Locally Linear Embedding Algorithm Research Articles

1D representation of locally linear embedding for image prediction

Image prediction is a very important step in image and video coding. LLE (locally linear embedding) is a famous algorithm of NLDR (nonlinear dimensionality reduction), and it is capable of projecting high dimensional image blocks into a low dimensional space of embedding. This paper is concerned with the image prediction by 1D representation of LLE algorithm. Two LLE algorithms have been studied. One is the general LLE algorithm, the other is the proposed distance-keeping based LLE algorithm, which has the merit of preserving the distance property in low dimensional space. 1D representation of LLE algorithms can hugely improve the CR (compression ratio). The training input and output of LLE algorithms are employed as training pair for ERA (embedding and reconstruction algorithm) of testing samples, and the training pair is as large as possible to overcome the inherent disadvantage of classical algorithms for image prediction, which only utilize the adjacent image blocks. Three stable ERAs have been proposed. The first is general ERA, the second is nearest neighbor based ERA, and the third is machine learning based ERA. The nearest neighbor based ERA has the best performance if the training samples are sufficient, while the machine learning based ERA has the best performance if the training samples are insufficient. Three DLAs (dictionary learning algorithms) for selecting training samples are presented. The first is exemplars based DLA, the second is K-means clustering based DLA, and the third is sparse representation based DLA. The K-means clustering based DLA has the best performance. A unified framework for intra-frame, inter-frame, multi-view, 3D and multi-view 3D image prediction, has been built according to the proposed algorithms. The performance of proposed algorithms for image prediction has been evaluated by simulation experimentations. The results of simulation experiments indicate that proposed algorithms are able to gain very high PSNR (peak signal to noise ratio). The results of simulation experiments also reveal that 1D representation of distance-keeping based LLE algorithm, machine learning based ERA, and K-means clustering based DLA are very effective and efficient for image prediction.

Evaluation of ShARP Passive Rainfall Retrievals over Snow-Covered Land Surfaces and Coastal Zones

AbstractUsing satellite measurements in microwave bands to retrieve precipitation over land requires proper discrimination of the weak rainfall signals from strong and highly variable background Earth surface emissions. Traditionally, land retrieval methods rely on a weak signal of rainfall scattering on high-frequency channels and make use of empirical thresholding and regression-based techniques. Because of the increased surface signal interference, retrievals over radiometrically complex land surfaces—snow-covered lands, deserts, and coastal areas—are particularly challenging for this class of retrieval techniques. This paper evaluates the results by the recently proposed Shrunken Locally Linear Embedding Algorithm for Retrieval of Precipitation (ShARP) using data from the Tropical Rainfall Measuring Mission (TRMM) satellite. The study focuses on a radiometrically complex region, partly covering the Tibetan highlands, Himalayas, and Ganges–Brahmaputra–Meghna River basins, which is unique in terms of its diverse land surface radiation regime and precipitation type, within the TRMM domain. Promising results are presented using ShARP over snow-covered land surfaces and in the vicinity of coastlines, in comparison with the land rainfall retrievals of the standard TRMM 2A12, version 7, product. The results show that ShARP can significantly reduce the rainfall overestimation due to the background snow contamination and markedly improve detection and retrieval of rainfall in the vicinity of coastlines. During the calendar year 2013, compared to TRMM 2A25, it is demonstrated that over the study domain the root-mean-square difference can be reduced up to 38% annually, while the improvement can reach up to 70% during the cold months of the year.

Application in Face Recognition Based on Improved Local Linear Embedding Algorithm and Artificial Vector Machine

In order to improve the accuracy of face recognition in a variety of gestures, a face recognition method of improved local linear embedding algorithm is proposed. First, facial features are extracted by Gabor transform and then dimensions of the facial features are reduced according to the local linear embedding algorithm to obtain characteristic vectors of face recognition. Finally, faces are recognized by using supporting vector machine. Simulation experiments have shown that algorithm in this paper can obtain a higher face recognition rate to a certain extent with a certain promotional effect.

