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With the development of Earth observation technology, very-high-resolution (VHR) image has become an important data source of change detection. Nowadays, deep learning methods have achieved conspicuous performance in the change detection of VHR images. Nonetheless, most of the existing change detection models based on deep learning require annotated training samples. In this paper, a novel unsupervised model called kernel principal component analysis (KPCA) convolution is proposed for extracting representative features from multi-temporal VHR images. Based on the KPCA convolution, an unsupervised deep siamese KPCA convolutional mapping network (KPCA-MNet) is designed for binary and multi-class change detection. In the KPCA-MNet, the high-level spatial-spectral feature maps are extracted by a deep siamese network consisting of weight-shared PCA convolution layers. Then, the change information in the feature difference map is mapped into a 2-D polar domain. Finally, the change detection results are generated by threshold segmentation and clustering algorithms. All procedures of KPCA-MNet does not require labeled data. The theoretical analysis and experimental results demonstrate the validity, robustness, and potential of the proposed method in two binary change detection data sets and one multi-class change detection data set.

Missing data widely exist in industrial processes and lead to difficulties in modelling, monitoring, fault diagnosis, and control. In this paper, we propose a nonlinear method to handle the missing data problem in the offline modelling stage or/and the online monitoring stage of statistical process monitoring. We provide a fast incremental nonlinear matrix completion (FINLMC) method for missing data imputation, which enables us to use kernel methods such as kernel principal component analysis (KPCA) to monitor nonlinear multivariate processes even when there are missing data. We also provide theoretical analysis for the effectiveness of the proposed method. Experiments show that the proposed method can reduce the false alarm rate and improve the fault detection rate in nonlinear processing monitoring with missing data. The proposed method FINLMC can also be used to solve missing data in other problems such as classification and process control.

Principal component analysis (PCA) and Kernel principal component analysis (KPCA) are fundamental methods in machine learning for dimensionality reduction. The former is a technique for finding this approximation in finite dimensions and the latter is often in an infinite dimensional reproducing Kernel Hilbert-space (RKHS). In this paper, we present a geometric framework for computing the principal linear subspaces in both (finite and infinite) situations as well as for the robust PCA case, that amounts to computing the intrinsic average on the space of all subspaces: the Grassmann manifold. Points on this manifold are defined as the subspaces spanned by $K$ K -tuples of observations. The intrinsic Grassmann average of these subspaces are shown to coincide with the principal components of the observations when they are drawn from a Gaussian distribution. We show similar results in the RKHS case and provide an efficient algorithm for computing the projection onto the this average subspace. The result is a method akin to KPCA which is substantially faster. Further, we present a novel online version of the KPCA using our geometric framework. Competitive performance of all our algorithms are demonstrated on a variety of real and synthetic data sets.

Subspace identification methods, such as canonical variate analysis (CVA), are non-iterative tools suitable for the state-space modelling of multi-input, multi-output (MIMO) processes, e.g. industrial processes, using input-output data. To learn nonlinear system behavior, kernel subspace techniques are commonly used. However, the issue of kernel design must be given more attention because the type of kernel can influence the kind of nonlinearities that the model can capture. In this paper, a new kernel design is proposed for CVA based identification, which is a mixture of a global and local kernel to enhance generalization ability and includes a mechanism to vary the influence of each process variable into the model response. During validation, model hyper-parameters were tuned using random search. The overall method is called Feature-Relevant Mixed Kernel Canonical Variate Analysis (FR-MKCVA). Using an evaporator case study, the trained FR-MKCVA models show a better fit to observed data than those of single-kernel CVA, linear CVA, and neural net models under both interpolation and extrapolation scenarios. This work provides a basis for future exploration of deep and diverse kernel designs for system identification.

As the power system develops from informatization to intelligence. Research on data services based on the Internet of Things (IoT) focuses more on application functions, but the research on the data quality of the IoT itself is insufficient. Long-term continuous operation of the big data IoT system has the risk of performance degradation or even partial fault, which leads to a decrease in the availability of collected data for intelligent analysis. In this article, based on the power IoT message data, the characteristics are established through a variety of improved detection methods, and then the abnormal data type is obtained through $Q$ learning and fusion of the random forest (RF) identification features. Finally, the topology of the specific power user IoT system is combined with kernel principal component analysis (KPCA) + improved RF algorithm getting the abnormal location of the IoT. The results show that the research method has a significantly higher positioning accuracy (from 61% to 97%) than the traditional RF method, and the combination method has more advantages in parameter adjustment and classification accuracy than directly using a multilayer perceptron (MLP).

Underwater ultraviolet radiation (UVR), which plays a significant role in photobiological and photochemical processes, is one of the key factors in marine ecosystems. A new algorithm KpcaUV, based on kernel principal component analysis (KPCA) and multiple linear regression (MLR), was proposed in this study for the retrieval of the UVR diffuse attenuation coefficient $ {K_{\mathrm {d}}(\lambda)}$ from remote sensing reflectance $ {R_{\mathrm {rs}}(\lambda)}$ in the global ocean. KPCA can be applied in all areas that principal components analysis (PCA) can be used. More importantly, KPCA can help mapping data into high dimensions and reducing the nonlinearity between inputs and outputs, which will improve the performance and robustness of algorithms when deriving large dynamic ranges parameters. Compared with SeaUVc, which is one of the most successful $ {K_{\mathrm {d}}(\lambda)}$ retrieval algorithms in UVR, the results showed that KpcaUV (with $ {R^{2}}$ : 0.970 and RMSE: 14.0%) performed similar to SeaUVc (with $\boldsymbol {R^{2}}$ : 0.963 and RMSE: 15.6%) when implemented with high-quality data. Nevertheless, KpcaUV was more robust and consistent than SeaUVc when implemented on the satellite images with different levels of quality control. The RMSD of SeaUVc had a significant reduction from 26.8% (QA ≥ 0.6) to 12.7% (QA = 1.0), and the RMSD of KpcaUV varied less than SeaUVc from 14.6% (QA ≥ 0.6) to 10.1% (QA = 1). Hence, considering its good nonlinear-problem-solving ability and robustness when applied to multiple satellites, KpcaUV proposed by this study can be used to obtain ${K_{\mathrm {d}}(380)}$ for the continuous observation of the large area.

