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As a powerful tool for real-time battery management, the extended Kalman filter (EKF) can achieve an online estimation for state of charge (SOC). The EKF, however, may yield biased estimates since the measured system suffers from the abnormal operation conditions, i.e., sensor faults, sensor bias and sensor noise. Thus, this paper proposes a robust extended Kalman filter based on maximum multi-kernel correntropy (MMKC-EKF) for SOC estimate when the system is subjected to complex non-Gaussian disturbances. To derive MMKC-EKF, a batch-mode regression is formulated by integrating the uncertainties of process and measurement, which is solved by using maximum multi-kernel correntropy (MMKC) criterion to suppress the influences of abnormal conditions. An effective optimization method is introduced to determine the free parameters of MMKC, and a fixed-point iteration method gives the state estimation. Then, the posterior error covariance matrix is updated with the help of total influence function, which contributes to the robustness improvement. In addition, a novel filtering scheme is presented for reducing computational complexity, which is beneficial for solving battery pack state estimation in practice. Extensive simulations are carried out for SOC estimate to validate the accuracy and robustness of the proposed MMKC-EKF in the Gaussian and non-Gaussian distributed process and measurement noises. • In MMKC-EKF, a batch-mode regression is established, which is optimized by the MMKC. • The fixed-point iteration algorithm and total influence are used to update the posterior state and error covariance matrix, respectively. • An effective optimization method is introduced to determine the free parameters of MMKC. • A novel design scheme is also adopted to save the computational time. [ABSTRACT FROM AUTHOR]

Minimum error entropy with fiducial points (MEEF) has received a lot of attention, due to its outstanding performance to curb the negative influence caused by non-Gaussian noises in the fields of machine learning and signal processing. However, the estimate of the information potential of MEEF involves a double summation operator based on all available error samples, which can result in large computational burden in many practical scenarios. In this paper, an efficient quantization method is therefore adopted to represent the primary set of error samples with a smaller subset, generating a quantized MEEF (QMEEF). Some basic properties of QMEEF are presented and proved from theoretical perspectives. In addition, we have applied this new criterion to train a class of linear-in-parameters models, including the commonly used linear regression model, random vector functional link network, and broad learning system as special cases. Experimental results on various datasets are reported to demonstrate the desirable performance of the proposed methods to perform regression tasks with contaminated data. [ABSTRACT FROM AUTHOR]

Although multi-view clustering has received widespread attention due to its far superior performance to single-view clustering, it still faces the following issues: (1) high computational cost, considering the introduction of multi-view information, reduces the clustering efficiency greatly; (2) complex noises and outliers, existed in real-world data, pose a huge challenge to the robustness of clustering algorithms. Currently, how to increase the efficiency and robustness has become two important issues of multi-view clustering. To cope with the above issues, an efficient correntropy-based multi-view clustering algorithm (ECMC) is proposed in this paper, which can not only improve clustering efficiency by constructing embedded anchor graph and utilizing nonnegative matrix factorization (NMF), but also enhance the robustness by exploring correntropy to suppress various noises and outliers. To further improve clustering efficiency, one of the factors of NMF is constrained to be an indicator matrix instead of a traditional non-negative matrix, so that the categories of samples can be obtained directly without any extra operation. Subsequently, a novel half-quadratic-based strategy is proposed to optimize the non-convex objective function of ECMC. Finally, extensive experiments on eight real-world datasets and eighteen noisy datasets show that ECMC can guarantee faster speed and better robustness than other state-of-the-art multi-view clustering algorithms. [ABSTRACT FROM AUTHOR]

There is a recent trend to leverage the power of graph neural networks (GNNs) for brain-network based psychiatric diagnosis, which, in turn, also motivates an urgent need for psychiatrists to fully understand the decision behavior of the used GNNs. However, most of the existing GNN explainers are either post-hoc in which another interpretive model needs to be created to explain a well-trained GNN, or do not consider the causal relationship between the extracted explanation and the decision, such that the explanation itself contains spurious correlations and suffers from weak faithfulness. In this work, we propose a granger causality-inspired graph neural network (CI-GNN), a built-in interpretable model that is able to identify the most influential subgraph (i.e., functional connectivity within brain regions) that is causally related to the decision (e.g., major depressive disorder patients or healthy controls), without the training of an auxillary interpretive network. CI-GNN learns disentangled subgraph-level representations α and β that encode, respectively, the causal and non-causal aspects of original graph under a graph variational autoencoder framework, regularized by a conditional mutual information (CMI) constraint. We theoretically justify the validity of the CMI regulation in capturing the causal relationship. We also empirically evaluate the performance of CI-GNN against three baseline GNNs and four state-of-the-art GNN explainers on synthetic data and three large-scale brain disease datasets. We observe that CI-GNN achieves the best performance in a wide range of metrics and provides more reliable and concise explanations which have clinical evidence. The source code and implementation details of CI-GNN are freely available at GitHub repository (https://github.com/ZKZ-Brain/CI-GNN/). [ABSTRACT FROM AUTHOR]

