Department of Foundational Mathematics

Department of Fundamental Maths
Mathematics Building, Block B
Xi'an Jiaotong-Liverpool University
111 Ren'ai Road Suzhou Dushu Lake Science and Education Innovation District , Suzhou Industrial Park
Suzhou,Jiangsu Province,P. R. China,215123

1. Dual algorithm for truncated fractional variation based image denoising

Author:Liang, HX;Zhang, JL


Abstract:Fractional-order derivative is attracting more and more attention of researchers in image processing because of its better property in restoring more texture than the total variation. To improve the performance of fractional-order variation model in image restoration, a truncated fractional-order variation model was proposed in Chan and Liang [Truncated fractional-order variation model for image restoration, J. Oper. Res. Soc. China]. In this paper, we propose a dual approach to solve this truncated fractional-order variation model on noise removal. The proposed algorithm is based on the dual approach proposed by Chambolle [An algorithm for total variation minimisation and applications, J. Math Imaging Vis. 20 (2004), pp. 89-97]. Conversely, the Chambolle's dual approach can be treated as a special case of the proposed algorithm with fractional order . The work of this paper modifies the result in Zhang et al. [Adaptive fractional-order multi-scale method for image denoising, J. Math. Imaging Vis. 43(1) (2012), pp. 39-49. Springer Netherlands 0924-9907, Computer Science, pp. 1-11, 2011], where the convergence is not analysed. Based on the truncation, the convergence of the proposed dual method can be analysed and the convergence criteria can be provided. In addition, the accuracy of the reconstruction is improved after the truncation is taken.
2. A multi-objective optimization model for bike-sharing    

Author:Shan, Yu ; Xie, Dejun ; Zhang, Rui

Source:ACM International Conference Proceeding Series,2019,Vol.

Abstract:The study proposes a multi-objective optimization model for bike-sharing industry by monitoring, with high accuracy, the user demand and providing the suitable number of bikes at selected stations. One of the key factors for designing an optimized bike sharing system is to balance the demand of pick-ups (drop-offs) around a given station and the number of available bikes (vacant lockers) in the station throughout the day. The model optimizes the location of bicycle stations and the number of parking slots that each station should have by taking account of the main contributing factors including the total budget of the bike sharing system, the popularity of riding in the city, and the expected proximity of the stations. A case study using the bike-sharing in New York was conducted to test theeffectiveness of themodel. © 2019 Association for Computing Machinery.
3. Chebyshev tau meshless method based on the highest derivative for fourth order equations

Author:Shao, WT;Wu, XH


Abstract:It is well known that the numerical integration process is much less sensitive than numerical differential process when dealing with the differential equations. After integration, accuracy is no longer limited by that of the slowly convergent series for the highest derivative, but only by that of the unknown function itself. In this paper, a Chebyshev tau meshless method based on the highest derivative (CTMMHD) is developed for fourth order equations on irregularly shaped domains with complex boundary conditions. The problem domain is embedded in a domain of regular shape. The integration and multiplication of Chebyshev expansions are given in matrix representations. Several numerical experiments including standard biharmonic problems, problems with variable coefficients and nonlinear problems are implemented to verify the high accuracy and efficiency of our method. (C) 2012 Elsevier Inc. All rights reserved.
4. SimpleGAN Stabilizing generative adversarial networks with simple distributions

Author:Zhang, Shufei ; Qian, Zhuang ; Huang, Kaizhu ; Zhang, Rui ; Hussain, Amir

Source:IEEE International Conference on Data Mining Workshops, ICDMW,2019,Vol.2019-November

Abstract:Generative Adversarial Networks (GANs) are powerful generative models, but usually suffer from hard training and poor generation. Due to complex data and generation distributions in high dimensional space, it is difficult to measure the departure of two distributions, which is however vital for training successful GANs. Previous methods try to alleviate this problem by choosing reasonable divergence metrics. Unlike previous methods, in this paper, we propose a novel method called SimpleGAN to tackle this problem transform original complex distributions to simple ones in the low dimensional space while keeping information and then measure the departure of two simple distributions. This novel method offers a new direction to tackle the stability of GANs. Specifically, starting from maximization of the mutual information between variables in the original high dimensional space and low dimensional space, we eventually derive to optimize a much simplified version, i.e. the lower bound of the mutual information. For experiments, we implement our proposed method on different baselines i.e. traditional GAN, WGAN-GP and DCGAN for CIFAR-10 dataset. Our proposed method achieves obvious improvement over these baseline models. © 2019 IEEE.
5. Offline Arabic Handwriting Recognition Using Deep Machine Learning: A Review of Recent Advances

Author:Ahmed, R;Dashtipour, K;Gogate, M;Raza, A;Zhang, R;Huang, KZ;Hawalah, A;Adeel, A;Hussain, A


