2DPCA Method Research Articles

Improved GAN-based deep learning approach for strain field prediction and failure analysis of precast bridge slab joints

Nonlinear finite element analysis (FEA) is crucial for understanding complex stress-strain behaviors and assessing potential structural failure risks. Building on the recent success of deep learning (DL) methods in physical field predictions, there has been growing interest in forecasting internal force fields of structures beyond the existing data scope. In this study, a data-driven strain field analysis model based on an improved Generative Adversarial Network (GAN) is proposed. To enrich the input data, this novel approach incorporates the Signed Distance Field (SDF) derived from the characteristics of the original Finite Element (FE) models. The generator, based on U-Net, is enhanced with channel attention mechanisms and loss penalty terms, forming the core of the improved GAN. The effectiveness of the proposed method is demonstrated using two parallel datasets comprising 3-Headed bar tension models across two planes. Subsequently, the generated strain field is subjected to feature extraction using the 2D-Principal Component Analysis (2D-PCA) method, followed by structural failure determination through the K-Nearest Neighbor (KNN) algorithm. The results indicate that the proposed improved approach achieves a significant reduction in Root Mean Square Error (RMSE) of 20.71 % and 13.21 % across the two datasets, with the structural failure determination method reaching an F1-score of 0.971. Thus, the intelligent strain field analysis method introduced here effectively predicts strain distributions and promptly identifies failure states, offering valuable insights for further numerical analysis and structural design.

Cosine 2DPCA With Weighted Projection Maximization.

Two-dimensional principal component analysis (2DPCA), known to be very sensitive to outliers, employs the square F -norm as the distance metric and only satisfies the optimal objective of maximizing projection variance. However, the objective of minimizing reconstruction errors for all samples is not optimized as much as possible. To handle the problem, a novel cosine objective function is first presented for maximizing weighted projection, in which the 2-norm of vectors with an adjustable power parameter is employed as the distance metric. Not only the objective with the maximum projection distance is accomplished in the cosine objective function, but also the objective with the minimum sum of reconstruction errors is also optimized indirectly. Then, the cosine 2DPCA (Cos-2DPCA) method is proposed, and the greedy iterative algorithm to solve Cos-2DPCA is also developed. The convergence and correlation of solutions are proved theoretically and discussed in detail. Finally, the series of experiments are carried out on the artificial dataset and eight standard datasets, respectively. The results demonstrate that the performances of Cos-2DPCA are significantly improved on the reconstruction, correlation, complexity, and classification, and it outperforms most of the existing robust 2DPCA methods.

A joint-norm distance metric 2DPCA for robust dimensionality reduction

Two-dimensional principal component analysis (2DPCA) is one of the most representative dimensionality reduction methods and the robustness degrades in the presence of noise. To improve the robustness, several 2DPCA methods using similar distance metrics were proposed to achieve the objective of the maximum projection distance or the minimum reconstruction error. However, these two objectives cannot be accomplished simultaneously or are constrained by the same projection matrix. To handle these problems, we propose a generalized robust 2DPCA method called 2DPCA-2-Lp, which joins 2-norm and lp-norm metrics in the objective function. It aims to maximize the ratio of projected vectors to image row vectors and to fulfill the dual objectives of directly maximizing projection distances and indirectly minimizing reconstruction errors. 2DPCA-2-Lp measures the distances between row vectors of matrices rather than the distances between matrices, thus remarkably enhancing the robustness. Furthermore, the relationship between reconstruction errors and projection distances for different parameter values is analyzed theoretically under the joint-norm metric. Then, the closed greedy iterative algorithm is developed for obtaining optimal solutions. Finally, extensive experimental results on four datasets show that 2DPCA-2-Lp outperforms most existing 2DPCA methods in terms of reconstruction and classification performances and has better robustness against noise.

Water Ice Detection Research in Utopia Planitia Based on Simulation of Mars Rover Full-Polarimetric Subsurface Penetrating Radar

The probe of China’s first Mars exploration mission, Tianwen-1, has been successfully launched. It will carry out scientific exploration on the topography, soil characteristics, water ice, climate, ionosphere, and physical fields of Mars. Different from other rovers landing on the moon and Mars, the Zhurong rover is equipped with a full polarimetric subsurface penetrating radar (FP-SPR) system for the first time. The radar’s mission is to depict the shallow subsurface structure of Mars and search for possible water ice. Therefore, in this paper, a 3D realistic structure model is established and numerically simulated based on the possible subsurface structure of Utopia Planitia (the landing area). Influencing factors such as topographical fluctuations, rocks, water ice, and the variation of dielectric constant of different layers are added to the model. The analysis of the acquired FP-SPR data set shows that the two-dimensional principal component analysis (2D-PCA) method can extract effective reflected signals from the radar data with noise interference and improve the data quality. These clearly imaged targets may be water ice blocks, so the application of 2D-PCA to FP-SPR data increases the imaging quality of suspected water ice targets. The results of this paper are the basis for future processing of the measured FP-SPR data on Mars, which will help to identify more details of subsurface structures.