Support vector data description (SVDD) has received a lot of attention due to its outstanding performance to perform one-class classification or novelty detection tasks. However, the same weight is directly imposed on all slack variables in the process of modeling, which may result in degraded learning performance when training data are contaminated by some outliers or mislabeled observations. In this paper, an extended SVDD model is therefore proposed by reformulating the original optimization problem of SVDD with a mixed exponential loss function. Since this loss function can emphasize the importance of the samples that tend to be the target class, and weaken the influence of those tending to be outliers, it can be viewed as a weighted SVDD. However, the weights in the new model are automatically calculated rather than being calculated in advance using some specific manners. To solve the optimization problem of the proposed model effectively, the half-quadratic optimization technique has been adopted to perform the optimization, generating a dynamic optimization algorithm. Meanwhile, the convergence and computational complexity of this dynamic optimization algorithm are analyzed from a theoretical respective. Experimental results on a synthetic data set and some publicly available real world data sets are reported to demonstrate the performance superiority of the new method in comparison with SVDD and other competitive SVDD variants. [ABSTRACT FROM AUTHOR]

The Unscented Kalman filter (UKF) based on maximum correntropy criterion (MCC) is robust to heavy-tailed non-Gaussian noise. However, the approximate linear measurement equation obtained by statistical linearization technique may be not accurate enough since it only uses prior information. In this paper, a robust stable iterative maximum correntropy criterion UKF (RS-IMCC-UKF) is proposed by using nonlinear measurement function directly and numerical stability methods. Different from the existing UKF algorithms, we only need to perform one-time unscented transformation in each filtering cycle, reducing the execution time of algorithm. Then a nonlinear enhancement model is constructed to handle predictions and observations simultaneously, which will be included in the cost function of robust MCC. In the process of iterative solution, thanks to the latest iteration values which are used to update the measurement information, RS-IMCC-UKF has more accurate results compared with traditional filters. In order to avoid non-positive definite characteristic in covariance matrix and the inverse operation in ill-conditioned matrix, the hyperbolic QR decomposition and Moore–Penrose pseudo-inversion are introduced to improve the numerical stability of the algorithm. Finally, a target tracking is modeled to verify the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

Concept factorization (CF) has shown the effectiveness in the field of data clustering. In this paper, a novel and robust semi-supervised CF method, called correntropy based semi-supervised concept factorization with adaptive neighbors (CSCF), is proposed with improved performance in clustering applications. Specifically, on the one hand, the CSCF method adopts correntropy as the cost function to increase the robustness for non-Gaussian noise and outliers, and combines two different types of supervised information simultaneously for obtaining a compact low-dimensional representation of the original data. On the other hand, CSCF assigns the adaptive neighbors for each data point to construct a good data similarity matrix for reducing the sensitiveness of data. Moreover, a generalized version of CSCF is derived for enlarging the clustering application ranges. Analysis is also presented for the relationship of CSCF with several typical CF methods. Experimental results have shown that CSCF has better clustering performance than several state-of-the-art CF methods. [ABSTRACT FROM AUTHOR]

Concept factorization (CF), unlike nonnegative matrix factorization (NMF), can handle data with negative values by approximating the original data with two low-dimensional nonnegative matrices and itself. Nevertheless, existing CF-based methods continue to suffer from the two issues specified as follows: (1) Their effectiveness is reduced by the high degree of factorization freedom and the two-stage mismatch between factorization and category acquisition, and (2) their robustness drops significantly when dealing with complex noise. In response to the aforementioned issues, we propose a robust spectral-embedded bilateral orthogonal concept factorization (RSOCF) model for clustering. It constrains the factor matrices as orthogonal matrices to decrease the freedom and obtain samples' categories directly after factorization, which can significantly improve clustering effectiveness. Moreover, correntropy is introduced into RSOCF to improve its robustness to complex noise. To optimize the non-convex RSOCF model, a half-quadratic-based algorithm is devised. Numerous experiments demonstrate that RSOCF surpasses other state-of-the-art methods in terms of clustering effectiveness and robustness. • A novel robust concept factorization-based clustering model is proposed. • A fast algorithm is proposed to optimize the non-convex model. • Numerous experiments validate its clustering effectiveness and robustness. [ABSTRACT FROM AUTHOR]