Random Forest (RF) is one of the mostly used machine learning techniques in fault detection and diagnosis of industrial systems. However, its implementation suffers from certain drawbacks when considering the correlations between variables. In addition, to perform a fault detection and diagnosis, the classical RF only uses the raw data by the direct use of measured variables. The direct raw data could yield to poor performance due to the data redundancies and noises. Thus, this paper proposes four improved RF methods to overcome the above-mentioned limitations. The developed methods aim to reduce at first the amount of the training data and select the first kernel principal components (KPCs) using different kernel principal component analysis (PCA) based dimensionality reduction schemes. Then, the retained KPCs are fed to the RF classifier for fault diagnosis purposes. Finally, the proposed techniques are applied to a wind energy conversion (WEC) system. Different case studies were investigated in order to illustrate the effectiveness and robustness of the developed techniques compared to the state-of-the-art methods. The obtained results show the low computation time and high diagnosis accuracy of the proposed approaches (an average accuracy of 91%).

The rapid increase in the number of remote sensing sensors makes it possible to develop multisource feature extraction and fusion techniques to improve the classification accuracy of surface materials. It has been reported that light detection and ranging (LiDAR) data can contribute complementary information to hyperspectral images (HSIs). In this article, a multiple feature-based superpixel-level decision fusion (MFSuDF) method is proposed for HSIs and LiDAR data classification. Specifically, superpixel-guided kernel principal component analysis (KPCA) is first designed and applied to HSIs to both reduce the dimensions and compress the noise impact. Next, 2-D and 3-D Gabor filters are, respectively, employed on the KPCA-reduced HSIs and LiDAR data to obtain discriminative Gabor features, and the magnitude and phase information are both taken into account. Three different modules, including the raw data-based feature cube (concatenated KPCA-reduced HSIs and LiDAR data), the Gabor magnitude feature cube, and the Gabor phase feature cube (concatenation of the corresponding Gabor features extracted from the KPCA-reduced HSIs and LiDAR data), can be, thus, achieved. After that, random forest (RF) classifier and quadrant bit coding (QBC) are introduced to separately accomplish the classification task on the aforementioned three extracted feature cubes. Alternatively, two superpixel maps are generated by utilizing the multichannel simple noniterative clustering (SNIC) and entropy rate superpixel segmentation (ERS) algorithms on the combined HSIs and LiDAR data, which are then used to regularize the three classification maps. Finally, a weighted majority voting-based decision fusion strategy is incorporated to effectively enhance the joint use of the multisource data. The proposed approach is, thus, named MFSuDF. A series of experiments are conducted on three real-world data sets to demonstrate the effectiveness of the proposed MFSuDF approach. The experimental results show that our MFSuDF can achieve the overall accuracy of 73.64%, 93.88%, and 74.11% for Houston, Trento, and Missouri University and University of Florida (MUUFL) Gulport data sets, respectively, when there are only three samples per class for training.

Feature design and selection is challenging because of huge data volume and high-mix production systems. Most engineers still rely on human experts to suggest the specific sensor channel and specific time frames of data from which to design the features. This study proposes a novel approach for important sensor screening to prioritize the useful sensor channels for FDC model development in semiconductor manufacturing. The proposed method can be used as a pre-processing step prior to feature extraction, and the selected sensor channels can be leveraged by process engineers for finer feature design. In this research, firstly, time series alignment kernels (TSAKs) are proposed to handle multivariate trace data. Then, the proposed method combines 5 different time series alignment kernels (TSAKs) with a feature selection algorithm, minimum Redundancy Maximum Relevance (mRMR), to identify the important sensor channels. Furthermore, a TSAK+Kernel Principal Component Analysis (KPCA) algorithm is proposed for a visualization tool. Lastly, the TSAK+Support Vector Machine (SVM) is employed for results validation. In this study, validation of the proposed method is based on both open-source datasets and the proprietary datasets from a real production line.

In this article, a new indoor localization technique with extreme learning machine (ELM) is proposed where only a small number of received signal strength indicator (RSSI) measurements are labeled. In the off-line learning phase, the iterative self organizing data analysis techniques algorithm (ISODATA) is used to divide the RSSI measurements into some measurement data subsets. Then the multi-kernel ELM (MK-ELM) method is utilized to perform classification learning and obtain the RSSI measurement classification function. For each RSSI measurement subset, a two-stage feature extraction algorithm using the kernel principal component analysis, the deep learning network and ELM method is proposed for RSSI measurement feature extraction. At last, the position regression function of each subset is obtained by the semi-supervised regression learning. In the on-line position estimation phase, using the measurement classification and feature extraction of the received RSSI measurement, the position is estimated based on the corresponding position regression function. The field tests show that the proposed algorithm can obtain more accurate position estimation than other existing ELM based localization approaches do.

Autonomous structural health monitoring (SHM) of a large number of bridges became a topic of paramount importance for maintenance purposes and safety reasons. This article proposes a set of machine learning (ML) tools to perform automatic detection of anomalies in a bridge structure from vibrational data. As a case study, we considered the Z-24 bridge for which an extensive database of accelerometric data is available. The proposed framework starts from the stabilization diagram obtained through operational modal analysis (OMA) to perform the clustering of modal frequencies and their tracking by density-based time-domain filtering. The features extracted are then fed to a one-class classification (OCC) algorithm to perform anomaly detection. In particular, we propose two new anomaly detectors, namely, one-class classifier neural network (OCCNN) and OCCNN 2 , that find the normal class (the boundary of the features space in normal operating conditions) through a two-step approach: coarse and fine boundary estimate. The detection algorithms are then compared with known methods based on the principal component analysis (PCA), the kernel PCA (KPCA), the Gaussian mixture model (GMM), and the autoassociative neural network (ANN). The proposed OCCNN solution presents increased accuracy and F 1 score over conventional algorithms, without the need to set critical parameters, while OCCNN 2 provides the best performance in terms of F 1 score, accuracy, and responsiveness.

Air pollution has become the fourth leading cause of premature death on Earth. Air pollution causes poor health and death; about one case out of every ten deaths worldwide is caused by air pollution, which is six times more than malaria. Human activities are the main cause of air pollution, such as chemical industries, road traffic, and fossil fuel power plants. Over the span of several years, monitoring air quality has become an exigent and essential task. In order to limit the health impact of air pollution and to ensure safe operation of chemical processes, it is necessary to quickly detect and locate instrumentation defects. There are several process monitoring techniques in the literature. Among these techniques is the one selected for this work for the detection and location of sensor faults: the kernel principal component analysis (KPCA) method, which was selected for its primary advantages of easy employment and less necessity for prior knowledge. Using the KPCA method for monitoring nonlinear systems, the calculation cost and the memory size are related to the number of initial data. This is currently a major limitation of the KPCA method, especially in industrial environments. In order to remedy this limitation, in this paper we propose a new method of detection and localization. The key idea of this approach is to extend the method of localization based on the principle of reconstruction-based contributions (RBC) by downsizing the kernel matrix in the characteristic space. The proposed technique is named reconstruction-based contribution reduced rank kernel principal component analysis(RBC-RRKPCA). The approach is demonstrated using real air quality monitoring network data and simulated data from the Tennessee Eastman process (TEP) as a challenging benchmark problem. We also present a comparative study of the performances of the conventional diagnostic technique RBC-KPCA and the proposed technique RBC-RRKPCA. The results in this paper reveal that the proposed technique achieves the highest detection and localization accuracy.