An improved LLE algorithm based on iterative shrinkage for machinery fault diagnosis

Local linear embedding (LLE) algorithm is widely utilized to feature extraction for fault diagnosis, but the diagnosis result is sensitive to reconstruction weight W of LLE. To make W more significant and robust, in this paper, ISLLE algorithm is proposed with the aid of iterative shrinkage technology and LLE algorithm. In ISLLE algorithm, a surrogate function is introduced, upon which the high-dimensional optimization problem can be decoupled into a set of one-dimensional equations, then W can be easily computed by iterative shrinkage method. In each iteration, the small and negative weight coefficients are eliminated, while the large ones are shrunk, which can be regarded as feature extraction and noise reduction. Hence, the signals processed by ISLLE are more beneficial to diagnosis. Three real datasets are used to examine the proposed method. The experimental results demonstrate that the proposed method is valid, and the performance of ISLLE outperforms that of the original LLE.

A novel sparse coding algorithm for classification of tumors based on gene expression data.

High-dimensional genomic and proteomic data play an important role in many applications in medicine such as prognosis of diseases, diagnosis, prevention and molecular biology, to name a few. Classifying such data is a challenging task due to the various issues such as curse of dimensionality, noise and redundancy. Recently, some researchers have used the sparse representation (SR) techniques to analyze high-dimensional biological data in various applications in classification of cancer patients based on gene expression datasets. A common problem with all SR-based biological data classification methods is that they cannot utilize the topological (geometrical) structure of data. More precisely, these methods transfer the data into sparse feature space without preserving the local structure of data points. In this paper, we proposed a novel SR-based cancer classification algorithm based on gene expression data that takes into account the geometrical information of all data. Precisely speaking, we incorporate the local linear embedding algorithm into the sparse coding framework, by which we can preserve the geometrical structure of all data. For performance comparison, we applied our algorithm on six tumor gene expression datasets, by which we demonstrate that the proposed method achieves higher classification accuracy than state-of-the-art SR-based tumor classification algorithms.

Super resolution face image based on locally linear embedding and local correlation

In this paper, we propose a new face hallucination algorithm based on Locally Linear Embedding and Local Correlation method (LC-LLE). The LC-LLE algorithm is an improved locally linear embedding (LLE) algorithm by combining LLE algorithm and local correlation coefficients. The main difference between LC-LLE and LLE algorithms is that LC-LLE uses two different measures for searching the nearest neighbors for matching the most similar patches, while LLE uses only Euclidean distance for searching the nearest neighbors. Specifically, we calculate the Euclidean distance between the low-resolution input patch and patches in the low-resolution training images to select z -NN (i.e. z number of nearest patches). Then, we use the inner product for local correlation computation between the input patch and selected z -NN to identify k nearest neighbors (i.e. k -NN). After that the reconstruction weights are derived using k -NN patches, and generate the high-resolution image patches based on the reconstruction weights. Finally, high-resolution patches are synthesized into the high-resolution image. Experimental results show that the proposed method achieves better performance for high-resolution image reconstruction than Ma's method with LLE and PCA methods.

High Voltage Equipment PD Pattern Recognition Based on BP Classifier

The corresponding discharge waveforms were detected by ultrasonic sensor. The dimension of feature vectors extracted from discharge waveforms were reduced by local linear embedding algorithm. The processed vectors were used as input to train and test BP_Adaboost classifier. Recognition results show that, high voltage reactor insulating defects recognition with this method can reduce the calculation and maintain a high recognition rate at the same time. This shows its effectiveness in the application of partial discharge pattern recognition.

Fault Diagnosis of Supervision and Homogenization Distance Based on Local Linear Embedding Algorithm

In view of the problems of uneven distribution of reality fault samples and dimension reduction effect of locally linear embedding (LLE) algorithm which is easily affected by neighboring points, an improved local linear embedding algorithm of homogenization distance (HLLE) is developed. The method makes the overall distribution of sample points tend to be homogenization and reduces the influence of neighboring points using homogenization distance instead of the traditional Euclidean distance. It is helpful to choose effective neighboring points to construct weight matrix for dimension reduction. Because the fault recognition performance improvement of HLLE is limited and unstable, the paper further proposes a new local linear embedding algorithm of supervision and homogenization distance (SHLLE) by adding the supervised learning mechanism. On the basis of homogenization distance, supervised learning increases the category information of sample points so that the same category of sample points will be gathered and the heterogeneous category of sample points will be scattered. It effectively improves the performance of fault diagnosis and maintains stability at the same time. A comparison of the methods mentioned above was made by simulation experiment with rotor system fault diagnosis, and the results show that SHLLE algorithm has superior fault recognition performance.

