Two-dimensional Locality Research Articles

Layer codes

Quantum computers require memories that are capable of storing quantum information reliably for long periods of time. The surface code is a two-dimensional quantum memory with code parameters that scale optimally with the number of physical qubits, under the constraint of two-dimensional locality. In three spatial dimensions an analogous simple yet optimal code was not previously known. Here we present a family of three dimensional topological codes with optimal scaling code parameters and a polynomial energy barrier. Our codes are based on a construction that takes in a stabilizer code and outputs a three-dimensional topological code with related code parameters. The output codes are topological defect networks formed by layers of surface code joined along one-dimensional junctions, with a maximum stabilizer check weight of six. When the input is a family of good quantum low-density parity-check codes the output codes have optimal scaling. Our results uncover strongly-correlated states of quantum matter that are capable of storing quantum information with the strongest possible protection from errors that is achievable in three dimensions.

Data-Driven Event Identification in the U.S. Power Systems Based on 2D-OLPP and RUSBoosted Trees

Accurate event identification is an essential part of situation awareness ability for power system operators. Therefore, this work proposes an integrated event identification algorithm for power systems. First, to obtain and filter suitable inputs for event identification, an event detection trigger based on the rate of change of frequency (RoCoF) is presented. Then, the wave arrival time difference-based triangulation method considering the anisotropy of wave propagation speed is utilized to estimate the location of the detected event. Next, the two-dimensional orthogonal locality preserving projection (2D-OLPP)-based method, which is suitable for multiple types of measured data, is employed to achieve higher effectiveness in extracting the event features compared with traditional one-dimensional projection and principle component analysis (PCA). Finally, the random undersampling boosted (RUSBoosted) trees-based classifier, which can mitigate the data sample imbalance issue, is utilized to identify the type of the detected event. The proposed approach is demonstrated using the actual measurement data of U.S. power systems from FNET/GridEye. Comparison results show that the proposed event identification algorithm can achieve better performance than existing approaches.

EEG Signal Classification Using Manifold Learning and Matrix‐Variate Gaussian Model

In brain-computer interface (BCI), feature extraction is the key to the accuracy of recognition. There is important local structural information in the EEG signals, which is effective for classification; and this locality of EEG features not only exists in the spatial channel position but also exists in the frequency domain. In order to retain sufficient spatial structure and frequency information, we use one-versus-rest filter bank common spatial patterns (OVR-FBCSP) to preprocess the data and extract preliminary features. On this basis, we conduct research and discussion on feature extraction methods. One-dimensional feature extraction methods like linear discriminant analysis (LDA) may destroy this kind of structural information. Traditional manifold learning methods or two-dimensional feature extraction methods cannot extract both types of information at the same time. We introduced the bilinear structure and matrix-variate Gaussian model into two-dimensional discriminant locality preserving projection (2DDLPP) algorithm and decompose EEG signals into spatial and spectral parts. Afterwards, the most discriminative features were selected through a weight calculation method. We tested the method on BCI competition data sets 2a, data sets IIIa, and data sets collected by our laboratory, and the results were expressed in terms of recognition accuracy. The cross-validation results were 75.69%, 70.46%, and 54.49%, respectively. The average recognition accuracy of new method is improved by 7.14%, 7.38%, 4.86%, and 3.8% compared to those of LDA, two-dimensional linear discriminant analysis (2DLDA), discriminant locality property projections (DLPP), and 2DDLPP, respectively. Therefore, we consider that the proposed method is effective for EEG classification.

Image denoising using 2D orthogonal locality preserving discriminant projection

Image denoising using a combination of non-local self-similarity and transformed domain techniques has become popular in past few years. Instead of working on independent pixels, patches extracted from the noisy image are grouped together based on structural similarity and noise elimination is performed in transformed domain. Orthogonal locality preserving projection and its variant that processes the images directly in matrix format have been used for image denoising recently. Locality preserving nature of these techniques takes care of similarity within image patches while learning the basis, hence reducing the task of grouping patches explicitly. Non-local self-similarity based image denoising approaches perform patch grouping based on structural similarity. Discriminant information, if considered can play pivotal role in achieving superior clustering of data and thereby is expected to enhance the quality of denoising. With this aim in mind, two-dimensional (2D) orthogonal locality preserving discriminant projection is formulated in this study. While learning the basis, along with the similarity, proposed approach also takes into account dissimilarity between patches. A global basis thus learnt from the noisy image is used for denoising and comparable denoising performance is shown relative to the state-of-the-art methods.