Owing to its ability to handle negative data and promising clustering performance, concept factorization (CF), an improved version of non-negative matrix factorization, has been incorporated into multi-view clustering recently. Nevertheless, existing CF-based multi-view clustering methods still have the following issues: (1) they directly conduct factorization in the original data space, which means its efficiency is sensitive to the feature dimension; (2) they ignore the high degree of factorization freedom of standard CF, which may lead to non-uniqueness factorization thereby causing reduced effectiveness; (3) traditional robust norms they used are unable to handle complex noises, significantly challenging their robustness. To address these issues, we establish a fast multi-view clustering via correntropy-based orthogonal concept factorization (FMVCCF). Specifically, FMVCCF executes factorization on a learned consensus anchor graph rather than directly decomposing the original data, lessening the dimensionality sensitivity. Then, a lightweight graph regularization term is incorporated to refine the factorization process with a low computational burden. Moreover, an improved multi-view correntropy-based orthogonal CF model is developed, which can enhance the effectiveness and robustness under the orthogonal constraint and correntropy criterion, respectively. Extensive experiments demonstrate that FMVCCF can achieve promising effectiveness and robustness on various real-world datasets with high efficiency. [ABSTRACT FROM AUTHOR]

Background noise and scale variation are common problems that have been long recognized in crowd counting. Humans glance at a crowd image and instantly know the approximate number of human and where they are through attention the crowd regions and the congestion degree of crowd regions with a global receptive field. Hence, in this paper, we propose a novel feedback network with Region-Aware block called RANet by modeling human's Top-Down visual perception mechanism. Firstly, we introduce a feedback architecture to generate priority maps that provide prior about candidate crowd regions in input images. The prior enables the RANet pay more attention to crowd regions. Then we design Region-Aware block that could adaptively encode the contextual information into input images through global receptive field. More specifically, we scan the whole input images and its priority maps in the form of column vector to obtain a relevance matrix estimating their similarity. The relevance matrix obtained would be utilized to build global relationships between pixels. Our method outperforms state-of-the-art crowd counting methods on several public datasets. [ABSTRACT FROM AUTHOR]

Accurate cluster photovoltaic power prediction (CPPP) is crucial for the operation and control of renewable energy grid-connected power systems. The traditional modeling strategies for CPPP such as direct aggregation (DA) and statistical upscaling (SU) have limitations such as error accumulation and upscaling factor uncertainty. To address these issues, this paper proposed a novel hybrid approach for CPPP by combining machine learning models with an improved SU technique. Firstly, a robust broad learning system (BLS) model, in which the Generalized Maximum Correntropy Criterion (GMCC) is used to replace the original mean square error (MSE) loss in BLS, is proposed to solve the problem of multiple outliers affecting the prediction accuracy of regional cluster stations, and it is called GBLS. Then, the Relevance Vector Machine (RVM) as an effective nonlinear regression model is further utilized to compensate for the prediction errors obtained by the GBLS to form the hybrid prediction model, namely GBLS-RVM. Moreover, to mitigate the uncertainty associated with scaling factors in traditional SU strategy, a new SU strategy is developed to refine the relationship between the reference station and the cluster sub-region, enabling direct modeling for regional power prediction. Finally, data from two PV clusters in different regions of China are used to validate the effectiveness of the proposed model, and the results show that under the improved SU strategy, the GBLS-RVM model, reduced RMSE by approximately 33.7% compared to the traditional BLS model, and the RMSE decreased by 12.89% and 30.2% when compared to traditional DA and traditional SU strategies. • A novel hybrid method for CPPP is developed by combining ML and improved SU technique. • A BLS with GMCC (GMCC-BLS) as a prediction model is developed to handle the outliers in measurement data. • An innovative error correction strategy based on RVM is proposed to improve prediction reliability. • A new SU technique is used to establish direct relationships between reference stations and subregions. [ABSTRACT FROM AUTHOR]