A modified local linear embedding algorithm based on neighbour selection

Dimension reduction plays an important role for effectively extracting useful information from data in practical solutions. Locally Linear Embedding LLE is a promising non-linear dimensionality reduction method. However, LLE has some limitations in dealing with the problem of uneven distribution of data, i.e. the number of neighbours influences the size of local region. To solve this problem, this paper proposes a modified LLE method named LLE+, through improving the similarity measure for neighbour selection. The experiments proved that LLE+ has a better dimension reduction performance.

Classification of Rice by Combining Electronic Tongue and Nose

One hundred twenty indica rice samples were determined by electronic tongue and electronic nose. The potential of the combinational approaches of electronic tongue and nose for rice analysis, with the aim of differentiating conventional and hybrid rice, was investigated. Principal component analysis (PCA) and locally linear embedding (LLE) were used to preprocess data from electronic systems. Support vector machine (SVM) model and K-nearest neighbors (KNN) model were established with the values from PCA and LLE algorithms as attributes. For the combination of electronic tongue and nose, the prediction accuracies of PCA-SVM, PCA-KNN, LLE-SVM, and LLE-KNN models were 55, 55, 85, and 80 %. The LLE-based models achieved better prediction accuracies than PCA-based models. These results demonstrated that LLE algorithm coupled with SVM or KNN for the combined electronic signals was effective in extracting and analyzing features for detecting rice. The LLE-SVM model achieved a little higher accuracy than the LLE-KNN model. It can be concluded that the combination of electronic systems coupled with LLE-based model have a great potential in the prediction of rice types.

Individual Identification Method for Group-Housed Pigs Based on Optimal Feature Extraction

In order to reduce the workload of farmers on individual identification of pigs, reduce interference to pigs, and raise automation and intelligent level of farms, a Matlab-based automatic classification system is set up. Firstly, top view video sequences are captured for group-housed pigs from pig barn, and the adaptive Gaussian mixture model based on prediction mechanism is used to detect the foreground objects. Then with morphological processing and hole filling, the targets are extracted as completely as possible from the background. Secondly, after building the sample image databases for each pig, color, texture and shape features are extracted and combined as the feature vector. Next, LLE (Locally Linear Embedding) algorithm is adopted to reduce the data dimension. Finally, hybrid kernel SVM (Support Vector Machine) classifier is designed to identify the pigs in test frames. Experimental results show that the recognition rate of pigs is 95.2%. For improving the recognition rate, decreasing cost and interference to pigs, the above method is proposed. Moreover, it can lay a foundation for future researches on group-housed pigs in behaviors, emotions, breathings and so on, which has good practical significance.

Local Linear Embedding Algorithm with Adaptively Determining Neighborhood

Local linear embedding is a kind of very competitive nonlinear dimensionality reduction technique with good representational capacity for a broader range of manifolds and high computational efficiency. However, it is based on the assumption that the whole data manifolds are evenly distributed so that it determines the neighborhood for all points with the same neighborhood size. Accordingly, it fails to nicely deal with most real problems that are unevenly distributed. This paper presents a new approach that takes the general conceptual framework of Hessian locally linear embedding so as to guarantee its correctness in the setting of local isometry for an open connected subset, but dynamically determines the local neighborhood size for each point. This approach estimates the approximate geodesic distance between any two points by the shortest path in the local neighborhood graph, and then determines the neighborhood size for each point by using the relationship between its local estimated geodesic distance matrix and local Euclidean distance matrix. This approach has clear geometry intuition as well as the better performance and stability. It deals with the sparsely sampled or noise contaminated data sets that are often unevenly distributed. The conducted experiments on benchmark data sets validate the proposed approach

Human Motion Capture Data Segmentation Based on LLE Algorithm

In this paper, we propose the motion sequence segmentation based on LLE (Locally Linear Embedding) algorithm. The method is to reduce the dimension of the high dimension motion sequence to obtain one-dimension feature curve. Then we use the feature curve to achieve motion sequence segmentation. Simulation results demonstrate that this method can achieve motion sequences segmentation and improve the accuracy rate greatly compared with the traditional algorithm.