Two-dimensional locality adaptive discriminant analysis

Two-dimensional Linear Discriminant Analysis (2DLDA), which is supervised and extracts the most discriminating features, has been widely used in face image representation and recognition. However, 2DLDA is inapplicable to many real-world situations because it assumes that the input data obeys the Gaussian distribution and emphasizes the global relationship of data merely. To handle this problem, we present a Two-dimensional Locality Adaptive Discriminant Analysis (2DLADA). Compared to 2DLDA, our method has two salient advantages: (1) it does not depend on any assumptions on the data distribution and is more suitable in real world applications; (2) it adaptively exploits the intrinsic local structure of data manifold. Performance on artificial dataset and real-world datasets demonstrate the superiority of our proposed method.

2DRLPP: Robust two-dimensional locality preserving projection with regularization

The recently proposed two-dimensional locality preserving projection (2DLPP) is an excellent matrix-based dimensionality reduction method. However, the formulation of 2DLPP may encounter several drawbacks in real-world applications, such as sensitiveness to outliers, non-orthogonal projections, and singularity problem. To alleviate these issues, in this paper, we propose a novel robust two-dimensional locality preserving projection (2DRLPP) for noisy image recognition. The proposed 2DRLPP preserves the local manifold structure of two-dimensional image space under the robust L1-norm criterion. Different from the existing 2DLPP, our 2DRLPP enjoys several incomparable advantages: (i) 2DRLPP extracts projections from matrix-based image space via the L1-norm locality preserving criterion rather than the L2-norm one, and hence it is more robust to outliers. (ii) The orthogonality constraint is further imposed on 2DRLPP to ensure its orthogonal projections. (iii) The introduced regularization term can not only control the model complexity but also guarantee the stability of solution. (iv) A simple but efficient iterative algorithm is presented to solve the corresponding L1-norm minimization problem, whose convergence is guaranteed theoretically. Extensive experimental results on three noisy face image datasets confirm the feasibility and robustness of the proposed approach.

Face feature extraction and recognition via local binary pattern and two-dimensional locality preserving projection

In this paper, we propose a novel face feature extraction approach based on Local Binary Pattern (LBP) and Two Dimensional Locality Preserving Projections (2DLPP) to enhance the texture features and preserve the space structure properties of a face image. LBP is firstly used to remove the effect of illumination and noise, which would enhance the detailed texture characteristics of face images. Then 2DLPP is performed to extract some prominent features and decrease the image dimension with space structure information. The Nearest Neighborhood Classifier (NNC) is used to recognize a face image at the end. In addition, the rule for dimension selection is studied from the results of experiments about choosing an appropriate feature dimension by 2DLPP computation. The experimental results on the Yale, the extended Yale B and CMU PIE C09 benchmark datasets showed that the proposed face feature extraction and recognition method achieves a better performance in comparison with similar techniques, and the proposed dimension selection rule can give an appropriate feature dimension in 2DLPP.

Face Recognition Based on Rearranged Modular Two-Dimensional Locality Preserving Projection

This paper proposes a novel algorithm for feature extraction for face recognition, namely the rearranged modular two-dimensional locality preserving projection (Rm2DLPP). In the proposed algorithm, the original images are first divided into modular blocks, then the subblocks are rearranged to form two-dimensional matrices and finally the two-dimensional locality preserving projection algorithm is applied directly on the arranged matrices. The advantage of the Rm2DLPP algorithm is that it can utilize the local block features and global spatial structures of 2D face images simultaneously. The performance of the proposed method is evaluated and compared with other face recognition methods on the ORL, AR and FERET databases. The experimental results demonstrate the effectiveness and superiority of the proposed approach.

Nuclear norm-based two-dimensional discriminant locality preserving projection for face recognition

Two-dimensional discriminant locality preserving projection (2DDLPP) is an effective method for image feature extraction. However, original 2DDLPP is based solely on the Euclidean distance, which is sensitive to noises and illumination changes in images. To overcome this drawback, we propose a method named nuclear norm-based two-dimensional discriminant locality preserving projection (NN2DDLPP). In NN2DDLPP, two optimal neighbor graphs are first built. Then the nuclear norm-based between-class scatter and within-class scatter are defined. Finally, in order to obtain an optimal projection matrix, the ratio of between-class scatter to within-class scatter is maximized. Using nuclear norm metric and labeled information, NN2DDLPP can both efficiently extract the discriminative features and improve the robustness to illumination changes and noises. Experiments carried out on several different face image databases validate that NN2DDLPP is efficacious for face recognition and better than other related works.

ISAR Target Recognition Based on Two-dimensional Locality Preserving Projection

It is well known that the relationship between different radar target data is often nonlinear, so the recognition rate will decrease if the traditional linear subspace methods are used to reduce the dimension of inverse synthetic aperture radar (ISAR) images. Recently, Locality Preserving Projections (LPP), a kind of manifold learning algorithm, is proposed for ISAR target recognition. But the ISAR images must be vectorized in LPP algorithm,which would result in the problem of singularity, and the local structural information from original images is easy to lose. In this paper, a novel ISAR target recognition algorithm is presented by using two-dimensional Locality Preserving Projections (2DLPP). The proposed 2DLPP algorithm is based directly on 2D ISAR images rather than 1D vectors as conventional LPP does. The simulated experimental results suggested that 2DLPP has better classification performance comparing to PCA,LDA and LPP.