When the wind turbine pitch system is in operation, due to the strong coupling of the internal structure of the system, it is difficult to accurately locate the fault only relying on prior knowledge. And when using the data-driven contribution graph method for fault location, due to the influence of the fault variable, the contribution value of the non-fault variable will become larger, which will cause a tailing effect and misdiagnosis. In this paper, a multiblock kernel principal component algorithm (MBKPCA) is proposed. In this algorithm, the variables of the pitch system operation process are divided into several variable blocks based on the historical fault data and perform faults based on the kernel principal component algorithm for each variable block diagnosis. Taking historical data of an area in North China as an actual calculation example, the proposed block kernel principal component analysis algorithm is compared with the traditional kernel principal component analysis algorithm. The results show that the MBKPCA can effectively reduce the “tailing effect” of the fault variable on the non-fault variable when the contribution graph method is used to identify the fault source, and the method can accurately locate the fault source and achieves higher detection accuracy.

Quantitative structure–activity relationship (QSAR) modeling is an established approach for drug discovery, but many QSAR datasets suffer from the curse of dimensionality, a challenge that is usually addressed by using dimensionality reduction techniques such as principal component analysis (PCA). However, although linear feature extraction techniques have low computational cost and can handle linear relationships between descriptors, they cannot handle the complex structures found in QSAR data. Hybridization of feature extraction techniques is an effective approach to address the challenges of high-dimensional datasets, and combining the benefits of at least two dimensionality reduction techniques has been successful in many fields. This paper proposes Auto-KPCA, a two-step hybrid feature extraction technique that leverages (i) the fast computational capability of kernel PCA (KPCA) and (ii) the performance of a deep generalized autoencoder in handling complex data structures. Based on classification accuracy, the proposed approach is compared to other feature extraction techniques on the same benchmark dataset. The capability of Auto-KPCA is then investigated further by testing four deep-learning classification models, namely a convolutional neural network, a recurrent neural network, a feedforward deep neural network, and long short-term memory. To the best of the authors’ knowledge, this study is the first to investigate hybridization of KPCA and a deep generalized autoencoder in the context of QSAR. The reported results (i) provide invaluable insights regarding the behavior of different techniques in predicting class labels and (ii) demonstrate increased classification accuracy and noticeably decreased mean square error when compared with KPCA and autoencoders.

Data collected from the supervisory control and data acquisition (SCADA) system are widely used in wind farms to detect wind turbines’ (WTs) faults. However, it is challenging to extract wind turbines’ performance trends and provide accurate alarms based on SCADA data with large operating conditions fluctuations. This article presents a fault detection frame of subspace reconstruction-based robust kernel principal component analysis (SR-RKPCA) model for wind turbines SCADA data to extract nonlinear features under discontinuous interference. First, to improve the stability of the fault detection model of wind turbines, an RKPCA method is developed to decompose the original signal, decomposed into principal component subspace and residual subspace. Second, the permutation entropy is adopted to measure the residual matrix components’ disturbance level and remove trendless noise components. Then, a combined index is developed for fault detection with the aid of the residual space matrix with trend information. Ultimately, the proposed SR-RKPCA method for wind turbine detection is verified by investigating wind turbine faults cases. The proposed method has outstanding robustness and a more vital ability to extract nonlinear features for fault detection than traditional principal component analysis (PCA)- or KPCA-based methods.

Fault diagnosis is of great importance to enhance the reliability and security of the complex chemical processes. However, many fault diagnosis methods cannot extract correlation information among attributes in the feature extraction procedure, resulting in the degradation of diagnosis performance. In this article, a novel framework is proposed for fault diagnosis of the chemical processes. First, in the framework, an enhanced kernel principal component analysis (eKPCA) is proposed to obtain the key features of the fault based on Hotelling’s $T^{2}$ and squared prediction error (SPE) statistics. Second, to learn the correlation information of the features, an enhanced naive Bayesian model (eNBM) is constructed with a multivariate Gaussian kernel function. Third, the dragonfly algorithm (DA) is employed to find the optimal smoothing parameter to improve the performance of eNBM. The framework is applied to make a fault diagnosis of Tennessee Eastman (TE) process. The experimental results show that the proposed framework is more effective compared with the already existed traditional approaches, such as deep learning.

As the state-of-the-art technology of Bayesian inference, based on low-dimensional principal components analysis (PCA) subspace inference methods can provide approximately accurate predictive distribution and well calibrated uncertainty. However, the main problem of PCA method is that it is a linear subspace feature extractor, and it cannot effectively represent the nonlinearly high-dimensional parameter space of deep neural networks (DNNs). Firstly, in this paper, in order to solve the main problem of the linear characteristics of PCA in high-dimensional space, we apply kernel PCA to extract higher-order statistical information in parameter space of DNNs. Secondly, to improve the efficiency of subsequent computation, we propose a strictly ordered incremental kernel PCA (InKPCA) subspace of parameter space within stochastic gradient descent (SGD) trajectories. In the proposed InKPCA subspace, we employ two approximation inference methods: elliptical slice sampling (ESS) and variational inference (VI). Finally, to further improve the memory efficiency of computing the kernel matrix, we apply Nystrom approximation to determine the suitable size of subsets in the original datasets. The novelty of this paper is that it is the first time to apply the proposed InKPCA subspace with Nystrom approximation for Bayesian inference in DNNs, and the results show that it can produce more accurate predictions and well-calibrated predictive uncertainty in regression and classification tasks of deep learning.

A novel gas recognition and concentration detection algorithm consisting of a dynamic wavelet convolutional neural network (DWCNN) and a many-to-many long short-term memory-recurrent neural network (LSTM-RNN), respectively, is proposed as a replacement for the traditional data processing algorithm in artificial olfaction. The proposed DWCNN gas recognition algorithm does not require gas signal preprocessing, and it directly converts the raw time-domain gas signal data to 64 * 64 2-D gray images as the input layer of a convolutional neural network (CNN). The experiments show that the recognition accuracy of CO, H2, and the gas mixture of CO and H2 is nearly 100%, and the many-to-many LSTM-RNN algorithm requires only a few labeled data from the steady-state values of the gas sensor array signals. In addition, comparisons with other neural network multilayer perceptrons (MLPs), gated recurrent unit (GRU) algorithms, and conventional algorithms, such as the Bayesian ridge, support vector machines (SVMs), decision tree, k-nearest neighbor (KNN), random forest, AdaBoost, gradient-boosting decision tree (GBDT), and bagging, revealed that the algorithm can obtain a higher concentration detection accuracy, which was evaluated using two different kernel functions for the kernel principal component analysis (KPCA) dimensionality reduction: polynomial and rbf. The experimental results demonstrated that the proposed many-to-many LSTM gas concentration detection model outperformed the abovementioned algorithms and can more accurately estimate the concentration of different gases while using less labeled data.

