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Journal articles on the topic 'Graph regularization'

Author: Grafiati

Published: 4 June 2021

Last updated: 31 January 2023

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1

Yang, Han, Kaili Ma, and James Cheng. "Rethinking Graph Regularization for Graph Neural Networks." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 5 (May 18, 2021): 4573–81. http://dx.doi.org/10.1609/aaai.v35i5.16586.

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The graph Laplacian regularization term is usually used in semi-supervised representation learning to provide graph structure information for a model f(X). However, with the recent popularity of graph neural networks (GNNs), directly encoding graph structure A into a model, i.e., f(A, X), has become the more common approach. While we show that graph Laplacian regularization brings little-to-no benefit to existing GNNs, and propose a simple but non-trivial variant of graph Laplacian regularization, called Propagation-regularization (P-reg), to boost the performance of existing GNN models. We provide formal analyses to show that P-reg not only infuses extra information (that is not captured by the traditional graph Laplacian regularization) into GNNs, but also has the capacity equivalent to an infinite-depth graph convolutional network. We demonstrate that P-reg can effectively boost the performance of existing GNN models on both node-level and graph-level tasks across many different datasets.

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2

Dal Col, Alcebiades, and Fabiano Petronetto. "Graph regularization multidimensional projection." Pattern Recognition 129 (September 2022): 108690. http://dx.doi.org/10.1016/j.patcog.2022.108690.

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Chen, Binghui, Pengyu Li, Zhaoyi Yan, Biao Wang, and Lei Zhang. "Deep Metric Learning with Graph Consistency." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 2 (May 18, 2021): 982–90. http://dx.doi.org/10.1609/aaai.v35i2.16182.

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Deep Metric Learning (DML) has been more attractive and widely applied in many computer vision tasks, in which a discriminative embedding is requested such that the image features belonging to the same class are gathered together and the ones belonging to different classes are pushed apart. Most existing works insist to learn this discriminative embedding by either devising powerful pair-based loss functions or hard-sample mining strategies. However, in this paper, we start from an another perspective and propose Deep Consistent Graph Metric Learning (CGML) framework to enhance the discrimination of the learned embedding. It is mainly achieved by rethinking the conventional distance constraints as a graph regularization and then introducing a Graph Consistency regularization term, which intends to optimize the feature distribution from a global graph perspective. Inspired by the characteristic of our defined ’Discriminative Graph’, which regards DML from another novel perspective, the Graph Consistency regularization term encourages the sub-graphs randomly sampled from the training set to be consistent. We show that our CGML indeed serves as an efficient technique for learning towards discriminative embedding and is applicable to various popular metric objectives, e.g. Triplet, N-Pair and Binomial losses. This paper empirically and experimentally demonstrates the effectiveness of our graph regularization idea, achieving competitive results on the popular CUB, CARS, Stanford Online Products and In-Shop datasets.

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Huang, Xiayuan, Xiangli Nie, and Hong Qiao. "PolSAR Image Feature Extraction via Co-Regularized Graph Embedding." Remote Sensing 12, no. 11 (May 28, 2020): 1738. http://dx.doi.org/10.3390/rs12111738.

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Dimensionality reduction (DR) methods based on graph embedding are widely used for feature extraction. For these methods, the weighted graph plays a vital role in the process of DR because it can characterize the data’s structure information. Moreover, the similarity measurement is a crucial factor for constructing a weighted graph. Wishart distance of covariance matrices and Euclidean distance of polarimetric features are two important similarity measurements for polarimetric synthetic aperture radar (PolSAR) image classification. For obtaining a satisfactory PolSAR image classification performance, a co-regularized graph embedding (CRGE) method by combing the two distances is proposed for PolSAR image feature extraction in this paper. Firstly, two weighted graphs are constructed based on the two distances to represent the data’s local structure information. Specifically, the neighbouring samples are sought in a local patch to decrease computation cost and use spatial information. Next the DR model is constructed based on the two weighted graphs and co-regularization. The co-regularization aims to minimize the dissimilarity of low-dimensional features corresponding to two weighted graphs. We employ two types of co-regularization and the corresponding algorithms are proposed. Ultimately, the obtained low-dimensional features are used for PolSAR image classification. Experiments are implemented on three PolSAR datasets and results show that the co-regularized graph embedding can enhance the performance of PolSAR image classification.

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Liu, Fei, Sounak Chakraborty, Fan Li, Yan Liu, and Aurelie C. Lozano. "Bayesian Regularization via Graph Laplacian." Bayesian Analysis 9, no. 2 (June 2014): 449–74. http://dx.doi.org/10.1214/14-ba860.

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Bo, Deyu, Binbin Hu, Xiao Wang, Zhiqiang Zhang, Chuan Shi, and Jun Zhou. "Regularizing Graph Neural Networks via Consistency-Diversity Graph Augmentations." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 4 (June 28, 2022): 3913–21. http://dx.doi.org/10.1609/aaai.v36i4.20307.

