Convergence of Gradient Descent Algorithm for a Recurrent Neuron. - Dongpo Xu; Zhengxue Li; Wei Wu 010; Xiaoshuai Ding; Di Qu (ISNN (3), 2007)

Convergence Analysis of Three Classes of Split-Complex Gradient Algorithms for Complex-Valued Recurrent Neural Networks. - Dongpo Xu; Huisheng Zhang; Lijun Liu (Neural Comput., 2010)

Convergence of gradient method for a fully recurrent neural network. - Dongpo Xu; Zhengxue Li; Wei Wu 010 (Soft Comput., 2010)

Convergence of a Batch Gradient Algorithm with Adaptive Momentum for Neural Networks. - Hongmei Shao; Dongpo Xu; Gaofeng Zheng (Neural Process. Lett., 2011)

Convergence of an online gradient method with inner-product penalty and adaptive momentum. - Hongmei Shao; Dongpo Xu; Gaofeng Zheng; Lijun Liu (Neurocomputing, 2012)

A new adaptive momentum algorithm for split-complex recurrent neural networks. - Dongpo Xu; Hongmei Shao; Huisheng Zhang (Neurocomputing, 2012)

Convergence of Chaos Injection-Based Batch Backpropagation Algorithm For Feedforward Neural Networks. - Huisheng Zhang; Xiaodong Liu 001; Dongpo Xu (ISNN (1), 2013)

A Quaternion Least Mean Phase adaptive estimator. - Sayed Pouria Talebi; Dongpo Xu; Anthony Kuh; Danilo P. Mandic (ICASSP, 2014)

The HC calculus, quaternion derivatives and caylay-hamilton form of quaternion adaptive filters and learning systems. - Yili Xia; Cyrus Jahanchahi; Dongpo Xu; Danilo P. Mandic (IJCNN, 2014)

Finite convergence of the learning algorithms for a modified multi-valued neuron. - Dongpo Xu; Shuang Liang (IJCNN, 2014)

Quaternion Gradient and Hessian. - Dongpo Xu; Danilo P. Mandic (CoRR, 2014)

Boundedness and Convergence of Split-Complex Back-Propagation Algorithm with Momentum and Penalty. - Huisheng Zhang; Dongpo Xu; Ying Zhang 003 (Neural Process. Lett., 2014)

Relaxed conditions for convergence of batch BPAP for feedforward neural networks. - Hongmei Shao; Jian Wang 010; Lijun Liu; Dongpo Xu; Wendi Bao (Neurocomputing, 2015)

Convergence analysis of an augmented algorithm for fully complex-valued neural networks. - Dongpo Xu; Huisheng Zhang; Danilo P. Mandic (Neural Networks, 2015)

The Theory of Quaternion Matrix Derivatives. - Dongpo Xu; Danilo P. Mandic (IEEE Trans. Signal Process., 2015)

Optimization in Quaternion Dynamic Systems: Gradient, Hessian, and Learning Algorithms. - Dongpo Xu; Yili Xia; Danilo P. Mandic (IEEE Trans. Neural Networks Learn. Syst., 2016)

Deterministic Convergence of Wirtinger-Gradient Methods for Complex-Valued Neural Networks. - Dongpo Xu; Jian Dong; Huisheng Zhang (Neural Process. Lett., 2017)

Convergence of Quasi-Newton Method for Fully Complex-Valued Neural Networks. - Dongpo Xu; Jian Dong; Chengdong Zhang (Neural Process. Lett., 2017)

The augmented complex-valued extreme learning machine. - Huisheng Zhang; Yuanyuan Wang; Dongpo Xu; Jing Wang; Lihong Xu (Neurocomputing, 2018)

Deterministic convergence of complex mini-batch gradient learning algorithm for fully complex-valued neural networks. - Huisheng Zhang; Ying Zhang 003; Shuai Zhu; Dongpo Xu (Neurocomputing, 2020)

Decreasing scaling transition from adaptive gradient descent to stochastic gradient descent. - Kun Zeng; Jinlan Liu; Zhixia Jiang; Dongpo Xu (CoRR, 2021)

Scaling transition from momentum stochastic gradient descent to plain stochastic gradient descent. - Kun Zeng; Jinlan Liu; Zhixia Jiang; Dongpo Xu (CoRR, 2021)

