Exponential Discriminant Analysis Research Articles

Joint mining of fluid knowledge and multi-sensor data for gas–water two-phase flow status monitoring and evolution analysis

Gas-water two-phase flow process widely exists in petroleum, chemical and other industrial processes, which is intricate, manifested by dynamic evolution of fluid structures and real-time fluctuation of flow parameters. Detailed description and real-time monitoring of flow status are of great significance to safe operation of industry processes. In this paper, a monitoring framework jointly mining the fluid knowledge and latent property behind multi-sensor data is proposed to address the issues of uncertainty and sample scarcity in transitional flow statuses, which enables real-time monitoring on structural evolution and parameter change of flow process. Firstly, the shared iterative algorithm with multi-task weight discovery is proposed to establish the relative semantic description system to characterize flow process knowledge by mining the relationship between multi-sensor data and different fluid semantic properties, which is helpful for interpretable monitoring of flow status structure and parameter information. Secondly, latent properties mined from multi-sensor data by sparse exponential discriminant analysis contribute to flow characterization completeness and discrimination. Thirdly, the process knowledge and latent information of flow status is transformed into different degrees of describable semantic and latent properties, which obtain relative representations of flow status in the joint description space realized by rank support vector machine. The results demonstrate that the method enables precise monitoring and detailed description of typical and uncertain flow statuses in the absence of transitional flow status modeling samples.

Knowledge-based tensor subspace analysis system for kinship verification

Most existing automatic kinship verification methods focus on learning the optimal distance metrics between family members. However, learning facial features and kinship features simultaneously may cause the proposed models to be too weak. In this work, we explore the possibility of bridging this gap by developing knowledge-based tensor models based on pre-trained multi-view models. We propose an effective knowledge-based tensor similarity extraction framework for automatic facial kinship verification using four pre-trained networks (i.e., VGG-Face, VGG-F, VGG-M, and VGG-S). Therefore, knowledge-based deep face and general features (such as identity, age, gender, ethnicity, expression, lighting, pose, contour, edges, corners, shape, etc.) were successfully fused by our tensor design to understand the kinship cue. Multiple effective representations are learned for kinship verification statements (children and parents) using a margin maximization learning scheme based on Tensor Cross-view Quadratic Exponential Discriminant Analysis. Through the exponential learning process, the large gap between distributions of the same family can be reduced to the maximum, while the small gap between distributions of different families is simultaneously increased. The WCCN metric successfully reduces the intra-class variability problem caused by deep features. The explanation of black-box models and the problems of ubiquitous face recognition are considered in our system. The extensive experiments on four challenging datasets show that our system performs very well compared to state-of-the-art approaches.

Novel online discriminant analysis based schemes to deal with observations from known and new classes: Application to industrial systems

In industrial systems, continuous monitoring of process conditions is crucial. Existing discriminant analysis methods, including quadratic discriminant analysis (QDA), Fisher discriminant analysis (FDA), exponential discriminant analysis (EDA), orthonormal discriminant vector (ODV) and kernel Fisher discriminant (KFD), have been widely used in fault classification literature. Although efficient in controlled environment, they may fail in practice as they discriminate through a closed space. They cannot recognize observations that do not belong to their training set. In this paper, we propose statistical subspaces to allow these methods to efficiently deal with unseen observations of unknown classes. Traditional discriminant functions are summarized, and then new decision schemes are presented. Continuous stirred tank reactor (CSTR) and Tennessee Eastman process (TEP) evaluated the performance of the proposed approach and applied it on five popular methods. The results show that the new space has superior performances in term of discrimination between known and unknown faults.

Different Faults Diagnosis and Classification on‐Line in Permanent Magnet Synchronous Machines Using Improved Exponential Discriminant Analysis

Reliability is an important performance for permanent magnet synchronous machine (PMSM) exploited to industrial applications and electric‐energy vehicles. Both air‐eccentricity and inter‐turn short circuit (ITSC) could induce the machine running in unbalanced status. Once not restored timely, the fault will lead to the whole drive system and its application damage. To enhance the reliability for PMSM, an effective fault diagnosis and classification method is necessary in advance. For this purpose, an improved exponential discriminant analysis (IEDA) algorithm is proposed and optimized. Further, the distortion characteristics of phase current signals with air‐eccentricity and ITSC are extracted and trained by the IEDA, which are applied for diagnosing whether the motor healthy or faulty and distinguishing fault types. Besides, the IEDA can not only identify fault type accurately but also estimate the fault degree precisely. Finally, compared to other common learning methods, several simulations and practical tests accompanying with diverse operating status are implemented, and their results can prove the proposed method has more accuracy and robustness than other methods. © 2020 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