Randomized autoencoder (RAE) has attracted much attention due to its strong capability of representation with fast learning speed. However, the mainstream RAEs are still designed for scalar/vector data, which inevitably destroys the structure information of tensor data. To alleviate this deficiency, a novel convolutions based matrix randomized autoencoder (MRAE) is developed for two-dimensional (2D) data in this paper, including a one-side MRAE (OMRAE) exploiting the row or column information and a double-side MRAE (DMRAE) that simultaneously extracts the row and column information by 2 parallel OMRAEs. To reduce meaningless encoded features, the within-class scatter matrix (WSI) and within-class interaction distance (WID) constraints are added into OMRAE resulting WSI-OMRAE and WID-OMRAE, respectively. To demonstrate the superiority, stacked MRAEs are embedded into hierarchical regularized least squares for one-class classification and comparisons with several state-of-the-art methods are provided. The source code would be available at https://github.com/ML-HDU/MRAE. • MRAE can learn from 2D data directly without breaking structure information. • WSI-OMRAE minimizes both reconstruction error and within-class scatter. • WID-OMRAE can learn intrinsic manifold structure with compact representation. • Adopting two-sides OMRAEs can perform row/column feature learning in parallel. [ABSTRACT FROM AUTHOR]

Accurate estimation of the state of health (SOH) is crucial for the safe and stable operation of lithium-ion batteries. However, since the labeled values may contain non-Gaussian noise which may lead to a decrease in the effectiveness of traditional data-driven based estimation methods. Therefore, a novel robust stacking integrated learning model (ILM) is proposed to enable accurate SOH estimation under non-Gaussian noises (or outliers) conditions. The mixture correntropy loss (MCL) is used in original extreme learning machine (ELM) and the gated recurrent unit (GRU) frameworks to develop novel robust learning models, i.e MCL-ELM and MCL-GRU, and they are used as the sub-models of the proposed ILM, which takes into account the generalization performance of the model and the overall trend of SOH over the time series. In addition, the entropy weighting method that can well reflect the differences between the sub-models is utilized to reduce the complexity of the stacked ILM. Furthermore, the local tangent space alignment is used to capture the local relationships between different loops to enhance the effectiveness of the extracted health features. Several numerical experiments are performed under different cases to validate the estimation effect of the proposed model by using two publicly available datasets, and the experimental results demonstrate that the maximum RMSE, MAE, and MAPE values of the proposed model are 1.391%, 0.932%, and 1.480%, respectively, under non-Gaussian noises conditions. • Robust ELM and GRU models using MCL are developed. • Novel robust stacking ILM via the combination of the MCL-ELM and MCL-GRU is proposed for SOH estimation. • The EWM is used to obtain the output results of multiple base learners in the proposed ILM. [ABSTRACT FROM AUTHOR]

• A novel spatial attention encoder is proposed, which builds global feature insight with long-range dependence to enhance perception. • We propose a context block decoder to aggregate contextual information as channel-specific bias of the features. • A feature fusion module with parallel branches considering expectation and residual property is proposed to realize adaptive information fusion. • We build an ESD dataset with 89.70% small defects collected from real industry an evaluation benchmark. Despite the promising development of Automatic Visual Inspection (AVI) in the manufacturing industry, detecting small-sized defects with fewer pixels coverage remains a challenging problem due to its insufficient attention and lack of semantic information. Most exsiting convolutional inspection methods overlook the long-range dependence of context and lack adaptive fusion strategies to exploit heterogeneous features. To address these issues in AVI, this paper proposes a novel contextual information and spatial attention based network (CANet), which consists of two steps, namely CAblock and LaplacianFPN, for effective perception and exploitation of small defect features. Specifically, CAblock extracts semantic information with rich context by encoding spatial long-range dependence and decoding contextual information as channel-specific bias through a Spatial Attention Encoder (SAE) and a Context Block Decoder (CBD), respectively. LaplacianFPN further performs adaptive feature fusion considering both feature consistency and heterogeneity via two parallel branches. As a benchmark, a self-built Engine Surface Defects (ESD) dataset collected in real industry containing 89.70% small defects is constructed. Experimental results show that CANet achieves mAP-50 improvements of 1.5% and 4.3% compared to state-of-the-art methods on NEU-DET and ESD, which demonstrates the effectiveness of the proposed method. The code is now available at https://github.com/xiuqhou/CANet. [ABSTRACT FROM AUTHOR]