Abstract:In pattern recognition, automatic handwriting recognition (AHWR) is an area of research that has developed rapidly in the last few years. It can play a significant role in broad-spectrum of applications rending from, bank cheque processing, application forms processing, postal address processing, to text-to-speech conversion. However, most research efforts are devoted to English-language only. This work focuses on developing Offline Arabic Handwriting Recognition (OAHR). The OAHR is a very challenging task due to some unique characteristics of the Arabic script such as cursive nature, ligatures, overlapping, and diacritical marks. In the recent literature, several effective Deep Learning (DL) approaches have been proposed to develop efficient AHWR systems. In this paper, we commission a survey on emerging AHWR technologies with some insight on OAHR background, challenges, opportunities, and future research trends.
6. Recursive least squares estimation methods for a class of nonlinear systems based on non-uniform sampling

Author:Liu, QL;Chen, FY;Ding, F;Alsaedi, A;Hayat, T


Abstract:Many dynamic processes in practice have nonlinear characteristics and must be described by using nonlinear models. It remains to be a challenging problem to build the models of such nonlinear systems and to estimate their parameters. This article studies the parameter estimation problem for a class of Hammerstein-Wiener nonlinear systems based on non-uniform sampling. By means of the auxiliary model identification idea, an auxiliary model-based recursive least squares algorithm is derived for the systems. In order to enhance the computational efficiency, an auxiliary model-based hierarchical least squares algorithm is proposed by utilizing the hierarchical identification principle. The simulation results confirm the effectiveness of the proposed algorithms.
7. Two-layer Mixture of Factor Analyzers with Joint Factor Loading

Author:Yang, X;Huang, KZ;Zhang, R;Goulermas, JY


Abstract:Dimensionality Reduction (DR) is a fundamental yet active research topic in pattern recognition and machine learning. When used in classification, previous research usually performs DR separately, and then inputs the reduced features to other available models, e.g., Gaussian Mixture Model (GMM). Such independent learning could however significantly limit the classification performance, since the optimal subspace given by a particular DR approach may not be appropriate for the following classification model. More seriously, for high-dimensional data classification in the face of a limited number of samples (called small sample size or S3 problem), independent learning of DR and classification model may even deteriorate the classification accuracy. To solve this problem, we propose a joint learning model, called Two-layer Mixture of Factor Analyzers with Joint Factor Loading (2L-MJFA) for classification. More specifically, our proposed model enjoys a two-layer mixture structure, or a mixture of mixtures structure, with each component (representing each specific class) as another mixture model of Factor Analyzer (MFA). Importantly, all the involved factor analyzers are intentionally designed to share the same loading matrix. On one hand, such joint loading matrix can be considered as the dimensionality reduction matrix; on the other hand, a joint common matrix would largely reduce the parameters, making the proposed algorithm very suitable for S3 problems. We describe our model definition and propose a modified EM algorithm to optimize the model. A series of experiments demonstrates that our proposed model significantly outperforms the other three competitive algorithms on five data sets.
8. Inductive Generalized Zero-Shot Learning with Adversarial Relation Network

Author:Yang, GY;Huang, KZ;Zhang, R;Goulermas, JY;Hussain, A


Abstract:We consider the inductive Generalized Zero Shot Learning (GZSL) problem where test information is assumed unavailable during training. In lack of training samples and attributes for unseen classes, most existing GZSL methods tend to classify target samples as seen classes. To alleviate such problem, we design an adversarial Relation Network that favors target samples towards unseen classes while enjoying robust recognition for seen classes. Specifically, through the adversarial framework, we can attain a robust recognizer where a small gradient adjustment to the instance will not affect too much the classification of seen classes but substantially increase the classification accuracy on unseen classes. We conduct a series of experiments extensively on four benchmarks i.e., AwA1, AwA2, aPY, and CUB. Experimental results show that our proposed method can attain encouraging performance, which is higher than the best of state-of-the-art models by 10.8%%, 14.0%%, 6.9%%, and 1.9%% on the four benchmark datasets, respectively in the inductive GZSL scenario. (The code is available on
9. Fourier cosine differential quadrature method for beam and plate problems


Source:Applied Mechanics and Materials,2012,Vol.138-139

Abstract:In this paper, we combined the Fourier cosine series and differential quadrature method (DQM) in barycentric form to develop a new method (FCDQM), which is applied to the 1D fourth order beam problem and the 2D thin isotropic plate problems. Furthermore, we solved the complex boundary conditions on irregular domains with DQM directly. The numerical results illustrate the stability, validity and good accuracy of the method in treating this class of engineering problems.
10. Natural boundary integral method for irregular plate problems