A weighted exponential discriminant analysis through side-information for face and kinship verification using statistical binarized image features

Side-information based exponential discriminant analysis (SIEDA) is more efficient than side-information based linear discriminant analysis (SILDA) in computing the discriminant vectors because it maximizes the Fisher criterion function. In this paper, we develop a novel criterion, named side-information based weighted exponential discriminant analysis (SIWEDA), that is based on the classical SIEDA method. We reformulate and generalize the classical Fisher criterion function in order to maximize it, with the property to pull as close as possible the intra-class samples (within-class samples), and push and repulse away as far as possible the inter-class samples (between-class samples). Thus, SIWEDA selects the eigenvalues of high significance and eliminate those with less discriminative information. To reduce the feature vector dimensionality and lighten the class intra-variability, we use SIWEDA and within class covariance normalization (WCCN) using the proposed statistical binarized image features (StatBIF). Moreover, we use score fusion strategy to extract the complementarity of different weighting scales of our StatBIF descriptor. We conducted experiments to evaluate the performance of the proposed method under unconstrained environment, using five datasets namely LFW, YTF, Cornell KinFace, UB KinFace and TSKinFace datasets, in the context of matching faces and kinship verification in the wild conditions. The experiments showed that the proposed approach outperforms the current state of the art. Very interestingly, our approach showed superior performance compared to methods based on deep metric learning.

On general matrix exponential discriminant analysis methods for high dimensionality reduction

Recently, some matrix exponential-based discriminant analysis methods were proposed for high dimensionality reduction. It has been shown that they often have more discriminant power than the corresponding discriminant analysis methods. However, one has to solve some large-scale matrix exponential eigenvalue problems which constitutes the bottleneck in this type of methods. The main contribution of this paper is twofold: First, we propose a framework of fast implementation on general matrix exponential-based discriminant analysis methods. The key is to equivalently transform large-scale matrix computation problems into much smaller ones. On the other hand, it was mentioned in Wang et al. (IEEE Trans Image Process 23:920–930, 2014) that the exponential model is more reliable than the original one and suppresses the sensitivity to pertubations. However, the interpretation is only heuristic, and to the best of our knowledge, there is no theoretical justification for reliability and stability of the matrix discriminant analysis methods. To fill in this gap, the second contribution of our work is to provide stability analysis for the fast exponential discriminant analysis method from a theoretical point of view. Numerical experiments illustrate the numerical behavior of the proposed algorithm, and demonstrate that our algorithm is more stable than many state-of-the-art algorithms for high dimensionality reduction.

Adaptive illumination-invariant face recognition via local nonlinear multi-layer contrast feature

Traditional face recognition method usually faces the challenge of varying lighting condition. In this paper, we propose an illumination-invariant local binary descriptor learning method for face recognition. Unlike local binary descriptor (LBP) and its variants, which usually utilize the rigid sign function for binarization despite of data distributions. We first determine a dynamic thresholds strategy including the information of illumination variation to extract nonlinear multi-layer contrast features. Specially, Exponential Discriminant Analysis (EDA) is designed to act as preprocessing which can contribute to improve the discriminative ability of the face image by enlarging the margin between different classes relative to the same class. To further improve the recognition performance, we combined our preliminary work, the adaptive fuzzy fusion framework, to integrate the recognition results for multi-scale features spaces. Extensive experiments conducted on four face databases validate the effectiveness of the proposed method for illumination face recognition.

Online Fault Diagnosis in Industrial Processes Using Multimodel Exponential Discriminant Analysis Algorithm

Fault diagnosis is used to identify the fault cause of the online abnormality, which is crucial for efficient and optimal operation of industrial processes. Due to the time-varying characteristics of fault process, the historical fault data may consist of multiple patterns and cannot be described accurately using a single model, which may result in poor performance of conventional multivariable statistical methods. In this brief, a multimodel exponential discriminant analysis (MEDA) algorithm is proposed for solving the aforementioned fault diagnosis problem. First, the samples of each fault class are clustered into different subclasses using the fast search and find of density peaks algorithm and the proposed cluster index. Subsequently, the between- and within-subclass exponential covariance matrices are calculated based on the subclasses and then the multimodel exponential discriminant model can be developed. Finally, recursively update the cluster center and the multimodel exponential discriminant model until the developed subclasses can be well separated and better discriminant performance can be obtained. Besides, a probabilistic MEDA algorithm and its corresponding online probabilistic diagnosis are also described to develop fuzzy model, so that the fault classes whose subclasses have fuzzy boundaries can also be effectively diagnosed. The Tennessee Eastman process is used to validate the diagnosis performance of the proposed MEDA algorithm, and the experimental results illustrate that the proposed algorithm can efficiently diagnose different classes of faults.