Simulation Research of Feature Extraction Method Based on Nonlinear Manifold Learning

This paper deals with the study of Locally Linear Embedding (LLE) and Hessian LLE nonlinear feature extraction for high dimensional data dimension reduction. LLE and Hessian LLE algorithm which reveals the characteristics of nonlinear manifold learning were analyzed. LLE and Hessian LLE algorithm simulation research was studied through different kinds of sample for dimensionality reduction. LLE and Hessian LLE algorithm’s classification performance was compared in accordance with MDS. The simulation experimental results show that LLE and Hessian LLE are very effective feature extraction method for nonlinear manifold learning.

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.

Adaptive Neighborhood Selection Method Based on Silhouette Index for Locally Linear Embedding

Abstract Locally linear embedding (LLE) is a highly popular manifold learning and nonlinear dimensionality reduction technique. However, the neighborhood parameters of the algorithm are sensitive to the mapping results and difficult to choose. In this paper, we propose an adaptive neighborhood selection method based on Silhouette index for LLE algorithm. From the point of the cluster quality of feature extraction, Silhouette index is applied to evaluate the cluster effect of the low-dimensional embedding structure, in order to determine the optimal neighborhood parameters of LLE algorithm. Applied to IRIS and compressor failure data, the new method can effectively extract the inherent characteristics of low-dimensional manifolds, and obviously improve the classification performance of pattern recognition. The experimental results validate the feasibility and effectiveness of the proposed method.

Automatic selection of parameters in LLE

Locally Linear Embedding (LLE) is a nonlinear dimensionality reduction technique, which preserves the local geometry of high dimensional space performing an embedding to low dimensional space. LLE algorithm has 3 free parameters that must be set to calculate the embedding: the number of nearest neighbors k, the output space dimensionality m and the regularization parameter a. The last one only is necessary when the value of k is greater than the dimensionality of input space or data are not located in general position, and it plays an important role in the embedding results. In this paper we propose a pair of criteria to find the optimum value for the parameters kand a, to obtain an embedding that faithfully represent the input data space. Our approaches are tested on 2 artificial data sets and 2 real world data sets to verify the effectiveness of the proposed criteria, besides the results are compared against methods found in the state of art.

Multimodality image registration using local linear embedding and hybrid entropy

Robust registration of multimodality medical images has become an active area of research in medical image processing and applications. Although mutual information (MI) has been successfully applied to image registration, it is worth noting that MI-based registration measure only takes statistical intensity information into account and does not use spatial features. In this paper, we propose a local linear embedding (LLE) and hybrid entropy based registration method that combines spatial information into registration measure. Due to the robustness to absolute intensity information of image pixels and stability in noisy environment, the ordinal features (OFs) with different orientations are extracted to represent spatial information in medical images. For high dimensional OFs, the LLE algorithm is used to dimensionality reduction and the inverse mapping of LLE is used to fuse complementary information of OFs together. Then a novel similarity measure based on hybrid entropy which integrates intensity with OF is defined to register multimodality images. The experimental results show that the proposed registration algorithm can effectively suppress and eliminate the influence of noise in images. Compared with some existing methods, the proposed algorithm is of higher precision and better robustness.

A reconstruction algorithm for human action based on LLE and KRR

Reconstruction of human action plays an important role in the field of image processing. In this paper, a new algorithm based on locally linear embedding (LLE) and kernel ridge regression (KRR) is proposed for the reconstruction of human action. On one hand, the images of colour and depth information are used to extract the human skeleton so that the training set of actions can be established. On the other hand, the training set is turned into an action vector library. Combined with the LLE algorithm, the human action of low-dimensional manifolds can be evaluated and the data of manifolds can be analysed. Furthermore, the human action can be reconstructed according to the KRR algorithms while the predicted convergence points of low-dimensional are inverse-mapped back to the high-dimensional Euclidean space. A lot of real experiments have been done to show that the proposed method of reconstruction of human action is greatly effective.

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.