitness training multimode and complete the feasibility of the long-distance runners’ physical fitness training multimode feasibility study Mode analysis. The simulation experiment results show that the proposed method has higher accuracy and shorter modeling time for multimode feasibility modeling of physical fitness training for long-distance runners.

Durability evaluation modelling of rebar Al<SUB align="right">2O<SUB align="right">3 nano-particles epoxy coating

In order to solve the problems of low accuracy and long time of traditional evaluation methods, the durability evaluation model of reinforced Al2O3 nanoparticles epoxy coating was constructed. The prepared Al2O3 nanoparticles were coated with epoxy coating on the steel surface to obtain the Al2O3 nanoparticles epoxy coating. The amount of nano-Al2O3, the adhesion of the coating and the corrosion resistance of the coating were used as the durability evaluation indexes. The improved local linear embedding method was used to preprocess the evaluation index data, and the relative importance of the index was calculated by the analytic hierarchy process (AHP), so as to build the durability evaluation model. The processed evaluation index data were input into the model to obtain the durability score. The experimental results show that the evaluation accuracy of the model is up to 98% and the time is 5s. The practical application effect is good.

Novel approach for automatic mid‐diastole frame detection in 2D echocardiography sequences for performing planimetry of the mitral valve orifice

The mitral valve orifice area is a reliable measure for evaluating mitral valve stenosis (MS) severity, which is obtained by the planimetry of the mid-diastole frame in the echocardiography sequences. Since the manual method for determining this frame is time-consuming and user-dependent, a novel automatic method has been proposed in this study. First, the region of interest (ROI) containing the mitral valve orifice region is detected using circular Hough transform and k-means algorithms. Then, the dimension reduction method is applied to the ROI of each frame to map it into a point in a 2D space. The performance of the local linear embedding (LLE), isometric mapping, kernel principal component analysis (PCA), and linear PCA algorithms has been evaluated in this study. Finally, a distance curve is obtained by calculating the Euclidean distance between consecutive points in 2D space, and the mid-diastole frame is determined by interpreting this curve. The proposed algorithm was validated using 2D echocardiography of the 20 MS patients. Finally, the LLE method showed the best result, and the average frame difference for 20 cases using the proposed method compared with the gold standard (the echo-cardiologist opinion) was 1.40.

Fault Detection Method of Luojia1-01 Satellite Attitude Control System Based on Supervised Local Linear Embedding

This paper is aimed at the telemetry data of Luojia1-01 satellite attitude control system, and carries out the research on high-dimensional data feature extraction and fault detection based on supervised local linear embedding (SLLE). Because the general linear feature extraction method can not mine the feature information of nonlinear high-dimensional telemetry data, a data feature extraction and fault detection method based on local linear embedding is designed. Combined with the statistics SPE and T 2 , the low-dimensional feature information is obtained for data statistics and monitoring faults. Due to the local linear embedded manifold learning method for the traditional batch processing mode is difficult to update and improve the database online, and the supervised local linear embedding method is introduced. The online sample feature extraction and fault detection schemes are designed, and the database is updated by updating the weight matrix through online samples. Finally, the effectiveness of the method is verified by Luojia1-01 satellite telemetry data. The results show that the fault detection method based on SLLE reduces the false alarm rate (FAR) by approximately 3% and the missing alarm rate (MAR) by approximately 10% compared with local linear embedding (LLE). This method effectively improves the detection capability of the anomalous state of Luojia1-01 satellite and has certain engineering application value.

Gearbox Fault Diagnosis Based on a Novel Hybrid Feature Reduction Method

The dimensionality reduction of the high-dimensional feature space is a critical part for data preprocessing, which directly affects the accuracy of fault diagnosis. In this paper, a novel hybrid algorithm named principal component locally linear embedding (PCLLE) is introduced to compress the original high-dimensional feature. This approach combines the optimization objectives of the principal component analysis (PCA) and locally linear embedding (LLE), which attempts to find a mapping that meets the optimization goals of PCA and LLE at the same time. It is applied on the gearbox fault diagnosis. In the experiment, the extracted fault-sensitive feature is compressed by PCLLE method. Then, the compressed feature is embedded with five classifiers for fault detection. To evaluate the performance of the proposed new method, the traditional PCA and LLE methods are introduced for comparison. Experimental results show that the PCLLE algorithm has good performance during the classification process compared with the traditional PCA and LLE method.