Robust Monitoring and Fault Isolation of Nonlinear Industrial Processes Using Denoising Autoencoder and Elastic Net

Robust process monitoring and reliable fault isolation in industrial processes usually encounter different challenges, including process nonlinearity and noise interference. In this brief, a novel method denoising autoencoder and elastic net (DAE–EN) is proposed to solve the aforementioned issues by effectively integrating DAE and EN. The DAE is first trained to robustly capture the nonlinear structure of the industrial data. Then, the encoder network is updated into a sparse model using EN, so that the key variables associated with each neuron can be selected. After that two statistics are developed based on the extracted systematic structure and the retained residual information. In addition, another statistic is also constructed by combining the aforementioned two statistics to provide an overall measurement for the process sample. In this way, a robust monitoring model can be constructed to monitor the abnormal status in industrial processes. After the fault is detected, the faulty neurons are identified by the sparse exponential discriminant analysis, so that the associated faulty variables along each faulty neuron can thus be isolated. Two real industrial processes are used to validate the performance of the proposed method. Experimental results show that the proposed method can effectively detect the abnormal samples in industrial processes and accurately isolate the faulty variables from the normal ones.

A Novel Hierarchical Detection and Isolation Framework for Quality-Related Multiple Faults in Large-Scale Processes

This paper is devoted to the industrial practices and theoretical approaches for detection and isolation of quality-related multiple faults in large-scale processes. In contrast to the previous schemes, the main innovations are as follows: 1) it is the first time a hierarchical detection and isolation framework for quality-related multiple faults in large-scale processes is developed; 2) a combination method of adaptive kernel canonical variable analysis and Bayesian fusion for real-time and hierarchical detection of varying and unknown quality-related multiple faults is presented; and 3) a robust sparse exponential discriminant analysis algorithm for accurate isolation of multimode quality-related multiple faults is proposed. Finally, the whole framework is applied to a typical large-scale process, i.e., hot strip mill process, where the performance and effectiveness are further demonstrated from real industrial data.

A New Hierarchical Framework for Detection and Isolation of Multiple Faults in Complex Industrial Processes

In actual production practice, the occurrence probability of multiple faults is much higher than that of a single fault. Since the composition of multiple faults is uncertain, it is difficult to establish a single model for multifault diagnosis. In this paper, a new hierarchical framework is proposed for solving multifault detection and isolation problems. First, an adaptive dynamic kernel independent component analysis method is proposed for time-varying and unknown multifault detection. After that, a sparse local exponential discriminant analysis method is developed for the multimodal multifault isolation problem. Finally, the Tennessee Eastman process is used to validate the performance of the proposed methods, and the experimental results show that the proposed methods can efficiently detect and isolate multiple faults.

Active learning based semi-supervised exponential discriminant analysis and its application for fault classification in industrial processes

For the industrial fault classification, exponential discriminant analysis (EDA) requires that all the training samples should be labeled; however, only a minority of the training samples are randomly labeled in real industrial processes. This motivates the formulation of the active learning based semi-supervised exponential discriminant analysis in this paper. Firstly, to make EDA applicable to the semi-supervised industrial scenario, scatter matrices are transformed into their regularization variants through combining unlabeled training samples. Moreover, to reduce the adverse effect of random labeling of training samples, the best versus second-best rule is employed to select more informative training samples in an active way to upgrade the model classification performance. And the obvious performance improvement of the proposed method is demonstrated with extensive experiments on synthesized data, the TE process and a real industrial process.

Sparse Exponential Discriminant Analysis and Its Application to Fault Diagnosis

Discriminant analysis, as a popular supervised classification method, has been successfully used in fault diagnosis, which, however, involves a linear combination of all variables, and thus may result in poor model interpretability and inaccurate classification performance. In this paper, a sparse exponential discriminant analysis (SEDA) algorithm is proposed for addressing those issues. The sparse discriminant model is developed by introducing the penalty of lasso or elastic net into the exponential discriminant analysis algorithm, so that the key variables responsible for the fault can be automatically selected. Since the formulated model is nonconvex, it is recast as an iterative convex optimization problem using the minorization–maximization algorithm. After that, a feasible gradient direction method is developed to solve the optimization problem effectively. The sparse solutions indicate the key faulty information to improve classification performance, and thus distinguish different faults more accurately. A simulation process and a real industrial process are used to test the performance of the proposed method, and the experimental results show that the SEDA algorithm can isolate the faulty variables and simplify the discriminant model by discarding variables with little significance.