Individuals driving private cars in the urban environments to fulll their travel needs have become one of the major daily activities. In particular, unlike the travel with floating cars such as taxis or ride-hailing vehicles, the travel behaviors of private cars exhibit a certain degree of regularity based on daily travel demands. Understanding such travel behavior facilitates many applications, e.g., intelligent transportation, smart city planning, and location-based services (LBS). In this paper, we focus on extracting the regular travel behavior of private cars based on trajectory data analysis. Specifically, first, we construct a trajectory similarity matrix since the similarity of trajectories reflects regular travel behavior. To achieve this, we introduce the stay time and propose an Improved Edit distance with Real Penalty (IERP) to measure the temporal-spatial distance between trajectories. Then, we employ Kernel Principal Component Analysis (KPCA) to reduce the feature dimension of the similarity matrix. Finally, to identify the travel regularity from large set of unlabeled trajectory data, we propose a classification method based on transfer learning to migrate existing knowledge with the purpose of solving learning problems in the target domain with only a small amount of labeled trajectory data or even no data. Extensive experiments using large-scale real-world trajectory data demonstrate that the proposed method can effectively identify the regular travel pattern of private cars and obtain superior accuracy when compared with the existing methods. Our findings on discovering regular travel behaviors of private cars can be directly applied to applications including destination prediction, PoI recommendation and route planning.

When dealing with complex nonlinear signals in intelligent system, by defining the inner product of two data vectors in the feature space, the kernel function can reflect the nonlinear mapping relationship between reproducing kernel Hilbert space (RKHS) and original data space. Therefore, by implementing classical linear adaptive filtering in RKHS space, the filtering operation can be expressed as a special relation of inner product with kernel function, which is referred to as “kernel trick.” As long as these algorithms can be expressed in the form of inner product, not only the convex least squares problem can be solved iteratively, but also the nonlinear adaptive filtering algorithms can be obtained, which have both general approximation characteristics and convexity. Therefore, the combination of kernel method and adaptive filtering algorithm is realized. On the other hand, since the Gram matrix is used, the dimension of kernel adaptive algorithm is determined by the number of data samples. When the number of observation sample point is increasing, the size of the state space increases exponentially with the growth of the dimension. Thereby, the kernel adaptive algorithm should solve the problem of online sparsification to avoid “curse of dimensionality.” As part II, based on online sparse kernel learning and the classical adaptive filtering algorithm, the kernel adaptive algorithms and online sparse algorithms are investigated in this paper. The main works of this paper have two aspects. First, combined with classical adaptive algorithm and kernel feature mapping, this paper investigates the basic concept of kernel adaptive algorithm and the realization mechanism of four kernel adaptive algorithm intensively: 1) kernel least mean squares; 2) kernel recursive least squares; 3) kernel affine projection algorithm; and 4) kernel principal component analysis. Second, in order to reduce the computational complexity, this paper studies some online sparse algorithms which include novel criterion, approximate linear dependency, sliding window, coherence criterion, surprise criterion, and so on. Finally, this paper summarizes the essence of existing conclusions of above algorithms and perspectives the future research direction.

The random forest (RF) classifier, which is a combination of tree predictors, is one of the most powerful classification algorithms that has been recently applied for fault detection and diagnosis (FDD) of industrial processes. However, RF is still suffering from some limitations such as the noncorrelation between variables. These limitations are due to the direct use of variables measured at nodes and therefore the only use of static information from the process data. Thus, this article proposes two enhanced RF classifiers, namely the Euclidean distance based reduced kernel RF (RK-RF $_{\text{ED}}$ ) and K-means clustering based reduced kernel RF (RK-RF $_{\text{Kmeans}}$ ), for FDD. Based on the kernel principal component analysis, the proposed classifiers consist of two main stages: feature extraction and selection, and fault classification. In the first stage, the number of observations in the training data set is reduced using two methods: the first method consists of using the Euclidean distance as dissimilarity metric so that only one measurement is kept in case of redundancy between samples. The second method aims at reducing the amount of the training data based on the K-means clustering technique. Once the characteristics of the process are extracted, the most sensitive features are selected. During the second phase, the selected features are fed to an RF classifier. An emulated grid-connected PV system is used to validate the performance of the proposed RK-RF $_{\text{ED}}$ and RK-RF $_{\text{Kmeans}}$ classifiers. The presented results confirm the high classification accuracy of the developed techniques with low computation time.

Quaternion kernel Fisher discriminant analysis (QKFDA) is proposed for feature level multimodal biometric recognition. In quaternion division ring, QKFDA extracts the most discriminative information from the quaternion fusion feature sets by maximizing the betweenclass variance while minimizing the within-class variance. A complete two-phases framework of QKFDA is developed: Quaternion kernel principal component analysis (QKPCA) plus Quaternion linear discriminant analysis(QLDA). Two experiments are designed: experiment I fuses four different features of face and plamprint, experiment II fuses three different features of face, plamprint and signature. The experimental results show that QKFDA is superior to both traditional feature fusion methods (series rule and weighted sum rule)and other quaternion feature fusion methods (QPCA, QFDA, QLPP and QKPCA).

Kernel principal component analysis (KPCA) is a well-established data-driven process modeling and monitoring framework that has long been praised for its performances. However, it is still not optimal for large-scale and uncertain systems. Applying KPCA usually takes a long time and a significant storage space when big data are utilized. In addition, it leads to a serious loss of information and ignores uncertainties in the processes. Consequently, in this paper, two uncertain nonlinear statistical fault detection methods using an interval reduced kernel principal component analysis (IRKPCA) are proposed. The main objective of the proposed methods is twofold. Firstly, reduce the number of observations in the data matrix through two techniques: a method, called IRKPCA $_{ED}$ , is based on Euclidean distance between samples as dissimilarity metric such that only one observation is kept in case of redundancy to build the reduced reference KPCA model, and another method, called IRKPCA $_{PCA}$ , is established on the PCA algorithm to treat the hybrid correlations between process variables and extract a reduced number of observations from the training data matrix. Secondly, address the problem of uncertainties in systems using a latent-driven technique based on interval-valued data. Taking into account sensors uncertainties via IRKPCA ensures better monitoring by reducing the computational and storage costs. The study demonstrated the feasibility and effectiveness of the proposed approaches for faults detection in two real world applications: Tennessee Eastman (TE) process and real air quality monitoring network (AIRLOR) data.