Source:Applied Mechanics and Materials,2012,Vol.138-139

Abstract:Natural boundary integral method is applied to deal with plate problems defined in irregular domains. We divide the solution into two parts, a particular solution for inhomogeneous biharmonic equation and the general solution for homogeneous biharmonic equation. For the former, the direct expansion method of boundary conditions is used to treat the arbitrary domains, and the processes of natural boundary integral method coupling with finite element method are omitted. Numerical experiments show that the method is very simple and of high accuracy.
11. Filtering-Based Parameter Identification Methods for Multivariable Stochastic Systems

Author:Xia, HF;Chen, FY


Abstract:This paper presents an adaptive filtering-based maximum likelihood multi-innovation extended stochastic gradient algorithm to identify multivariable equation-error systems with colored noises. The data filtering and model decomposition techniques are used to simplify the structure of the considered system, in which a predefined filter is utilized to filter the observed data, and the multivariable system is turned into several subsystems whose parameters appear in the vectors. By introducing the multi-innovation identification theory to the stochastic gradient method, this study produces improved performances. The simulation numerical results indicate that the proposed algorithm can generate more accurate parameter estimates than the filtering-based maximum likelihood recursive extended stochastic gradient algorithm.
12. Improve Deep Learning with Unsupervised Objective

Author:Zhang, SF;Huang, KZ;Zhang, R;Hussain, A


Abstract:We propose a novel approach capable of embedding the unsupervised objective into hidden layers of the deep neural network (DNN) for preserving important unsupervised information. To this end, we exploit a very simple yet effective unsupervised method, i.e. principal component analysis (PCA), to generate the unsupervised "label" for the latent layers of DNN. Each latent layer of DNN can then be supervised not just by the class label, but also by the unsupervised "label" so that the intrinsic structure information of data can be learned and embedded. Compared with traditional methods which combine supervised and unsupervised learning, our proposed model avoids the needs for layer-wise pre-training and complicated model learning e.g. in deep autoencoder. We show that the resulting model achieves state-of-the-art performance in both face and handwriting data simply with learning of unsupervised "labels".
13. Boundary reduction technique and rational Sinc domain decomposition method

Author:Du, LL;Wu, XH;Kong, WB


Abstract:Sine method is widely used for solving the boundary value problems because of the ease with which it may handle the presence of singularities or unbounded domains. In this paper, the domain decomposition method is used to deal with problems with interior layers and problems posed on irregular domains. With boundary reduction technique, the functional values on internal points can be eliminated. The scheme is based on a direct approach based on the corresponding compatibility matching conditions between sub-domains. Numerical experiments show that rational Sine domain decomposition method based on the interpolation of the highest derivatives (RSIHD-DDM) is effective for treating problems with interior layers or boundary layers on irregular domains. (C) 2012 Elsevier Ltd. All rights reserved.
14. Improving Disentanglement-Based Image-to-Image Translation with Feature Joint Block Fusion

Author:Zhang, ZJ;Zhang, R;Wang, QF;Huang, KZ


Abstract:Image-to-image translation aims to change attributes or domains of images, where the feature disentanglement based method is widely used recently due to its feasibility and effectiveness. In this method, a feature extractor is usually integrated in the encoder-decoder architecture generative adversarial network (GAN), which extracts features from domains and images, respectively. However, the two types of features are not properly combined, resulting in blurry generated images and indistinguishable translated domains. To alleviate this issue, we propose a new feature fusion approach to leverage the ability of the feature disentanglement. Instead of adding the two extracted features directly, we design a joint block fusion that contains integration, concatenation, and squeeze operations, thus allowing the generator to take full advantage of the two features and generate more photo-realistic images. We evaluate both the classification accuracy and Frechet Inception Distance (FID) of the proposed method on two benchmark datasets of Alps Seasons and CelebA. Extensive experimental results demonstrate that the proposed joint block fusion can improve both the discriminability of domains and the quality of translated image. Specially, the classification accuracies are improved by 1.04%% (FID reduced by 1.22) and 1.87%% (FID reduced by 4.96) on Alps Seasons and CelebA, respectively.
15. Rational Sinc method based on interpolation of highest derivatives


Source:Communication on Applied Mathematics and Computation,2011,Vol.25

Abstract:A rational Sine method based on the interpolation of the highest derivatives (RSIHD) is discussed in this paper to deal with interior layer problems and problems defined in irregular domains.A new formula is derived which is named the rational Sinc-barycentric interpolation to solve some problems with mixed nonhomogeneous boundary conditions and problems on irregular domains.Furthermore, a new transformation is applied in the RSIHD.Using this transformation,the RSIHD can deal with problems with an interior layer efficiently.Some numerical examples are given to verify the new method.
16. An effective Chebyshev tau meshless domain decomposition method based on the integration-differentiation for solving fourth order equations