DIEDA: discriminative information based on exponential discriminant analysis combined with local features representation for face and kinship verification

Face and kinship verification using facial images is a novel and challenging problem in computer vision. In this paper, we propose a new system that uses discriminative information, which is based on the exponential discriminant analysis (DIEDA) combined with multiple scale descriptors. The histograms of different patches are concatenated to form a high dimensional feature vector, which represents a specific descriptor at a given scale. The projected histograms for each zone use the cosine similarity metric to reduce the feature vector dimensionality. Lastly, zone scores corresponding to various descriptors at different scales are fused and verified by using a classifier. This paper exploits discriminative side information for face and kinship verification in the wild (image pairs are from the same person or not). To tackle this problem, we take examples of the face samples with unlabeled kin relations from the labeled face in the wild dataset as the reference set. We create an optimized function by minimizing the interclass samples (with a kin relation) and maximizing the neighboring interclass samples (without a kinship relation) with the DIEDA approach. Experimental results on three publicly available face and kinship datasets show the superior performance of the proposed system over other state-of-the-art techniques.

Issue Highlights

The Canadian Journal of Chemical EngineeringVolume 96, Issue 2 p. 423-423 Issue HighlightsFree Access Issue Highlights First published: 02 January 2018 https://doi.org/10.1002/cjce.22973AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat 426 Online Incipient Fault Diagnosis Based on Kullback–Leibler Divergence and Recursive Principle Component Analysis Yi Chai, Songbing Tao, Wanbiao Mao, Ke Zhang and Zhiqin Zhu For principal component analysis (PCA), the Hotelling's T2, that is the most common used statistical distance, can fail in detecting small shifts such as a sensor incipient fault with low fault-to-noise ratio (FNR). In this study, a realistic online diagnosis method for incipient faults with low FNR is presented utilizing the Kullback-Leibler divergence (KLD) and recursive PCA. From simulations, it is shown that the proposed approach can detect, isolate, and estimate the sensor incipient fault of the multivariate AR system successfully. 444 Modified Partial Least Square for Diagnosing Key-Performance-Indicator-Related Faults Siyuan He, Youqing Wang and Changqing Liu Faults related to a key performance indicator (KPI) should be paid much attention in the field of multivariate statistical process monitoring. To detect KPI faults, the process data should be divided into KPI-related and KPI-unrelated parts; however, all existing methods did not decompose the residual space according to KPI. In this study, balancing the influence of principal component space and residual space on KPI, the authors find the suitable projection matrix for partial least square (PLS), which can achieve perfect partition of process data in terms of KPI. The novel modification is named as KPI-PLS. 463 Fault Diagnosis Based on the Integration of Exponential Discriminant Analysis and Local Linear Embedding Ruixuan Wang, Jing Wang, Jinglin Zhou and Haiyan Wu The paper proposes two fault diagnosis methods based on the fusion of the exponential discriminant analysis and manifold learning methods, LLEDA and NPEDA. LLEDA, a parallel strategy, focuses on the global supervised discriminant with the tradeoff of local nonlinearity preserving. NPEDA, a cascaded strategy, implements the discriminant analysis with each data firstly constructed by the linear weighted combination of its neighbours. These methods both combine the global discriminant analysis with local structure preserving, so they are particularly suitable for the feature extraction of data with strong nonlinearity and high dimensions. References 1 Y. Chai, S. Tao, W. Mao, K. Zhang, Z. Zhu, Can. J. Chem. Eng. 2018, 96, 426. 2 S. He, Y. Wang, C. Liu, Can. J. Chem. Eng. 2018, 96, 444. 3 R. Wang, J. Wang, J. Zhou, H. Wu, Can. J. Chem. Eng. 2018, 96, 463 Volume96, Issue2February 2018Pages 423-423 ReferencesRelatedInformation

