Table of Content

30 November 2019, Volume 7 Issue 4

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Preface: Special Issue on Optimization Models and Algorithms in Artificial Intelligence

Ya-Xin Peng, Shao-Yi Du, Tie-Yong Zeng

2019, 7(4):  511-513.  doi:10.1007/s40305-019-00278-5

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Layer-Wise Pre-Training Low-Rank NMF Model for Mammogram-Based Breast Tumor Classification

Wen-Ming Wu, Xiao-Hui Yang, Yun-Mei Chen, Juan Zhang, Dan Long, Li-Jun Yang, Chen-Xi Tian

2019, 7(4):  515-537.  doi:10.1007/s40305-019-00262-z

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Image-based breast tumor classification is an active and challenging problem. In this paper, a robust breast tumor classification framework is presented based on deep feature representation learning and exploiting available information in existing samples. Feature representation learning of mammograms is fulfilled by a modified nonnegative matrix factorization model called LPML-LRNMF, which is motivated by hierarchical learning and layer-wise pre-training (LP) strategy in deep learning. Low-rank (LR) constraint is integrated into the feature representation learning model by considering the intrinsic characteristics of mammograms. Moreover, the proposed LPML-LRNMF model is optimized via alternating direction method of multipliers and the corresponding convergence is analyzed. For completing classification, an inverse projection sparse representation model is introduced to exploit information embedded in existing samples, especially in test ones. Experiments on the public dataset and actual clinical dataset show that the classification accuracy, specificity and sensitivity achieve the clinical acceptance level.

Quadratic Kernel-Free Least Square Twin Support Vector Machine for Binary Classification Problems

Qian-Qian Gao, Yan-Qin Bai, Ya-Ru Zhan

2019, 7(4):  539-559.  doi:10.1007/s40305-018-00239-4

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In this paper, a new quadratic kernel-free least square twin support vector machine (QLSTSVM) is proposed for binary classification problems. The advantage of QLSTSVM is that there is no need to select the kernel function and related parameters for nonlinear classification problems. After using consensus technique, we adopt alternating direction method of multipliers to solve the reformulated consensus QLSTSVM directly. To reduce CPU time, the Karush-Kuhn-Tucker (KKT) conditions is also used to solve the QLSTSVM. The performance of QLSTSVM is tested on two artificial datasets andseveral Universityof CaliforniaIrvine(UCI) benchmarkdatasets. Numerical results indicate that the QLSTSVM may outperform several existing methods for solving twin support vector machine with Gaussian kernel in terms of the classification accuracy and operation time.

Truncated Fractional-Order Total Variation Model for Image Restoration

Raymond Honfu Chan, Hai-Xia Liang

2019, 7(4):  561-578.  doi:10.1007/s40305-019-00250-3

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Fractional-order derivative is attracting more and more interest from researchers working on image processing because it helps to preserve more texture than total variation when noise is removed. In the existing works, the Grunwald-Letnikov fractional-order derivative is usually used, where the Dirichlet homogeneous boundary condition can only be considered and therefore the full lower triangular Toeplitz matrix is generated as the discrete partial fractional-order derivative operator. In this paper, a modified truncation is considered in generating the discrete fractional-order partial derivative operator and a truncated fractional-order total variation (tFoTV) model is proposed for image restoration. Hopefully, first any boundary condition can be used in the numerical experiments. Second, the accuracy of the reconstructed images by the tFoTV model can be improved. The alternating directional method of multiplier is applied to solve the tFoTV model. Its convergence is also analyzed briefly. In the numerical experiments, we apply the tFoTV model to recover images that are corrupted by blur and noise. The numerical results show that the tFoTV model provides better reconstruction in peak signal-to-noise ratio (PSNR) than the full fractional-order variation and total variation models. From the numerical results, we can also see that the tFoTV model is comparable with the total generalized variation (TGV) model in accuracy. In addition, we can roughly fix a fractional order according to the structure of the image, and therefore, there is only one parameter left to determine in the tFoTV model, while there are always two parameters to be fixed in TGV model.