Cloud Colonography is proposed in this paper, using different types of cloud computing environments. Databases from the Computed Tomographic Colonography (CTC) screening tests among several hospitals are explored. These networked databases are going to be available in the near future via cloud computing technologies. Associated Multiple Databases (AMD) was developed in this study to handle multiple CTC databases. When AMD is used for assembling databases, it can achieve very high classification accuracy. The proposed AMD has the potential to play a role of the core classifier in the cloud computing framework. AMD for multiple institutions databases yields high detection performance of polyps using Kernel principal component analysis (KPCA). Two cases in the proposed cloud platform are private and public. We adapted a university cluster as a private platform, and Amazon Elastic Compute Cloud (EC2) as a public. The computation time, memory usage, and running costs were compared using three representative databases between private and public cloud environments. The proposed parallel processing modules improved the computation time, especially in the public cloud environments. The successful development of a cloud computing environment that handles large amounts of data will make Cloud Colonography feasible for a new health care service.

Robust principal component analysis (RPCA) can recover low-rank matrices when they are corrupted by sparse noises. In practice, many matrices are, however, of high-rank and hence cannot be recovered by RPCA. We propose a novel method called robust kernel principal component analysis (RKPCA) to decompose a partially corrupted matrix as a sparse matrix plus a high or full-rank matrix with low latent dimensionality. RKPCA can be applied to many problems such as noise removal and subspace clustering and is still the only unsupervised nonlinear method robust to sparse noises. Our theoretical analysis shows that, with high probability, RKPCA can provide high recovery accuracy. The optimization of RKPCA involves nonconvex and indifferentiable problems. We propose two nonconvex optimization algorithms for RKPCA. They are alternating direction method of multipliers with backtracking line search and proximal linearized minimization with adaptive step size. Comparative studies in noise removal and robust subspace clustering corroborate the effectiveness and superiority of RKPCA., Comment: The paper was accepted by IEEE Transactions on Neural Networks and Learning Systems

Atmosphere ion mobility is an important electrical parameter related to the filamentary ion flow field of high voltage direct current (HVDC) transmission lines and other characteristics of the glow and streamer corona discharge. Many machine learning (ML)-based algorithms have already been widely used in the prediction of air discharge. This article proposes a genetic algorithm (GA)-support vector regression (SVR) combined with kernel principal components analysis (PCA) to predict the ion mobility, involving dimensionality reduction, feature selection, parameter optimization of SVR. Kernel PCA could reduce the dimension of data and GA with adaptive probability parameters is employed to optimize the parameters of SVR model. An improved parallel-plates ion generator is employed to produce corona discharge and then measure the saturation ion current density and then obtain the training data and testing data of ion mobility. The prediction results show that the proposed algorithm outperforms the other methods in terms of mean relative error and mean squared error criteria. In addition, the parameters of model and data features have a major influence on the performance of the prediction algorithm. Based on the measured data and reference data, the prediction result obtained on ion mobility under different humidity shows a satisfactory generalization and effectiveness of proposed model for the prediction.

Apple fruits can be easily damaged, and bruises occur on peels during harvest, transportation and storage, which could decrease fruit quality. This paper proposed an apple bruise grading method based on hyperspectral imaging (HSI). The spectral information of sound apples (Yantai Fuji 8) was first captured using a hyperspectral reflectance imaging device (386-1016 nm). These apples were then mechanically damaged by the same impact forces, and the bruised regions were exposed to room temperature for at most 120 min. The spectral data of the bruised apples at four different exposure times (30 min, 60 min, 90 min and 120 min) were obtained. The spectral data were preprocessed using Procrustes analysis (PA) to enable a more diverse distribution of the spectra among different patterns. To both accurately maintain the spectral information of different patterns and reduce the dimensions of the spectra, piecewise nonlinear curve fitting (PWCF) was presented using the least squares algorithm, where the resultant fitting coefficients from different spectral intervals were catenated into a low-dimension feature descriptor. The feature descriptors were then fed to an error-correction output coding-based support vector machine (ECOC-SVM) to grade the bruised apples. To further evaluate the performance of the presented PWCF, conventional algorithms, including the successive projections algorithm (SPA), genetic algorithm (GA), principal component analysis (PCA) and kernel principal component analysis (KPCA), were introduced for comparison. Experimental results showed that the proposed method obtained the best grading accuracy (97.33%) compared to the other methods.

Principal component analysis (PCA) is a widely used unsupervised method for dimensionality reduction. The kernelized version is called kernel principal component analysis (KPCA), which can capture the nonlinear data structure. KPCA is derived from the Gram matrix, which is not robust when outliers exist in the data. This may yield the principal axis in the feature space deviated by outliers, leading to misinterpretation of the principal components. In this paper, we propose a robust method for KPCA with a reformulation in Euclidean space to construct a robust KPCA method, where an error measurement is introduced into the loss function, and l 2,1 -regularization is added to the loss function. The idea of l 2,1 -regularization of the proposed method is motivated by sparse PCA via variable projection. However, because orthogonality is not satisfied in the proposed method, orthonormal bases are obtained by using the Gram-Schmidt orthonormalization process. In the experiments, a toy example and real data are used for outlier detection to verify the method's performance and effectiveness. In the toy example, the proposed method reduces the influence of outliers and detects more outliers than KPCA. For the real data, the proposed method improves detection in comparison to other existing methods.

In order to guarantee and improve the product quality, the data-driven fault detection technique has been widely used in industry. For three-way datasets of batch process in industry process (i.e., batch × variable × time), a novel method named functional local kernel principal component analysis (FLKPCA) is proposed. Since the variables' trajectories often show functional nature and can be considered as smooth functions rather than just vectors. Firstly, the variables' trajectory is expressed as the combination of smooth basis functions using functional data analysis (FDA), which means that the datasets of batches process would be transformed from the three-ways array into two-ways function matrix. Then, kernel locality preserving projections (LKPCA) is used to perform dimensionality reduction on two-way function matrix directly. Different from kernel principal component analysis (KPCA). LKPCA aims at preserving the both local and global structure of the data in a new optimization objective. Consequently, FLKPCA could more effectively seek the potential information that hidden in the three-ways datasets. Lastly, the effectiveness of the proposed approach is illustrated by the benchmark of fed-batch penicillin fermentation process and the hot strip rolling process.

