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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]

Concept factorization (CF) has attracted widespread attention for its promising performance in document clustering. Among various CF variants, graph-regularized CF is the most impressive type, which can improve clustering effectiveness by exploring structural information. Nevertheless, their clustering efficiency is restricted by the following considerations: (1) the introduction of the full-sample graph is accompanied by an increase in computational complexity; (2) most of them require intensive multiplications in optimization, which impair the optimization efficiency. To address these issues, in this work, we propose an anchor-graph regularized orthogonal concept factorization (AROCF) method to enhance the clustering efficiency and effectiveness in document clustering tasks. Firstly, AROCF approximates the full-sample graph with a small-scale anchor graph to reduce the complexity of graph construction from quadratic to linear. Then, one of the factor matrices is constrained as the cluster indicator matrix in our method, which can avoid extra efficiency loss in K-means after optimization. Finally, an orthogonal constraint is employed to restrict the freedom of factorization to increase the clustering effectiveness. To optimize the AROCF model, we develop a fast optimization strategy by combining the trace and orthogonality of matrices. Extensive experiments on various document datasets demonstrate the effectiveness and efficiency of AROCF. [ABSTRACT FROM AUTHOR]