2D-LPCCA and 2D-SPCCA: Two new canonical correlation methods for feature extraction, fusion and recognition

Abstract Two-dimensional canonical correlation analysis (2D-CCA) is an effective and efficient method for two-view feature extraction and fusion. Since it is a global linear method, it fails to find the nonlinear correlation between different features. In contrast, in this paper we propose a novel two-view method named as two-dimensional locality preserving canonical correlation analysis (2D-LPCCA), which uses the neighborhood information to discover the intrinsic structure of data. In other words, it uses many local linear problems to approximate the global nonlinear case. In addition, inspired by sparsity preserving projections (SPP), the two-dimensional sparsity preserving canonical correlation analysis (2D-SPCCA) framework is also developed, which consists of three models. Experimental results on real world databases demonstrate the viability of the formulation, they also show that the classification results of our methods are higher than the other’s.

Nuclear Norm-Based 2DLPP for Image Classification

Two-dimensional locality preserving projections (2DLPP) that use 2D image representation in preserving projection learning can preserve the intrinsic manifold structure and local information of data. However, 2DLPP is based on the Euclidean distance, which is sensitive to noise and outliers in data. In this paper, we propose a novel locality preserving projection method called nuclear norm-based two-dimensional locality preserving projections (NN-2DLPP). First, NN-2DLPP recovers the noisy data matrix through low-rank learning. Second, noise in data is removed and the learned clean data points are projected on a new subspace. Without the disturbance of noise, data points belonging to the same class are kept as close to each other as possible in the new projective subspace. Experimental results on six public image databases with face recognition, object classification, and handwritten digit recognition tasks demonstrated the effectiveness of the proposed method.

Multi-Algorithm of Palmprint Recognition System Based on Fusion of Local Binary Pattern and Two-Dimensional Locality Preserving Projection

This work based on fusion of multi-algorithm used for palmprint identification system. This piece of work is primary addressing different mechanism like Competitive Valley Hand Detection methods (CHVD) which used for extract Region of Interest (ROI). While in feature extraction the work was divided into three scenarios based on feature extraction like Local Binary Pattern (LBP), Two-Dimensional Locality Preserving Projection (2DLPP) and fusion of LBP+2DLPP.The experimental results show that fusion of LBP and 2DLPP give the best result with high accuracy reach to 98.55% which improve by 1.22% and 2.85% for LBP and 2DLPP respectively when they are applied separately.

Supervised bilateral two-dimensional locality preserving projection algorithm based on Gabor wavelet

Bilateral two-dimensional locality preserving projection (B2DLPP) is an effective method for unsupervised linear dimensionality reduction, which directly extracts face features from image matrices based on locality criterion. Motivated by B2DLPP, this paper proposes a supervised bilateral two-dimensional locality preserving projection (SB2DLPP). Different from B2DLPP, the proposed method takes into account the class information when constructing the similarity matrix. It increases inter-class distance in the projection space so that better right and left-projection matrices are obtained. Furthermore, a Gabor-based supervised bilateral two-dimensional locality preserving projection method is proposed for face recognition. Gabor wavelet representations are adopted for face images to make the proposed method robust to illumination variations and facial expression changes. Then, SB2DLPP is applied to reduce feature dimension. The performance of the proposed method is evaluated and compared with other traditional face recognition schemes on the FERET, Yale and JAFFE databases. The experiment results demonstrate the effectiveness and superiority of the proposed approach.

Two-dimensional discriminant locality preserving projections (2DDLPP) and its application to feature extraction via fuzzy set

This paper presents a new method for image feature extraction, namely, the fuzzy 2D discriminant locality preserving projections (F2DDLPP) based on the 2D discriminant locality preserving projections (2DDLPP) and fuzzy set theory. Firstly, we calculate the membership degree matrix by fuzzy k-nearest neighbor (FKNN), then we incorporate the membership degree matrix into the definition of the intra-class scatter matrix and inter-class scatter matrix, respectively. Secondly, we can get the fuzzy intra-class scatter matrix and fuzzy inter-class scatter matrix, respectively. The FKNN is implemented to achieve the distribution information of original samples, and this information is utilized to redefine corresponding scatter matrices. So, F2DDLPP can extract discriminative features from overlapping (outlier) samples which is different to the conventional 2DDLPP. Finally, Experiments on the Yale, ORL face databases, USPS database and PolyU palmprint database are demonstrated to verify the effectiveness of the proposed algorithm.