Efficient Tensor-Based 2D+3D Face Verification

We propose a novel approach for face verification by encoding 2D and 3D face images as a high order tensor. To perform tensor dimensionality reduction for both the unsupervised and supervised cases, we propose multilinear whitened principal component analysis (MWPCA) and tensor exponential discriminant analysis (TEDA), respectively. MWPCA is utilized to solve the small sample size problem in the high-dimensional space and to improve the discrimination power achieved by classical MPCA. In the supervised case, we extend multilinear discriminant analysis to TEDA in order to emphasize the discriminant data included in the null space of the within-class scatter matrix of each tensor’s mode. Additionally, TEDA enlarges the margin between samples belonging to different classes via distance diffusion mappings. Our proposed approach can be seen as a novel data fusion method based on tensor representation. Indeed, the histograms of different local descriptors extracted from both 2D and 3D face modalities are combined through different tensor modes. The extensive experimental evaluation carried out on FRGC v2.0, Bosphorus, and CASIA 2D and 3D face databases indicates that the proposed approach performs significantly better than the state-of-the-art approaches.

Fault diagnosis based on the integration of exponential discriminant analysis and local linear embedding

Industrial process data have the characteristics of high dimensions and nonlinearity, so it is very important to extract the data features for fault diagnosis. Two kinds of improved exponential discriminant analysis methods, local linear exponential discriminant analysis (LLEDA) and neighbourhood preserving embedding discriminant analysis (NPEDA), are proposed and the fault diagnosis schemes based on the two methods are given. The two methods both combine the global discriminant analysis with the local structure preserving. LLEDA is a parallel strategy to find a trade‐off projection vector between the local geometric structure preserving and the global data classification. NPEDA is a cascaded strategy whose dimensionality reduction process is implemented in two serial steps. The two methods emphasize the intrinsic structure of the data while utilizing the global discriminant information, so they have better discrimination power than the traditional EDA method. Finally, a typical penicillin fermentation simulation platform and Tennessee Eastman process are used to verify the performance of the proposed methods.

A novel statistical and multiscale local binary feature for 2D and 3D face verification

In this paper, we propose a face verification framework using 2D and 3D images. We first introduce a novel face descriptor based on the local statistics of the 2D and 3D images. In the proposed framework, the novel descriptor is combined with three other popular and effective local descriptors, namely, Local Binary Patterns (LBP), Local Phase Quantization (LPQ) and Binarized Statistical Image Features (BSIF). The multiscale variants of these four descriptors are investigated seeking better performance. To reduce the feature vector dimensionality and mitigate the class intra-variability, we use Exponential Discriminant Analysis (EDA) and Within Class Covariance Normalization (WCCN), respectively. Finally, a score level fusion scheme is adopted to combine different face descriptors and modalities. An extensive evaluation of the proposed framework is carried out on two publicly available and largely used 2D+3D face databases, namely FRGC v2.0 and CAISA 3D. Promising results that favorably compare to the state of the art are obtained.

Inexact implementation using Krylov subspace methods for large scale exponential discriminant analysis with applications to high dimensionality reduction problems

Exponential discriminant analysis (EDA) is a generalized discriminant analysis method based on matrix exponential. It can essentially overcome the intrinsic difficulty of small-sample-size problem that exists in the classical linear discriminant analysis (LDA). However, for data with high dimensionality, one has to solve a large matrix exponential eigenproblem in this method, and the time complexity is dominated by the computation of exponential of large matrices. In this paper, we propose two inexact Krylov subspace algorithms for solving the large matrix exponential eigenproblem efficiently. The contribution of this work is threefold. First, we consider how to compute matrix exponential-vector products efficiently, which is the key step in the Krylov subspace method. Second, we compare the discriminant analysis criterion of EDA and that of LDA from a theoretical point of view. Third, we establish the relationship between the accuracy of the approximate eigenvectors and the distance to nearest neighbor classifier, and show why the matrix exponential eigenproblem can be solved approximately in practice. Numerical experiments on some real-world databases show the superiority of our new algorithms over their original counterpart for face recognition.

Two-dimensional exponential discriminant analysis for small sample size in face recognition

Appearance-based face recognition methods usually require converting 2D face images to 1D column vectors. Due to high dimensionality and few available samples, the performance becomes unsatisfactory. In this paper, we propose a novel technique called two-dimensional exponential discriminant analysis 2DEDA which extracts important features for classification directly from 2D face images. 2DEDA is especially suitable when the available sample size is small. Experimental results on two publicly available datasets viz. AR and CMU-PIE demonstrate the efficacy of the proposed technique, outperforming two-dimensional principal component analysis 2DPCA and two-dimensional linear discriminant analysis 2DLDA. The performance of the algorithms is evaluated in terms of average classification accuracy.