Author:Shao, WT;Wu, XH


Abstract:In this paper, we present a method, which combines the Chebyshev tau meshless method based on the integration-differentiation (CTMMID) with Domain Decomposition Method (DDM), and apply it to solve the fourth order problem on irregular domains. This method, i.e. CTMMID-DDM, is an improvement of our previous job. In early work, it shows that the CTMMID can solve the fourth order problems well in square domain, and leads to the condition number which grows like O(N-4), but it becomes worse when we apply it on irregular domains directly. DDMs extend the applicability of spectral methods to handle complex geometries and large-scale problems. Numerical results show that CTMMID-DDM works well, it circumvents the ill-conditioning problem, further attains a improvement in solution accuracy, and also makes us feasible to solve the problems with boundary layers. (C) 2014 Elsevier Inc. All rights reserved.
17. Multi-view visual surveillance and phantom removal for effective pedestrian detection

Author:Ren, J;Xu, M;Smith, JS;Zhao, HM;Zhang, R


Abstract:To increase the robustness of detection in intelligent video surveillance systems, homography has been widely used to fuse foreground regions projected from multiple camera views to a reference view. However, the intersections of non-corresponding foreground regions can cause phantoms. This paper proposes an algorithm based on geometry and colour cues to cope with this problem, in which the homography between different camera views and the Mahalanobis distance between the colour distributions of every two associated foreground regions are considered. The integration of these two matching algorithms improves the robustness of the pedestrian and phantom classification. Experiments on real-world video sequences have shown the robustness of this algorithm.
18. Special Issue Editorial: Cognitively-Inspired Computing for Knowledge Discovery

Author:Huang, KZ;Zhang, R;Jin, XB;Hussain, A


19. Statistical inference for dependent stress-strength reliability of multi-state system using generalized survival signature

Author:Bai, XC;Li, XR;Balakrishnan, N;He, M


Abstract:In reliability analysis of the stress-strength models, it is generally assumed that an individual only has one type of strength. However, in some situation, an individual, which has several types of independent or dependent strengths, is subjected several types of independent stresses in the working environment. Hence, we define a new multi-state stress-strength model for multi-state system consisting of n multi-state components with several types of strengths. In this paper, we discuss inferential procedures for stress-strength reliability of such multi-state system using generalized survival signature in two cases, viz., independent strengths and dependent strengths. Based on the assumption that the strengths and stresses variables follow exponential distributions, the exact expressions for stress-strength reliability of system in different states are derived in case of independent strengths. When the strengths are dependent, we utilize the Gumbel copula to depict the dependence structure of strengths. Additionally, two semiparametric methods, viz., method-of-moment and maximum pseudo-likelihood estimation, are used to estimate the dependence parameter. Then, maximum likelihood estimation, asymptotic confidence interval estimation and bootstrap percentile confidence interval estimation based on the aforementioned two semiparametric methods for the dependence parameter are provided, separately, to estimate the stress-strength reliability of system in different states. Monte Carlo simulations are performed to compare the performances of the proposed estimation methods. Finally, a real data analysis is provided to illustrate the proposed procedures. (C) 2021 Elsevier B.V. All rights reserved.
20. Self-training field pattern prediction based on kernel methods

Author:Jiang,Haochuan;Huang,Kaizhu;Zhang,Xu Yao;Zhang,Rui

Source:Semi-Supervised Learning: Background, Applications and Future Directions,2018,Vol.

Abstract:Conventional predictors often regard input samples as identically and independently distributed (i.i.d.). Such an assumption does not always hold in many real scenarios, especially when patterns occur as groups, where each group shares a homogeneous style. These tasks are named as the field prediction, which can be divided into the field classification and the field regression. Traditional i.i.d.-based machine learning models would always face degraded performance. By breaking the i.i.d. assump- tion, one novel framework called Field SupportVector Machine (F-SVM) with both classification (F-SVC) and regression (F-SVR) purposes is in- troduced in this chapter. To be specific, the proposed F-SVM predictor is investigated by learning simultaneously both the predictor and the Style Normalization Transformation (SNT) for each group of data (called field). Such joint learning is proved to be even feasible in the high-dimensional kernel space. An efficient alternative optimization algorithm is further designed with the final convergence guaranteed theoretically and experimentally. More importantly, a self-training based kernelized algorithm is also developed to incorporate the F-SVM model with the unknown field during the training phase by learning the transductive SNT to transfer the trained field information to this unknown style data. A series of experiments are conducted to verify the effectiveness of the F-SVM model with both classification and regression tasks by promoting the classification accuracy and declining regression error. Empirical results demonstrate that the proposed F-SVM achieves in several benchmark datasets the best performance so far, significantly better than those state-of-the-art predictors.
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