Git Recognition with Incomplete GEI Based on Random Forests

Abstract. This paper proposes an incomplete GEI gait recognition method based on Random Forests. There are numerous methods exist for git recognition,but they all lead to high dimensional feature spaces. To address the problem of high dimensional feature space, we propose the use of the Random Forest algorithm to rank features' importance . In order to efficiently search throughout subspaces, we apply a backward feature elimination search strategy.This demonstrate static areas of a GEI also contain useful information.Then, we project the selected feature to a low-dimensional feature subspace via the newly proposed two-dimensional locality preserving projections (2DLPP) method.Asa sequence,we further improve the discriminative power of the extracted features. Experimental results on the CASIA gait database demonstrate the effectiveness of the proposed method.

Two-dimensional bilinear preserving projections for image feature extraction and classification

Two-dimensional locality preserving projections (2DLPP) was recently proposed to extract features directly from image matrices based on locality preserving criterion. A significant drawback of 2DLPP is that it only works on one direction (left or right) to reduce the dimensionality of the image matrices and thus too many coefficients are needed for image representation in low-dimensional subspace. In this paper, we propose a novel method called two-dimensional bilinear preserving projections (2DBPP) for image feature extraction. We generalized the image-based (2D-based) feature extraction techniques into bilinear cases, in which 2DLPP is a special case of our proposed method. In order to obtain the bilinear projections, we proposed an iteration method by solving the corresponding generalized eigen-equations. Moreover, analyses show that 2DBPP has stronger locality preserving abilities than 2DLPP. By using the label information and defining different local neighborhood graphs, the proposed framework is further extended to supervised case. Experiments on three databases show that 2DBPP and its supervised extension are superior to some other image-based state-of-the-art techniques.

A New Extension of Locality Preserving Projections for Image Feature Extraction

This paper proposes a novel algorithm for image feature extraction, namely, the two-directional two-dimensional locality preserving projection, ((2D)2LPP), which can find an embedding from two directions that not only preserves local information and detect the intrinsic image manifold structure, but also combines the both information between rows and those between columns simultaneously. We also combine the advantages of (2D)2LPP and LDA, and propose a new framework for feature extraction as two-stage: “(2D)2LPP+LDA.” The LDA step is performed to further reduce the dimension of feature matrix in the (2D)2LPP subspace. Experimental results on ORL face databases demonstrate the effectiveness of the proposed methods.

Face recognition based on two dimensional locality preserving projections in frequency domain

In this paper we propose a new face recognition method based on two-dimensional locality preserving projections (2DLPP) in frequency domain. For this purpose, we first introduce the two-dimensional locality preserving projections. Then the 2DLPP in frequency domain is proposed for face recognition. In fact, two dimensional discrete cosine transform (2DDCT) is used as a pre-processing step and it transforms the face image signals from spatial domain into frequency domain aiming to reduce the effects of illumination and pose changes in face recognition. Then 2DLPP is applied on the upper left corner blocks of the 2DDCT transformed matrices, which represent main energy of each original image. For demonstration, the Olivetti Research Laboratory (ORL), YALE, FERET and YALE-B face datasets are used to compare the proposed approach with the conventional 2DLPP and 2DDCT approaches with the nearest neighborhood (NN) classifier. The experimental results show that the proposed 2DLPP in frequency domain is superior over the 2DLPP in spatial domain and 2DDCT itself in frequency domain.

Improved discriminant locality preserving projections for face and palmprint recognition

We propose in this paper two improved manifold learning methods called diagonal discriminant locality preserving projections (Dia-DLPP) and weighted two-dimensional discriminant locality preserving projections (W2D-DLPP) for face and palmprint recognition. Motivated by the fact that diagonal images outperform the original images for conventional two-dimensional (2D) subspace learning methods such as 2D principal component analysis (2DPCA) and 2D linear discriminant analysis (2DLDA), we first propose applying diagonal images to a recently proposed 2D discriminant locality preserving projections (2D-DLPP) algorithm, and formulate the Dia-DLPP method for feature extraction of face and palmprint images. Moreover, we show that transforming an image to a diagonal image is equivalent to assigning an appropriate weight to each pixel of the original image to emphasize its different importance for recognition, which provides the rationale and superiority of using diagonal images for 2D subspace learning. Inspired by this finding, we further propose a new discriminant weighted method to explicitly calculate the discriminative score of each pixel within a face and palmprint sample to duly emphasize its different importance, and incorporate it into 2D-DLPP to formulate the W2D-DLPP method to improve the recognition performance of 2D-DLPP and Dia-DLPP. Experimental results on the widely used FERET face and PolyU palmprint databases demonstrate the efficacy of the proposed methods.