Stock price manipulation uses illegitimate means to artificially influence market prices of several stocks. It causes massive losses and undermines investors' confidence and the integrity of the stock market. Several existing research works focused on detecting a specific manipulation scheme using supervised learning but lacks the adaptive capability to capture different manipulative strategies. This begets the assumption of model parameter values specific to the underlying manipulation scheme. In addition, supervised learning requires the use of labelled data which is difficult to acquire due to confidentiality and the proprietary nature of trading data. The proposed research establishes a detection model based on unsupervised learning using Kernel Principal Component Analysis (KPCA) and applied increased variance of selected latent features in higher dimensions. A proposed Multidimensional Kernel Density Estimation (MKDE) clustering is then applied upon the selected components to identify abnormal patterns of manipulation in data. This research has an advantage over the existing methods in overcoming the ambiguity of assuming values of several parameters, reducing the high dimensions obtained from conventional KPCA and thereby reducing computational complexity. The robustness of the detection model has also been evaluated when two or more manipulative activities occur within a short duration of each other and by varying the window length of the dataset fed to the model. Validation on multiple datasets and a comprehensive assessment of the model performance has been conducted without providing any prior information about the location of the manipulation. The results show a significant performance enhancement in terms of the F-measure values and a significant reduction in false alarm rate (FAR) has been achieved.

Abnormality detection in medical images is a one-class classification problem for which existing methods typically involve variants of kernel principal component analysis or one-class support vector machines. However, existing methods rely on highly-curated training sets with full supervision, often using heuristics for model fitting or ignore the variances of the data within principal subspaces. In contrast, we propose novel methods that can work with imperfectly curated datasets using robust statistical learning, by extending the multivariate generalized-Gaussian distribution to a reproducing kernel Hilbert space (RKHS) and employing it within a mixture model. We propose a novel semi-supervised extension of our learning scheme, showing that a small amount of expert feedback through high-quality labeled data of the outlier class can boost performance. We propose expectation maximization for our semi-supervised robust mixture-model learning in RKHS, using solely the Gram matrix and without the explicit lifting map. Our methods incorporate optimal component means, principal directions, and variances for abnormality detection. Results on four large public datasets on retinopathy and cancer, compared against a variety of contemporary methods, show that our method gives benefits over the state of the art in one-class classification for abnormality detection.

Industrial data usually have nonlinear or multimodal characteristics which do not meet the data assumptions of statistics in principal component analysis (PCA). Therefore, PCA has a lower fault detection rate in industrial processes. Aiming at the above limitations of PCA, a fault detection method using principal component difference based on k-nearest neighbors (Diff-PCA) is proposed in this paper. First, find the k nearest neighbors set of each sample in the training data set and calculate its mean vector. Second, build an augmented vector using each sample and its corresponding mean vector. Third, calculate the loading matrix and score matrix using PCA. Next, calculate the estimated scores using the mean vector of each sample and missing data imputation technique for PCA. At last, build two new statistics using the difference between the real scores and estimated scores to detect faults. In addition, the fault diagnosis method based on contribution plots of monitored variables is also proposed in this paper. In Diff-PCA, the difference skill can eliminate the impact of the nonlinear and multimodal structure on fault detection. Meanwhile, the monitored subspaces by the two new statistics are different from that by T2 and SPE in PCA. The efficiency of the proposed strategy is implemented in two numerical cases (nonlinear and multimode) and the Tennessee Eastman (TE) processes. The fault detection results indicate that Diff-PCA outperforms the conventional PCA, Kernel PCA, dynamic PCA, principal component-based k nearest neighbor rule and k nearest neighbor rule.

Computational approaches for synthesizing new chemical compounds have resulted in a major explosion of chemical data in the field of drug discovery. The quantitative structure–activity relationship (QSAR) is a widely used classification and regression method used to represent the relationship between a chemical structure and its activities. This research focuses on the effect of dimensionality-reduction techniques on a high-dimensional QSAR dataset. Because of the multi-dimensional nature of QSAR, dimensionality-reduction techniques have become an integral part of its modeling process. Principal component analysis (PCA) is a feature extraction technique with several applications in exploratory data analysis, visualization and dimensionality reduction. However, linear PCA is inadequate to handle the complex structure of QSAR data. In light of the wide array of current feature-extraction techniques, we perform a comparative empirical study to investigate five feature-extraction techniques: PCA, kernel PCA, deep generalized autoencoder (dGAE), Gaussian random projection (GRP), and sparse random projection (SRP). The experiments are performed on a high-dimensional QSAR dataset, which comprises 6394 features. The transformed low-dimensional dataset is inputted into a deep learning classification model to predict a QSAR biological activity. Three approaches are adopted to validate and measure the proposed techniques: (i) comparing the performance of the classification models, (ii) visualizing the relationship (correlation) between features in the low-dimension Euclidean space, and (iii) validating the proposed techniques using an external dataset. To the best of our knowledge, this study is the first to investigate and compare the aforementioned feature-extraction techniques in QSAR modeling context. The results obtained provide invaluable insights regarding the behavior of different techniques with both negative and positive classes. With linear PCA as a baseline, we prove that the investigated techniques substantially outperform the baseline in multiple accuracy measures and demonstrate useful ways of extracting significant features.

Recent advances in remote sensing have shown great potential for different kind of applications like vegetation and crop supervision. Using hyperspectral images (HSI), this process can be performed over large areas of land, allowing for a fast and non-invasive analysis of variables such as water stress, diseases, type of crops, among many others. In this context, representative spatial-spectral features are crucial to develop the data classification process of hyperspectral remote sensing images. In this way, the use of deep learning networks has shown a remarkable classification performance in many applications as the processing of hyperspectral images. In this paper, a data classification model that use kernel PCA (K-PCA) and inception network architecture to generate deep spatial-spectral features is proposed. The features generated are used to label the different kind of classes into the HSI. The labeling process uses a logistic regression (LR) algorithm. This model was validated using six different datasets. The experiments performed shown that the proposed strategy allows improving the data classification performance regarding the results obtained by the traditional stacked layer model of convolutional neural networks (CNN). Quantitatively speaking, the overall accuracy over all experiments of the proposed model for all tested datasets is greater than 92%.