Diagnosis Using Brain Tumors Two-Dimensional Principal Component Analysis (2D-PCA) with K-nearest Neighbor (KNN) Classification Algorithm

The rapid development of computer technology has brought more and more benefits to human life. Currently, computers can make decisions by imitating the human brain to be used in the health sector to play a role in solving existing problems. One of the technologies used is digital image processing technology on MRI images of brain tumors. Brain tumor images have various variations and large dimensions; therefore, an appropriate method is needed to recognize images maximally. Dimensional reduction uses the Two-Dimensional Principal Component Analysis (2DPCA) method. The classification process uses the K-Nearest Neighbor (KNN) method by calculating the euclidean distance (Euclidean Distance). From 3 tests with the number of data 200 images, the results of the accuracy of the 1st test were 90.0% with 60 test data and 140 training data, the second test was 85.0% with 80 test data and 120 training data, and the 3rd test is worth 83.0% with 100 test data and 100 training data. Based on the research above, it can be concluded that the highest accuracy is obtained in the 1st test, while the lowest accuracy is on the 3rd test. The more amount of training data compared to the test data, the greater the accuracy value obtained. This research is expected to be a reference for further research so that the results obtained are more optimal.

AN ADOPTION OF 2D-PCA/ICA BASED POST-PROCESSING DIMENSIONALITY REDUCTION ALGORITHM FOR FACIAL RECOGNITION SYSTEM

Face images undergo considerable amount of variations in pose, facial expression and illumination condition. This large variation in facial appearances of the same individual makes most Existing Face Recognition Systems (E-FRS) lack strong discrimination ability and timely inefficient for face representation due to holistic feature extraction technique used. In this paper, a novel face recognition framework, which is an extension of the standard (PCA) and (ICA) denoted as two-dimensional Principal Component Analysis (2D-PCA) and two-dimensional Independent Component Analysis (2D-ICA) respectively is proposed. The choice of 2D was advantageous as image covariance matrix can be constructed directly using original image matrices. The face images used in this study were acquired from the publicly available ORL and AR Face database. The features belonging to similar class were grouped and correlation calculated in the same order. Each technique was decomposed into different components by employing multi-dimensional grouped empirical mode decomposition using Gaussian function. The nearest neighbor (NN) classifier is used for classification. The results of evaluation showed that the 2D-PCA method using ORL database produced RA of 92.5%, PCA produced RA of 75.00%, ICA produced RA of 77.5%, 2D-ICA produced RA of 96.00%. However, 2D-PCA methods using AR database produced RA of 73.56%, PCA produced RA of 62.41%, ICA produced RA of 66.20%, 2D-ICA method produced RA of 77.45%. This study revealed that the developed face recognition framework algorithm achieves an improvement of 18.5% and 11.25% for the ORL and AR databases respectively as against PCA and ICA feature extraction techniques. Keywords: computer vision, dimensionality reduction techniques, face recognition, pattern recognition

Facial recognition using two-dimensional principal component analysis and k-nearest neighbor: a case analysis of facial images

Science and Technology Innovation in Computer Science, especially in the facial image is increasingly needed in the Industrial Era of 4.0. The problem: How to use the working pattern of the Two-Dimensional Principal Component Analysis (2DPCA) method that integrated with K-Nearest Neighbors (KNN) in the Facial Image Recognition for various purposes? The purpose of this study, to analyze the Facial Image Recognition based on the method of Two-Dimensional Principal Component Analysis (2DPCA) which is integrated with KNN. This research uses the method of Two-Dimensional Principal Component Analysis (2DPCA) for the feature extraction process and the KNN classification method is applied to perform the data classification process so that the desired accuracy value is obtained. Research subjects use the image database from UCI repository, consists of 190 black and white face images of people taken with varying pose (straight, left, right, up), expression (neutral, happy, sad, angry), and size. The result of this study is the performance analysis of Facial Image Recognition based on the method of Two-Dimensional Principal Component Analysis (2DPCA) that is integrated with k-Nearest Neighbors (KNN).