• The UKF with EKRSL is developed by using the fixed-point iteration; • An enhanced EKRSL-UKF is proposed via an exponential function of innovation; • The proposed EnEKRSL-UKF is used for robust DSE. The traditional unscented Kalman filter (UKF) with mean square error (MSE) criterion for dynamic state estimation (DSE) is sensitive for unknown non-Gaussian noise and outliers. Leading to biased state estimates. This paper proposes a novel robust UKF with extended kernel risk-sensitive loss (EKRSL) for DSE considering unknown non-Gaussian process and measurement noises. Instead of MSE criterion, a novel robust EKRSL via the generalized Gaussian density is defined in KRSL framework, and we further develop a new robust UKF using the EnKRSL(called EKRSL-UKF). To obtain the recursive form of EKRSL-UKF, the statistical linear regression model is used and the fixed-point iteration is further utilized to iteratively get the optimal state estimate. An error constrained method is also introduced to restrict the error to address the numerical instability problem caused by large outliers. Furthermore, an enhanced EKRSL-UKF is established by using an exponential function of innovation to improve the estimation accuracy in the presence of noise uncertainties. Numerical results carried out on the IEEE 39-bus test system demonstrate that the proposed method can achieve desired robustness without loss of estimation accuracy under various conditions. [ABSTRACT FROM AUTHOR]

• A novel hypergraph based semi-supervised SNMF method is proposed for image clustering. • A new hypergraph based pairwise constraints propagation algorithm is presented. • The proposed method is analysed in terms of convergence, supervisory information, and computational complexity. • Extensive experiments confirm the effectiveness of the proposed method in clustering applications. Semi-supervised symmetric nonnegative matrix factorization (SNMF) has been shown to be a significant method for both linear and nonlinear data clustering applications. Nevertheless, existing SNMF-based methods only adopt a simple graph to construct the similarity matrix, and cannot fully use the limited supervised information for the construction of the similarity matrix. To overcome the drawbacks of previous SNMF-based methods, a new semi-supervised SNMF-based method called hypergraph based semi-supervised SNMF (HSSNMF), is proposed in this paper for image clustering. Specifically, HSSNMF adopts a predefined hypergraph to build a similarity matrix for capturing the high-order relationships of samples. By exploiting a new hypergraph based pairwise constraints propagation (HPCP) algorithm, HSSNMF propagates the pairwise constraints of the limited data points to the entire data points, which can make full use of the limited supervised information and construct a more informative similarity matrix. Using the multiplicative updating algorithm, a discriminative assignment matrix can then be obtained by solving the optimization problem of HSSNMF. Moreover, analyses of the convergence, supervisory information, and computational complexity of HSSNMF are presented. Finally, extensive clustering experiments have been conducted on six real-world image datasets, and the experimental results have demonstrated the superiority of HSSNMF while compared with several state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Kalman filters (KFs) are widely used for state-of-charge (SOC) estimation of Li-ion batteries due to their excellent dynamic tracking capability. Especially the cubature KF (CKF), with the computational efficiency and nonlinear processing ability, is an outstanding candidate for SOC estimation. However, the actual working conditions are complex and changeable, and the measurement data is usually accompanied by non-Gaussian noise (outliers). Therefore, the performance of the original CKF with minimum mean square error (MMSE) criterion may be degraded seriously in these cases. In order to enhance the robustness of CKF, the MMSE in the CKF framework is substituted by the generalized maximum correntropy criterion (GMCC), and thus a robust CKF with GMCC (GMCC-CKF) is developed by fixed point iteration approach in this work. Furthermore, a SOC estimation model via the GMCC-CKF is proposed to improve estimation accuracy under non-Gaussian noise environments. The simulation results show that, compared with the traditional KFs, the proposed GMCC-CKF can accurately estimate the SOC of lithium batteries under different temperatures and operating conditions considering non-Gaussian noise interference. The results of mean absolute error (MAE) and root mean square error (RMSE) are less than 1%, which verifies the excellent performance of GMCC-CKF. • GMCC is introduced into the CKF framework to develop a novel robust CKF. • The proposed GMCC-CKF method is applied for robust SOC estimation under non-Gaussian noise interferences. • Some simulations under different conditions are performed to evaluate the performance of the proposed method. [ABSTRACT FROM AUTHOR]