얼굴 인식을 위한 연립 대각화와 국부 선형 임베딩

Locally linear embedding (LLE) [1] is a type of manifold algorithms, which preserves inner product value between high-dimensional data when embedding the high-dimensional data to low-dimensional space. LLE closely embeds data points on the same subspace in low-dimensional space, because the data points have significant inner product values. On the other hand, if the data points are located orthogonal to each other, these are separately embedded in low-dimensional space, even though they are in close proximity to each other in high-dimensional space. Meanwhile, it is well known that the facial images of the same person under varying illumination lie in a low-dimensional linear subspace [2]. In this study, we suggest an improved LLE method for face recognition problem. The method maximizes the characteristic of LLE, which embeds the data points totally separately when they are located orthogonal to each other. To accomplish this, all of the subspaces made by each class are forced to locate orthogonally. To make all of the subspaces orthogonal, the simultaneous Diagonalization (SD) technique was applied. From experimental results, the suggested method is shown to dramatically improve the embedding results and classification performance.

HYPERSPECTRAL IMAGE CLASSIFICATION USING LOCAL SPECTRAL ANGLE-BASED MANIFOLD LEARNING

Locally linear embedding (LLE) depends on the Euclidean distance (ED) to select the k-nearest neighbors. However, the ED may not reflect the actual geometry structure of data, which may lead to the selection of ineffective neighbors. The aim of our work is to make full use of the local spectral angle (LSA) to find proper neighbors for dimensionality reduction (DR) and classification of hyperspectral remote sensing data. At first, we propose an improved LLE method, called local spectral angle LLE (LSA-LLE), for DR. It uses the ED of data to obtain large-scale neighbors, then utilizes the spectral angle to get the exact neighbors in the large-scale neighbors. Furthermore, a local spectral angle-based nearest neighbor classifier (LSANN) has been proposed for classification. Experiments on two hyperspectral image data sets demonstrate the effectiveness of the presented methods.

Variable selection based on locally linear embedding mapping for near-infrared spectral analysis

Locally linear embedding (LLE) is a nonlinear dimensionality reduction method that can preserve the relationship between samples in the mapping space. The neighbors in high dimensional space will keep their relative position in LLE space. A method based on the effect of the variables on the relative position of the samples in LLE space was proposed for variable selection in NIR spectral analysis. In the method, the spectra are mapped into LLE space with all variables at first, and then the mapping is repeated by removing a variable from the spectra. Therefore, the movement of the samples in LLE space caused by a variable can be used to evaluate the effect of the variable on the spectra. The variables that cause a large movement will be the important ones to affect the relationship of the spectra. For further selection of the informative variables specific to the target component, a forward stepwise selection is applied to the variables selected by LLE method. To validate the performance of the proposed method, it was applied to the partial least squares (PLS) modeling of three NIR spectral datasets of corn, pharmaceutical tablets and tobacco lamina samples. Results show that the proposed method can effectively select the informative variables from the NIR spectra, and build a parsimonious model by using several tens of selected variables.

An Incremental Locally Linear Embedding Algorithm with Non-Negative Constraints of the Weights

Locally Linear Embedding (LLE) is a batch method. When new sample is added, the whole algorithm must be run repeatedly and all the former computational results are discarded. In the paper, the LLE algorithm processing on new sample points is analyzed. For the insufficient precision of the processing of traditional incremental LLE, an incremental LLE algorithm based on non-negative constraints of the weights is proposed. Non-negative constraints of linear weights are imposed on the new sample points in the projection process. The simple fitting of the original algorithm from the engineering application is avoided by the proposed algorithm and the problem of the constantly updating of the whole manifold is solved at the case of new samples being added. Compared with the traditional incremental LLE method, S-curve simulation data and engineering examples analysis show the feasibility and effectiveness of the proposed algorithm.

Improved Locally Linear Embedding Based Method for Nonlinear System Fault Detection

In order to detect faults of nonlinear systems, an approach based on improved Locally Linear Embedding (LLE) was proposed. Firstly, the raw data was projected to lower dimensional space by LLE. In this step, tangent space distance was introduced to LLE and certain enhancement had also been made to intrinsic dimension estimation to make the approach more efficient and robust. Secondly, the inner class distance of data was calculated as an index of fault detection. To demonstrate the effectiveness of the improved LLE method, it is applied to Tennessee Eastman (TE) process and compared with kernel principle component analysis (KPCA) method. By simulation analysis, the false negative rate of the proposed approach achieves 4.498% in average, which is much better than 77.53% of KPCA, certifying the effectiveness of the approach to nonlinear fault detection.