Domain adaptation, which aims at learning an accurate classifier for a new domain (target domain) using labeled information from an old domain (source domain), has shown promising value in remote sensing fields yet still been a challenging problem. In this letter, we focus on knowledge transfer between hyperspectral remotely sensed images in the context of land-cover classification under unsupervised setting where labeled samples are available only for the source image. Specifically, a discriminative transfer joint matching (DTJM) method is proposed, which matches source and target features in the kernel principal component analysis space by minimizing the empirical maximum mean discrepancy, performs instance reweighting by imposing an $\ell _{2,1}$ -norm on the embedding matrix, and preserves the local manifold structure of data from different domains and meanwhile maximizes the dependence between the embedding and labels. The proposed approach is compared with some state-of-the-art feature extraction techniques with and without using label information of source data. Experimental results on two benchmark hypersepctral data sets show the effectiveness of the proposed DTJM.

In this paper, a novel multi-scale total variation method is proposed to extract structural features from hyperspectral images (HSIs), which consists of the following steps. First, the spectral dimension of the HSI is reduced with an averaging-based method. Then, the multi-scale structural features (MSFs), which are insensitive to image noise, are constructed with a relative total variation-based structure extraction technique. Finally, the MSFs are fused together using kernel principal component analysis (KPCA), so as to obtain the KPCA-fused MSFs for classification. Experimental results on three publicly available hyperspectral datasets, including both well-known, long-used data, and a recent dataset obtained from an international contest, demonstrate the competitive performance over several state-of-the-art classification approaches in this field. Moreover, the robustness of the proposed method to the small-sample-size problem and serious image noise is also demonstrated.

In this paper, we introduce a closed-form sparse Bayesian kernel Poisson regression (SBKPR) model for count data regression problems based on the sparse Bayesian learning (SBL) approach. In Bayesian setting, a Gaussian prior is given to the model parameter, which is not the conjugate distribution of Poisson regression. Hence, the model parameters cannot be integrated analytically, which leads to the inference intractable problem. In this paper, the log-gamma Gaussian approximation method is proposed to solve this analytically intractable problem, which can give out the closed-form solutions. Furthermore, an individual Gaussian prior is given to the model parameters, which can enhance the flexibility of the proposed method. Finally, sparse solutions can be obtained by applying SBL, which can benefit the learning efficiency and reduce the computational time in practical applications. Experimental results demonstrate that the proposed SBKPR model can outperform some state-of-the-art count data regression models on both toy data and real-world data.

This paper presents a Synthetic Aperture Radar (SAR) image classification algorithm based on multi-feature using Fruit Fly Optimization Algorithm (FOA) and Least Square Support Vector Machine (LS-SVM). First, pixel-based information derived from three elements of coherency matrix, six parameters obtained by $H/\alpha /A$ decomposition and Freeman decomposition techniques, and three polarimetric parameters including the total receive power (SPAN), pedestal height, and Radar Vegetation Index (RVI), as well as region-based information derived from eight texture parameters obtained by Grey Level Co-occurrence Matrix (GLCM) are combined to use as the features of land cover. Second, Kernel Principal Component Analysis (KPCA) is used to reduce the dimensionality of the multi-feature data derived from the integration of the pixel-based and region-based information. Third, LS-SVM is used as the classifier in this study due to its fast solving speed and desirable classification capability. Since the input parameters of LS-SVM significantly affect the classification performance, we employ FOA to obtain the optimized input parameters. Finally, the experiments on two fully polarimetric SAR images of various crops with a limited number of samples are implemented by the proposed method and other commonly used methods, respectively. The results show that the proposed method can attain better classification performances compared with other methods.

Kernel principal component analysis (KPCA) has been widely used in nonlinear process monitoring since it can capture the nonlinear process characteristics. However, it suffers from high computational complexity and poor scalability while dealing with real-time process monitoring and large-scale process monitoring. In this paper, a novel dimension reduction technique, local and global randomized principal component analysis (LGRPCA), is proposed for nonlinear process monitoring. The proposed LGRPCA method first maps the input space onto a feature space to reveal nonlinear patterns through random Fourier features. With the aid of random Fourier features, the proposed LGRPCA method is scalable and with much lower computational and storage costs. To exploit the underlying local and global structure information in the feature space, local structure analysis is integrated into the framework of global variance information extraction. The resulting LGRPCA can provide an improved representation of input data than the traditional KPCA. Thus, the proposed LGRPCA method is quite suitable for real-time process monitoring and large-scale process monitoring. $T^{2}$ and squared prediction error (SPE) statistic control charts are built for fault detection using the proposed LGRPCA method. Furthermore, contribution plots to LGRPCA-based $T^{2}$ and SPE ( $Q$ ) statistics are established to identify the root cause variables through a sensitivity analysis principle. The superior performance of the proposed LGRPCA-based nonlinear process monitoring method is demonstrated through a numerical example and the comparative study of the Tennessee Eastman benchmark process.

© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works This paper proposes a novel leak monitoring framework aims to improve the operation of water distribution network (WDN). To do that, an online statistical hypothesis test based leak detection is proposed. The main advantages of the developed method are first to deal with the higher required computational time for detecting leaks and then, to update the KPCA model according to the dynamic change of the process. Thus, this can be performed to massive and online datasets. Simulation results obtained from simulated WDN data demonstrate the effectiveness of the proposed technique.

Fault diagnosis has received considerable attention because its implementation can effectively prevent costly and even catastrophic downtime. However, quickly identifying faults and accurately obtaining diagnosis results from a feature set of rotating machinery are still a problem. To this end, this paper proposes an effective method based on a weighted extreme learning machine (WELM) with wavelet packet decomposition (WPD) and kernel principal component analysis (KPCA). The feature set affecting classification accuracy can be obtained using WPD and KPCA. By taking feature reliability into consideration, a new type of improvement to the extreme learning machine (ELM), i.e., WELM, is proposed by associating the hidden layer and input layer with a weight matrix. The WELM model can help in guaranteeing a quick and an accurate identification of fault status. To verify the superiority of the fault identification speed and accuracy of the proposed method, results from other methods, namely, using the sensitive features based on WPD and KPCA with ELM, a back-propagation neural network, and a support vector machine, were compared. The experimental results indicate that the proposed method can effectively improve the accuracy and quickly diagnose the fault. The average accuracy of fault classification could reach 95.45%, and the computation time of WELM was only 0.0156 s.

With the ever-increasing penetration level of renewable generation sources, a modern power system is facing more inevitable uncertainties that could lead to weakly damped oscillations. Detecting coherency among synchronous generators is one of the key steps of situational awareness for a given power system with a very high level of renewable penetration. In this paper, a wide-area measurement system (WAMS) based coherency detection algorithm employing the kernel principal component analysis (KPCA) and clustering analysis based on affinity propagation (AP) is proposed for a power system with extensive penetration of renewable generation sources. First, several trajectory similarity indexes are presented for determining the similarity between the trajectories of any two generators in the center of inertia coordinate. Second, a KPCA-based method is presented to integrate the trajectory similarity indexes for addressing the correlations among multiple indexes. Next, the AP-based clustering analysis method is utilized to detect the coherency among synchronous generators without the need of prespecifying the number of clusters. Finally, Southern China power system and a part of northern China power system with Zhangbei wind farms included, both with very high levels of renewable generation penetration, are utilized to demonstrate the proposed WAMS-based coherency detection methodology, and the application to actual Guangdong power system in south China to verify the applicability and practicality.