Convergence of the RMSProp deep learning method with penalty for nonconvex optimization. - Dongpo Xu; Shengdong Zhang; Huisheng Zhang; Danilo P. Mandic (Neural Networks, 2021)

Predicting the Antigenic Relationship of Foot-and-Mouth Disease Virus for Vaccine Selection Through a Computational Model. - Jingxuan Qiu; Tianyi Qiu; Qingli Dong; Dongpo Xu; Xiang Wang; Qi Zhang; Jing Pan; Qing Liu (IEEE ACM Trans. Comput. Biol. Bioinform., 2021)

SGD-rα: A real-time α-suffix averaging method for SGD with biased gradient estimates. - Jianqi Luo; Jinlan Liu; Dongpo Xu; Huisheng Zhang (Neurocomputing, 2022)

Convergence analysis of AdaBound with relaxed bound functions for non-convex optimization. - Jinlan Liu; Jun Kong; Dongpo Xu; Miao Qi; Yinghua Lu (Neural Networks, 2022)

Target Detection Based on Improved Hausdorff Distance Matching Algorithm for Millimeter-Wave Radar and Video Fusion. - Dongpo Xu; Yunqing Liu; Qian Wang; Liang Wang; Renjun Liu (Sensors, 2022)

UAdam: Unified Adam-Type Algorithmic Framework for Non-Convex Stochastic Optimization. - Yiming Jiang 013; Jinlan Liu; Dongpo Xu; Danilo P. Mandic (CoRR, 2023)

The HR-Calculus: Enabling Information Processing with Quaternion Algebra. - Danilo P. Mandic; Sayed Pouria Talebi; Clive Cheong Took; Yili Xia; Dongpo Xu; Min Xiang; Pauline Bourigault (CoRR, 2023)

Quaternion Extreme Learning Machine Based on Real Augmented Representation. - Huisheng Zhang; Zaiqiang Wang; Dehao Chen; Shuai Zhu; Dongpo Xu (IEEE Signal Process. Lett., 2023)

Convex Quaternion Optimization for Signal Processing: Theory and Applications. - Shuning Sun; Qiankun Diao; Dongpo Xu; Pauline Bourigault; Danilo P. Mandic (IEEE Trans. Signal Process., 2023)

Last-iterate convergence analysis of stochastic momentum methods for neural networks. - Jinlan Liu; Dongpo Xu; Yinghua Lu; Jun Kong; Danilo P. Mandic (Neurocomputing, 2023)

Batch Gradient Training Method with Smoothing Group L0 Regularization for Feedfoward Neural Networks. - Ying Zhang 003; Jianing Wei; Dongpo Xu; Huisheng Zhang (Neural Process. Lett., 2023)

Stochastic momentum methods for non-convex learning without bounded assumptions. - Yuqing Liang; Jinlan Liu; Dongpo Xu (Neural Networks, 2023)

Performance bounds of complex-valued nonlinear estimators in learning systems. - Huisheng Zhang; Chunmei Qi; Qingqing Ma; Dongpo Xu (Neurocomputing, 2023)

Convergence analysis for sparse Pi-sigma neural network model with entropy error function. - Qinwei Fan; Fengjiao Zheng; Xiaodi Huang; Dongpo Xu (Int. J. Mach. Learn. Cybern., 2023)

Quaternion Recurrent Neural Network with Real-Time Recurrent Learning and Maximum Correntropy Criterion. - Pauline Bourigault; Dongpo Xu; Danilo P. Mandic (IJCNN, 2024)

PbsNRs: predict the potential binders and scaffolds for nuclear receptors. - Genhui Zheng; Dingfeng Wu; Xiuxia Wei; Dongpo Xu; Tiantian Mao; Deyu Yan; Wenhao Han; Xiaoxiao Shang; Zikun Chen; Jingxuan Qiu; Kailin Tang; Zhiwei Cao; et al. (Briefings Bioinform., 2024)

UAdam: Unified Adam-Type Algorithmic Framework for Nonconvex Optimization. - Yiming Jiang 013; Jinlan Liu; Dongpo Xu; Danilo P. Mandic (Neural Comput., 2024)

Decentralized stochastic sharpness-aware minimization algorithm. - Simiao Chen; Xiaoge Deng; Dongpo Xu; Tao Sun 005; Dongsheng Li 001 (Neural Networks, 2024)