Generalized two-dimensional PCA based on $$\ell _{2,p}$$-norm minimization

To exploit the information from two-dimensional structured data, two-dimensional principal component analysis (2-DPCA) has been widely used for dimensionality reduction and feature extraction. However, 2-DPCA is sensitive to outliers which are common in real applications. Therefore, many robust 2-DPCA methods have been proposed to improve the robustness of 2-DPCA. But existing robust 2-DPCAs have several weaknesses. First, these methods cannot be robust enough to outliers. Second, to center a sample set mixed with outliers using the L2-norm distance is usually biased. Third, most methods do not preserve the nice property of 2-DPCA (rotational invariance), which is important for learning algorithm. To alleviate these issues, we present a generalized robust 2-DPCA, which is named as 2-DPCA with $$\ell _{2,p}$$ -norm minimization ( $$\ell _{2,p}$$ -2-DPCA), for image representation and recognition. In $$\ell _{2,p}$$ -2-DPCA, $$\ell _{2,p}$$ -norm is employed as the distance metric to measure the reconstruction error, which can alleviate the effect of outliers. Therefore, the proposed method is robust to outliers and preserves the desirable property of 2-DPCA which is invariant to rotational and well characterizes the geometric structure of samples. Moreover, most existing robust PCA methods estimate sample mean from database with outliers by averaging, which is usually biased. Sample mean are treated as an unknown variable to remedy the bias of computing sample mean in $$\ell _{2,p}$$ -2-DPCA. To solve $$\ell _{2,p}$$ -2-DPCA, we propose an iterative algorithm, which has a closed-form solution in each iteration. Experimental results on several benchmark databases demonstrate the effectiveness and advantages of our method.

A Novel Image Description With the Stretched Natural Vector Method: Application to Face Recognition

Nowadays there is growing research interest in designing high performance algorithms for automatic facial recognition systems, and an efficient computational approach is required. Accurate face recognition, however, is difficult due to facial complexity. In this paper, we propose a novel and efficient facial image representation named the Stretched Natural Vector (SNV) method which is defined on the intensity values in a grayscale image matrix, where each entry in an intensity matrix records the level of gray at a single pixel in a m×n array. We prove that the SNV defined in this context can distinguish photo matrices in strict one-to-one fashion. This is to say it is theoretically possible to fully recover a grayscale image matrix from the corresponding complete SNV. Experiments on a number of datasets demonstrate that our truncated SNV method compares favorably both in recognition accuracy and efficiency (measured in wall-clock time) against “Full-Pixel” algorithm, Principal Component Analysis (PCA) method, and even its widely used variants - two dimensional PCA (2DPCA) method and two dimensional Euler PCA (2D-EPCA) method.

Generalized Centered 2-D Principal Component Analysis.

Most existing robust principal component analysis (PCA) and 2-D PCA (2DPCA) methods involving the l2 -norm can mitigate the sensitivity to outliers in the domains of image analysis and pattern recognition. However, existing approaches neither preserve the structural information of data in the optimization objective nor have the robustness of generalized performance. To address the above problems, we propose two novel center-weight-based models, namely, centered PCA (C-PCA) and generalized centered 2DPCA with l2,p -norm minimization (GC-2DPCA), which are developed for vector- and matrix-based data, respectively. The C-PCA can preserve the structural information of data by measuring the similarity between the data points and can also retain the PCA's original desirable properties such as the rotational invariance. Furthermore, GC-2DPCA can learn efficient and robust projection matrices to suppress outliers by utilizing the variations between each row of the image matrix and employing power p of l2,1 -norm. We also propose an efficient algorithm to solve the C-PCA model and an iterative optimization algorithm to solve the GC-2DPCA model, and we theoretically analyze their convergence properties. Experiments on three public databases show that our models yield significant improvements over the state-of-the-art PCA and 2DPCA approaches.

Rapid identification of rainstorm disaster risks based on an artificial intelligence technology using the 2DPCA method

An artificial intelligence technology with the two-dimensional principal component analysis (2DPCA) method is introduced into the early identification of rainstorm risks. The characteristic subspace for historical rainstorm events can be constructed through the 2DPCA method. When identifying an ongoing rainfall process, the most similar rainstorm event can be found through comparing the features of the ongoing rainfall to the events in the characteristic subspace. Taking the most similar historical rainstorm event found as a reference, the possible duration and intensity of the ongoing rainfall process can be estimated, thus achieving early identification of rainstorm risks. Two groups of validation experiments are performed based on a database including 116 rainstorm events observed in Shenzhen metropolis, China. The validation shows that although the ratio of historical events to validation events impacts the performance of identification, the identified historical events are generally similar to the ongoing rainfall processes in terms of rainfall duration, range of influence, magnitude, and maximum single-station rainfall.