Identification Method of Tool Wear Based on Locally Linear Embedding and Support Vector Machine

Aiming at the nonlinear characteristics of the tool wear Acoustic Emission signal, tool wear state identification method is proposed based on local linear embedding and vector machine supported. The local linear embedding algorithm makes high dimensional information down to low dimension feature space through commutation, and thus to compress the data for highlighting signal features. This algorithm well compensates for the weakness of linear dimension reduction failing to find datasets nonlinear structure. In this paper, acoustic emission signal is firstly made by phase space reconstruction. Using local linear embedding method, the high dimension space mapping data points are reflected into low-dimensional space corresponding data points, then extracting tool wear state characteristics, and using vector machine supported classifier to identify classification of the tool wear conditions. Experimental results show that this method is used for the exact recognition of the tool wear state, and has widespread tendency.

An Improved Locally Linear Embedding Method for Feature Extraction

In this work, a feature extraction approach based on improved Locally Linear Embedding(LLE) is proposed. In the algorithm, tangent space distance is introduced to LLE, which overcomes the shortcoming of original LLE method based on Euclidean distance. It can satisfy the requirement of locally linear much better and so can express the I/O mapping quality better than classical method. Simulation results are given to demonstrate the effectiveness of the improved LLE method.

Supervised Locally Linear Embedding for Fault Diagnosis

Fault diagnosis is a kind of pattern recognition problem and how to extract diagnosis features and improve recognition performance is a difficult problem. Local Linear Embedding (LLE) is an unsupervised non-linear technique that extracts useful features from the high-dimensional data sets with preserved local topology. But the original LLE method is not taking the known class label information of input data into account. A new characteristics similarity-based supervised locally linear embedding (CSSLLE) method for fault diagnosis is proposed in this paper. The CSSLLE method attempts to extract the intrinsic manifold features from high-dimensional fault data by computing Euclidean distance based on characteristics similarity and translate complex mode space into a low-dimensional feature space in which fault classification and diagnosis are carried out easily. The experiments on benchmark data and real fault dataset demonstrate that the proposed approach obtains better performance compared to SLLE, and it is an accurate technique for fault diagnosis.

CLASSIFICATION-ORIENTED LOCALLY LINEAR EMBEDDING

The locally linear embedding (LLE) algorithm is hypothetically able to find a lower dimensional space than a linear method for preserving a data manifold originally embedded in a high dimensional space. However, uneven sampling over the manifold in real-world data ultimately causes LLE to suffer from the disconnected-neighborhood problem. Consequently, the final dimensionality required for the data manifold is multiplied by the number of disjoint groups in the complete data representation. In addition, LLE as an unsupervised method is unable to suppress between-class connections. This means that samples from different classes are mixed during reconstruction. This study presents CLLE, a classification-oriented LLE method that uses class label information from training samples to guide unsupervised LLE. The criterion for neighbor selection is redesigned using class-conditional likelihood as well as Euclidean distance. This algorithm largely eliminates fractured classes and lowers the incidence of connections between classes. Also, a reconnection technique is proposed as a supporting method for ensuring a fully connected neighborhood graph, so that CLLE is able to extract the fewest features. Experiments with simulated and real data show that CLLE exceeds the performance of linear methods. Comparable classification performance can be achieved by CLLE using fewer features. In comparison with LLE, CLLE demonstrates a higher aptitude for and flexibility towards classification.

Face detection in gray scale images using locally linear embeddings

The problem of face detection remains challenging because faces are non-rigid objects that have a high degree of variability with respect to head rotation, illumination, facial expression, occlusion, and aging. This paper employs a novel technique, known as locally linear embedding (LLE), for solving the face detection problem. The LLE method performs dimensionality reduction on data for learning and classification purposes. Proposed by Roweis and Saul, the intent of LLE is to determine a locally linear fit so that each data point can be represented by a linear combination of its closest neighbors. The first objective of this research is to apply the LLE algorithm to 2D facial images to obtain their representation in a sub-space under the specific conditions stated above. The low-dimensional data are then used to train support vector machine (SVM) classifiers to label windows in images as being either face or non-face. Six different databases of cropped facial images, corresponding to variations in head rotation, illumination, facial expression, occlusion and aging, were used to train and test the classifiers. The second objective was to evaluate the feasibility of using the combined efficacy of the six SVM classifiers in a two-stage face detection approach. Experimental results obtained demonstrated that the performance of the proposed method was similar and sometimes better when compared to other face detection methods, thus indicating a viable and accurate technique.