Shuffling-type gradient method with bandwidth-based step sizes for finite-sum optimization. - Yuqing Liang; Yang Yang; Jinlan Liu; Dongpo Xu (Neural Networks, 2024)

A novel predefined-time neurodynamic approach for mixed variational inequality problems and applications. - Jinlan Zheng; Xingxing Ju; Naimin Zhang; Dongpo Xu (Neural Networks, 2024)

An Iterative Algorithm for Quaternion Eigenvalue Problems in Signal Processing. - Qiankun Diao; Jinlan Liu; Naimin Zhang; Dongpo Xu (IEEE Signal Process. Lett., 2024)

Price's Theorem for Quaternion Variables. - Qiankun Diao; Dongpo Xu; Shuning Sun; Danilo P. Mandic (IEEE Signal Process. Lett., 2024)

mPage: Probabilistic Gradient Estimator With Momentum for Non-Convex Optimization. - Yuqing Liang; Hui Su; Jinlan Liu; Dongpo Xu (IEEE Trans. Signal Process., 2024)

ABNGrad: adaptive step size gradient descent for optimizing neural networks. - Wenhan Jiang; Yuqing Liang; Zhixia Jiang; Dongpo Xu; Linhua Zhou (Appl. Intell., 2024)

Cross-Modal Supervised Human Body Pose Recognition Techniques for Through-Wall Radar. - Dongpo Xu; Yunqing Liu; Qian Wang; Liang Wang; Qiuping Shen (Sensors, 2024)

Almost sure convergence of stochastic composite objective mirror descent for non-convex non-smooth optimization. - Yuqing Liang; Dongpo Xu; Naimin Zhang; Danilo P. Mandic (Optim. Lett., 2024)

Convergence Analysis of Online Gradient Method for High-Order Neural Networks and Their Sparse Optimization. - Qinwei Fan; Qian Kang; Jacek M. Zurada; Tingwen Huang; Dongpo Xu (IEEE Trans. Neural Networks Learn. Syst., 2024)

A new algorithm for removing random motion noise of human body based on total variation. - Yunqing Liu; Jiaqi Shang; Wei Chu; Fei Yan; Dongpo Xu; Siyuan Wu; He Huang; Xin Chen (Biomed. Signal Process. Control., 2025)

An adaptive gradient method with transformation bound. - Wenhan Jiang; Kun Zeng; Zhixia Jiang; Dongpo Xu (Neurocomputing, 2025)

A neurodynamic approach with fixed-time convergence for complex-variable pseudo-monotone variational inequalities. - Jinlan Zheng; Xingxing Ju; Naimin Zhang; Dongpo Xu (Neurocomputing, 2025)

DMAdam: Dual averaging enhanced adaptive gradient method for deep neural networks. - Wenhan Jiang; Jinlan Liu; Naimin Zhang; Dongpo Xu (Knowl. Based Syst., 2025)

Sharpness-Aware Minimization method with momentum acceleration for deep neural networks. - Helei Kang; Yiming Jiang 013; Jinlan Liu; Dongpo Xu (Knowl. Based Syst., 2025)

AdaVAM: Adaptive variance-aware momentum for accelerating deep neural network training. - Jinlan Liu; Wenhan Jiang; Xin Deng; Dongpo Xu (Knowl. Based Syst., 2025)

Optimizing beamforming in quaternion signal processing using projected gradient descent algorithm. - Qiankun Diao; Dongpo Xu; Shuning Sun; Danilo P. Mandic (Signal Process., 2025)

On the Convergence of Decentralized Stochastic Gradient Descent With Biased Gradients. - Yiming Jiang 013; Helei Kang; Jinlan Liu; Dongpo Xu (IEEE Trans. Signal Process., 2025)

Cramér-Rao Lower Bounds for Unconstrained and Constrained Quaternion Parameters. - Shuning Sun; Dongpo Xu; Qiankun Diao; Danilo P. Mandic (IEEE Trans. Signal Process., 2025)

Convergence of Adam for non-convex objectives: relaxed hyperparameters and non-ergodic case. - Yuqing Liang; Meixuan He; Jinlan Liu; Dongpo Xu (Mach. Learn., 2025)

A robust stochastic quasi-Newton algorithm for non-convex machine learning. - Hanger Liu; Yuqing Liang; Jinlan Liu; Dongpo Xu (Appl. Intell., 2025)