The Comparison of Signature Verification Result Using 2DPCA Method and SSE Method

The rate of speed and validation verify to be a reference of quality information and reliable results. Everyone has signature characteristics but it will be difficult to match original signatures with a clone. Two Dimensional Principal Component Analysis (2DPCA) method, Sum Equal Error (SSE) method includes a method that can provide accurate data verification value of 90% - 98%. Results of scanned signatures, converted from RGB image - grayscale - black white (binary color). The extraction process of each method requires experimental data as a data source in pixel size. Digital image consists of a collection of pixels then each image is converted in a matrix. Preprocessing Method 2 DPCA each data is divided into data planning and data testing. Extraction on SSE method, each data sought histogram value and total black value. This study yields a comparison of the suitability of the extraction results of each method. Both of these methods have a data accuracy rate of 97% - 98%. When compared to the results of the accuracy of image verification with 2DPCA method: SSE is 97%: 96%. With the same data source will be tested result of 2DPCA method with SSE method.

R1 -2-DPCA and Face Recognition.

2-D principal component analysis (2-DPCA) is one of the successful dimensionality reduction approaches for image classification and representation. However, 2-DPCA is not robust to outliers. To tackle this problem, we present an efficient robust method, namely R 1 -2-DPCA for feature extraction. R 1 -2-DPCA aims to seek the projection matrix such that the projected data have the maximum variance, which is measured by R 1 -norm. Compared with most existing robust 2-DPCA methods, our model is not only robust to outliers but also helps encode discriminant information. Accordingly, we develop a nongreedy iterative algorithm, which has not only a closed-form solution in each iteration but also a good convergence, to solve our model. Moreover, to further improve classification performance, we employ nuclear norm as the distance metric in the classification phase. Extensive experiments on several face databases illustrate that our proposed method is superior to most existing robust 2-DPCA methods.

A New Damage Index Using FRF Data, 2D-PCA Method and Pattern Recognition Techniques

A pattern recognition-based damage detection method using a brand-new damage index (DI) obtained from the frequency response function (FRF) data is proposed in this paper. One major issue of using the FRF data is the large size of input variables. The proposed method reduces the dimension of the initial FRF data and transforms it into new damage indices by applying a data reduction technique called the two-dimensional principal component analysis (2D-PCA). The proposed damage indices can be used as the unique patterns. After introducing the damage indices, a dataset of damage scenarios and related patterns is composed. Pattern recognition techniques such as the artificial neural networks and look-up-table (LUT) method are employed to find the most similar known DI to the unknown DI obtained for the damaged structure. As the result of this procedure, the actual damage location and severity can be determined. In this paper, the 2D-PCA and LUT method for damage detection is introduced for the first time. The damage identification of a truss bridge and a two-story frame structure is performed for verification of the proposed method, considering all single damage cases as well as many multiple damage scenarios. In addition, the robustness of the proposed algorithm to measurement noise was investigated by polluting the FRF data with 5%, 10%, 15% and 20% noises.

Research on the Application and Comparison of PCA & 2DPCA in Face Recognition

Face recognition technology considers one of the hot spots in the field of pattern recognition, and it is also one of the difficulties in the field of pattern recognition. In this paper, the principal component analysis (PCA) algorithm and its application in the face recognition technology has been studied primarily. Firstly, discusses the traditional 1DPCA algorithm. Secondly, based on the previously mentioned 1DPCA algorithm, the 2DPCA algorithm, which improves algorithm, is put forward. Simulation results showed that the 2DPCA method is superior to the traditional PCA method for its avoidance of the transformation from image array to one-dimensional vector. The programmable procedures of 1DPCA and 2DPCA designed in the thesis have high recognition rate, and pose theoretically important influence and application value.

2D-PCA Representation and Sparse Representation for Image Recognition

The two-dimensional principal component analysis (2D-PCA) method has been widely applied in fields of image classification, computer vision, signal processing and pattern recognition. The 2D-PCA algorithm also has a satisfactory performance in both theoretical research and real-world applications. It not only retains main information of the original face images, but also decreases the dimension of original face images. In this paper, we integrate the 2D-PCA and spare representation classification (SRC) method to distinguish face images, which has great performance in face recognition. The novel representation of original face image obtained using 2D-PCA is complementary with original face image, so that the fusion of them can obviously improve the accuracy of face recognition. This is also attributed to the fact the features obtained using 2D-PCA are usually more robust than original face image matrices. The experiments of face recognition demonstrate that the combination of original face images and new representations of the original face images is more effective than the only original images. Especially, the simultaneous use of the 2D-PCA method and sparse representation can extremely improve accuracy in image classification. In this paper, the adaptive weighted fusion scheme automatically obtains optimal weights and it has no any parameter. The proposed method is not only simple and easy to achieve, but also obtains high accuracy in face recognition.