In this brief, kernel principal component analysis (KPCA) is reinterpreted as the solution to a convex optimization problem. Actually, there is a constrained convex problem for each principal component, so that the constraints guarantee that the principal component is indeed a solution, and not a mere saddle point. Although these insights do not imply any algorithmic improvement, they can be used to further understand the method, formulate possible extensions, and properly address them. As an example, a new convex optimization problem for semisupervised classification is proposed, which seems particularly well suited whenever the number of known labels is small. Our formulation resembles a least squares support vector machine problem with a regularization parameter multiplied by a negative sign, combined with a variational principle for KPCA. Our primal optimization principle for semisupervised learning is solved in terms of the Lagrange multipliers. Numerical experiments in several classification tasks illustrate the performance of the proposed model in problems with only a few labeled data. ispartof: IEEE Transactions on Neural Networks and Learning Systems vol:29 issue:8 pages:3863-3869 ispartof: location:United States status: published

Correntropy is a second order statistical measure in kernel space, which has been successfully applied in robust learning and signal processing. In this paper, we define a nonsecond order statistical measure in kernel space, called the kernel mean- ${p}$ power error (KMPE), including the correntropic loss (C-Loss) as a special case. Some basic properties of KMPE are presented. In particular, we apply the KMPE to extreme learning machine (ELM) and principal component analysis (PCA), and develop two robust learning algorithms, namely ELM-KMPE and PCA-KMPE. Experimental results on synthetic and benchmark data show that the developed algorithms can achieve better performance when compared with some existing methods.

Many actuators and sensors made by smart materials have hysteresis feature which is a complex nonlinear phenomenon with multivalued mapping. Accurate identification of hysteresis pattern in those sensors and actuators is helpful for improving the modeling and control strategies of the systems. In this paper, a general framework of the pattern clustering of hysteretic time series is developed on the basis of tensor decomposition. First, high-dimensional multivariate data of hysteresis objects are transformed into three-order hysteresis tensors. Then the multilinear principal component analysis (MPCA) is utilized to reduce the dimensionality of hysteresis tensors. Afterward, a novel tensor ${k}$ -means clustering (CTKmeans) based on tensor distance and cycle variation feature initialization is developed for the clustering of tensor objects. In order to evaluate the performance of the proposed approach, the experiment of hysteresis feature test using polyvinylidene fluoride (PVDF)-based pressure sensors is implemented. The measured high-dimensional hysteresis time series of PVDF successively undergoes the procedures of filtering, segmentation, MPCA dimensionality reduction and CTKmeans clustering. The experimental results show that the MPCA can capture more significant inherent features of hysteresis objects than the principal component analysis (PCA) or the kernel PCA in the dimensionality reduction. In terms of tensor distance and cycle variation feature initialization, the CTKmeans outperforms the random-initialization-based tensor ${k}$ -means and standard ${k}$ -means in the clustering of hysteresis tensors. With the tensor decomposition approach of multivariate time series, the hysteresis objects with nonlinear multivalued mapping features can be effectively identified by the combination of MPCA and CTKmeans.

High-dimensional data present in the real world is often corrupted by noise and gross outliers. Principal component analysis (PCA) fails to learn the true low-dimensional subspace in such cases. This is the reason why robust versions of PCA, which put a penalty on arbitrarily large outlying entries, are preferred to perform dimension reduction. In this paper, we argue that it is necessary to study the presence of outliers not only in the observed data matrix but also in the orthogonal complement subspace of the authentic principal subspace. In fact, the latter can seriously skew the estimation of the principal components. A reinforced robustification of principal component pursuit is designed in order to cater to the problem of finding out both types of outliers and eliminate their influence on the final subspace estimation. Simulation results under different design situations clearly show the superiority of our proposed method as compared with other popular implementations of robust PCA. This paper also showcases possible applications of our method in critically tough scenarios of face recognition and video background subtraction. Along with approximating a usable low-dimensional subspace from real-world data sets, the technique can capture semantically meaningful outliers.

Recently, some online kernel principal component analysis (KPCA) techniques based on the generalized Hebbian algorithm (GHA) were proposed for use in large data sets, defining kernel components using concise dictionaries automatically extracted from data. This brief proposes two new online KPCA extraction algorithms, exploiting orthogonalized versions of the GHA rule. In both the cases, the orthogonalization of kernel components is achieved by the inclusion of some low complexity additional steps to the kernel Hebbian algorithm, thus not substantially affecting the computational cost of the algorithm. Results show improved convergence speed and accuracy of components extracted by the proposed methods, as compared with the state-of-the-art online KPCA extraction algorithms.

In this paper, a novel approach to fault detection for nonlinear processes is proposed. It is based on a manifold learning called modified kernel semi-supervised local linear embedding. Local linear embedding (LLE) is widely applied to fault detection of complex industrial process. However, the LLE only preserves the local structure information of the sample, which ignores the global characteristics of the original data. The main contributions of the presented approach are as follows: 1) in order to utilize labeled data, the semi-supervised learning is introduced into LLE; 2) the regularization term is added to the calculation of local reconstruction weights matrix to strengthen the anti-noise ability in nonlinear processing; and 3) in order to extract the global and local characteristic of the observation data, the kernel principal component analysis objective function is integrated with the objective function of LLE. Experimental results on the production process of fused magnesia verify the performance of the proposed method.

Kernel principal component analysis (KPCA) is a powerful and widely applied nonlinear feature extraction technique. However, as originally proposed, KPCA may be cumbersome or infeasible in large-scale datasets, which motivated the development of low-complexity iterative extraction algorithms, mainly aiming image processing applications. Recently, some online KPCA extraction algorithms were proposed, but most of them suffer from low-convergence speed. This paper proposes a new algorithm based on fixed-point iterative equations for KPCA extraction, expanding kernel components using a compact dictionary, dynamically built from data, according to a user-defined accuracy parameter. The algorithm relies on simple equations, can track nonstationary environments, and requires reduced storage, enabling its use in real-time applications operating in low-cost embedded hardware. Results involving open-access image datasets show improved accuracy and convergence speed, as well as permitted effective improvements in practical image applications, as compared to state-of-art online KPCA techniques.