Generative Adversarial Networks with Joint Distribution Moment Matching

Yi-Ying Zhang, Chao-Min Shen, Hao Feng, Preston Thomas Fletcher, Gui-Xu Zhang

2019, 7(4):  579-597.  doi:10.1007/s40305-019-00248-x

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Generative adversarial networks (GANs) have shown impressive power in the field of machine learning. Traditional GANs have focused on unsupervised learning tasks. In recent years, conditional GANs that can generate data with labels have been proposed in semi-supervised learning and have achieved better image quality than traditional GANs. Conditional GANs, however, generally only minimize the difference between marginal distributions of real and generated data, neglecting the difference with respect to each class of the data. To address this challenge, we propose the GAN with joint dis tribution moment matching (JDMM-GAN) for matching the joint distribution based on maximum mean discrepancy, which minimizes the differences of both the marginal and conditional distributions. The learning procedure is iteratively conducted by the stochastic gradient descent and back-propagation. We evaluate JDMM-GAN on several benchmark datasets, including MNIST, CIFAR-10 and the Extended Yale Face. Compared with the state-of-the-art GANs, JDMM-GAN generates more realistic images and achieves the best inception score for CIFAR-10 dataset.

Longitudinal Image Analysis via Path Regression on the Image Manifold

Shi-Hui Ying, Xiao-Fang Zhang, Ya-Xin Peng, Ding-Gang Shen

2019, 7(4):  599-614.  doi:10.1007/s40305-019-00251-2

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Longitudinal image analysis plays an important role in depicting the development of the brain structure, where image regression and interpolation are two commonly used techniques. In this paper, we develop an efficient model and approach based on a path regression on the image manifold instead of the geodesic regression to avoid the complexity of the geodesic computation. Concretely, first we model the deformation by diffeomorphism; then, a large deformation is represented by a path on the orbit of the diffeomorphism group action. This path is obtained by compositing several small deformations, which can be well approximated by its linearization. Second, we introduce some intermediate images as constraints to the model, which guides to form the best-fitting path. Thirdly, we propose an approximated quadratic model by local linearization method, where a closed form is deduced for the solution. It actually speeds up the algorithm. Finally, we evaluate the proposed model and algorithm on a synthetic data and a real longitudinal MRI data. The results show that our proposed method outperforms several state-of-the-art methods.

Super-Edge-Connectivity and Zeroth-Order Randić Index

Zhi-Hong He, Mei Lu

2019, 7(4):  615-628.  doi:10.1007/s40305-018-0221-7

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Define the zeroth-order Randić index R⁰(G)=∑_x∈V(G) 1/√d_G (x), where d_G(x) denotes the degree of the vertex x. In this paper, we present two sufficient conditions for graphs and triangle-free graphs to be super-edge-connected in terms of the zeroth-order Randić index, respectively.

Evolution Model Based on Prior Information for Narrow Joint Segmentation

Xin Wang, Shuai Xu, Zhen Ye, Chao-Zheng Zhou, Jing Qin

2019, 7(4):  629-642.  doi:10.1007/s40305-019-00265-w

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Automated segmentation of hip joint computed tomography images is significantly important in the diagnosis and treatment of hip joint disease. In this paper, we propose an automatic hip joint segmentation method based on a variational model guided by prior information. In particular, we obtain prior features by automatic sample selection, get a discriminative function by training these selected samples and then integrate this prior information into our variational model. Numerical results demonstrate that the proposed method has high accuracy in segmenting narrow joint regions.

Existence of Weakly Cooperative Equilibria for Infinite-Leader-Infinite-Follower Games

Zhe Yang, Qing-Bin Gong

2019, 7(4):  643-654.  doi:10.1007/s40305-018-0236-0

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In this paper, we first generalize Yang and Ju's (J Glob Optim 65:563-573, 2016) result in Hausdorff topological vector spaces. Second, we introduce the model of leader-follower games with infinitely many leaders and followers, that is, infiniteleader-infinite-follower game. We next introduce the notion of weakly cooperative equilibria for infinite-leader-infinite-follower games and prove the existence result.