One-dimensional vs. two-dimensional based features: Plant identification approach

The number of endangered species has been increased due to shifts in the agricultural production, climate change, and poor urban planning. This has led to investigating new methods to address the problem of plant species identification/classification. In this paper, a plant identification approach using 2D digital leaves images was proposed. The approach used two features extraction methods based on one-dimensional (1D) and two-dimensional (2D) and the Bagging classifier. For the 1D-based methods, Principal Component Analysis (PCA), Direct Linear Discriminant Analysis (DLDA), and PCA+LDA techniques were applied, while 2DPCA and 2DLDA algorithms were used for the 2D-based method. To classify the extracted features in both methods, the Bagging classifier, with the decision tree as a weak learner was used. The five variants, i.e. PCA, PCA+LDA, DLDA, 2DPCA, and 2DLDA, of the approach were tested using the Flavia public dataset which consists of 1907 colored leaves images. The accuracy of these variants was evaluated and the results showed that the 2DPCA and 2DLDA methods were much better than using the PCA, PCA+LDA, and DLDA. Furthermore, it was found that the 2DLDA method was the best one and the increase of the weak learners of the Bagging classifier yielded a better classification accuracy. Also, a comparison with the most related work showed that our approach achieved better accuracy under the same dataset and same experimental setup.

Two-dimensional principal component analysis based on Schatten p-norm for image feature extraction

In this paper, we propose a novel Schatten p-norm-based two-dimensional principal component analysis (2DPCA) method, which is named after 2DPCA-Sp, for image feature extraction. Different from the conventional 2DPCA that is based on Frobenius-norm, 2DPCA-Sp learns an optimal projection matrix by maximizing the total scatter criterion based on Schatten p-norm in the low-dimensional feature space. Since p can take different values, 2DPCA-Sp is regarded as a general framework of 2DPCA. We also propose an iterative algorithm to solve the optimization problem of 2DPCA-Sp with 0<p<1, which is simple, effective, and easy to implement. Experimental results on several popular image databases show that 2DPCA-Sp with 0<p<1 is robust to impact factors (e.g. illuminations, view directions, and expressions) of images.

2DPCA versus PCA for face recognition

Dimensionality reduction methods play an important role in face recognition. Principal component analysis (PCA) and two-dimensional principal component analysis (2DPCA) are two kinds of important methods in this field. Recent research seems like that 2DPCA method is superior to PCA method. To prove if this conclusion is always true, a comprehensive comparison study between PCA and 2DPCA methods was carried out. A novel concept, called column-image difference (CID), was proposed to analyze the difference between PCA and 2DPCA methods in theory. It is found that there exist some restrictive conditions when 2DPCA outperforms PCA. After theoretical analysis, the experiments were conducted on four famous face image databases. The experiment results confirm the validity of theoretical claim.

Cross grouping strategy based 2DPCA method for face recognition

Grouping strategy exactly specifies the form of covariance matrix, therefore it is very essential. Most 2DPCA methods use the original 2D image matrices to form the covariance matrix which actually means that the strategy is to group the random variables by row or column of the input image. Because of their grouping strategies these methods have two main drawbacks. Firstly, 2DPCA and some of its variants such as A2DPCA, DiaPCA and MatPCA preserve only the covariance information between the elements of these groups. This directly implies that 2DPCA and these variants eliminate some covariance information while PCA preserves such information that can be useful for recognition. Secondly, all the existing methods suffer from the relatively high intra-group correlation, since the random variables in a row, column, or a block are closely located and highly correlated. To overcome such drawbacks we propose a novel grouping strategy named cross grouping strategy. The algorithm focuses on reducing the redundancy among the row and the column vectors of the image matrix. While doing this the algorithm completely preserves the covariance information of PCA between local geometric structures in the image matrix which is partially maintained in 2DPCA and its variants. And also in the proposed study intra-group correlation is weak according to the 2DPCA and its variants because the random variables spread over the whole face image. These make the proposed algorithm superior to 2DPCA and its variants. In order to achieve this, image cross-covariance matrix is calculated from the summation of the outer products of the column and the row vectors of all images. The singular value decomposition (SVD) is then applied to the image cross-covariance matrix. The right and the left singular vectors of SVD of the image cross-covariance matrix are used as the optimal projective vectors. Further in order to reduce the dimension LDA is applied on the feature space of the proposed method that is proposed method+LDA. The exhaustive experimental results demonstrate that proposed grouping strategy for 2DPCA is superior to 2DPCA, its specified variants and PCA, and proposed method outperforms bi-directional PCA+LDA.