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Despite the remarkable performance of graph neural networks (GNNs) in semi-supervised learning, it is criticized for not making full use of unlabeled data and suffering from over-fitting. Recently, graph data augmentation, used to improve both accuracy and generalization of GNNs, has received considerable attentions. However, one fundamental question is how to evaluate the quality of graph augmentations in principle? In this paper, we propose two metrics, Consistency and Diversity, from the aspects of augmentation correctness and generalization. Moreover, we discover that existing augmentations fall into a dilemma between these two metrics. Can we find a graph augmentation satisfying both consistency and diversity? A well-informed answer can help us understand the mechanism behind graph augmentation and improve the performance of GNNs. To tackle this challenge, we analyze two representative semi-supervised learning algorithms: label propagation (LP) and consistency regularization (CR). We find that LP utilizes the prior knowledge of graphs to improve consistency and CR adopts variable augmentations to promote diversity. Based on this discovery, we treat neighbors as augmentations to capture the prior knowledge embodying homophily assumption, which promises a high consistency of augmentations. To further promote diversity, we randomly replace the immediate neighbors of each node with its remote neighbors. After that, a neighbor-constrained regularization is proposed to enforce the predictions of the augmented neighbors to be consistent with each other. Extensive experiments on five real-world graphs validate the superiority of our method in improving the accuracy and generalization of GNNs.

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7

Le, Tuan M. V., and Hady W. Lauw. "Semantic Visualization with Neighborhood Graph Regularization." Journal of Artificial Intelligence Research 55 (April 28, 2016): 1091–133. http://dx.doi.org/10.1613/jair.4983.

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Visualization of high-dimensional data, such as text documents, is useful to map out the similarities among various data points. In the high-dimensional space, documents are commonly represented as bags of words, with dimensionality equal to the vocabulary size. Classical approaches to document visualization directly reduce this into visualizable two or three dimensions. Recent approaches consider an intermediate representation in topic space, between word space and visualization space, which preserves the semantics by topic modeling. While aiming for a good fit between the model parameters and the observed data, previous approaches have not considered the local consistency among data instances. We consider the problem of semantic visualization by jointly modeling topics and visualization on the intrinsic document manifold, modeled using a neighborhood graph. Each document has both a topic distribution and visualization coordinate. Specifically, we propose an unsupervised probabilistic model, called SEMAFORE, which aims to preserve the manifold in the lower-dimensional spaces through a neighborhood regularization framework designed for the semantic visualization task. To validate the efficacy of SEMAFORE, our comprehensive experiments on a number of real-life text datasets of news articles and Web pages show that the proposed methods outperform the state-of-the-art baselines on objective evaluation metrics.

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8

Long, Mingsheng, Jianmin Wang, Guiguang Ding, Dou Shen, and Qiang Yang. "Transfer Learning with Graph Co-Regularization." Proceedings of the AAAI Conference on Artificial Intelligence 26, no. 1 (September 20, 2021): 1033–39. http://dx.doi.org/10.1609/aaai.v26i1.8290.

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Transfer learning proves to be effective for leveraging labeled data in the source domain to build an accurate classifier in the target domain. The basic assumption behind transfer learning is that the involved domains share some common latent factors. Previous methods usually explore these latent factors by optimizing two separate objective functions, i.e., either maximizing the empirical likelihood, or preserving the geometric structure. Actually, these two objective functions are complementary to each other and optimizing them simultaneously can make the solution smoother and further improve the accuracy of the final model. In this paper, we propose a novel approach called Graph co-regularized Transfer Learning (GTL) for this purpose, which integrates the two objective functions seamlessly into one unified optimization problem. Thereafter, we present an iterative algorithm for the optimization problem with rigorous analysis on convergence and complexity. Our empirical study on two open data sets validates that GTL can consistently improve the classification accuracy compared to the state-of-the-art transfer learning methods.

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Long, Mingsheng, Jianmin Wang, Guiguang Ding, Dou Shen, and Qiang Yang. "Transfer Learning with Graph Co-Regularization." IEEE Transactions on Knowledge and Data Engineering 26, no. 7 (July 2014): 1805–18. http://dx.doi.org/10.1109/tkde.2013.97.

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10

Lezoray, Olivier, Abderrahim Elmoataz, and Sébastien Bougleux. "Graph regularization for color image processing." Computer Vision and Image Understanding 107, no. 1-2 (July 2007): 38–55. http://dx.doi.org/10.1016/j.cviu.2006.11.015.

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11

Górska, Joanna, and Zdzisław Skupień. "A partial refining of the Erdős-Kelly regulation." Opuscula Mathematica 39, no. 3 (2019): 355–60. http://dx.doi.org/10.7494/opmath.2019.39.3.355.

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The aim of this note is to advance the refining of the Erdős-Kelly result on graphical inducing regularization. The operation of inducing regulation (on graphs or multigraphs) with prescribed maximum vertex degree is originated by D. König in 1916. As is shown by Chartrand and Lesniak in their textbook Graphs & Digraphs (1996), an iterated construction for graphs can result in a regularization with many new vertices. Erdős and Kelly have presented (1963, 1967) a simple and elegant numerical method of determining for any simple \(n\)-vertex graph \(G\) with maximum vertex degree \(\Delta\), the exact minimum number, say \(\theta =\theta(G)\), of new vertices in a \(\Delta\)-regular graph \(H\) which includes \(G\) as an induced subgraph. The number \(\theta(G)\), which we call the cost of regulation of \(G\), has been upper-bounded by the order of \(G\), the bound being attained for each \(n\ge4\), e.g. then the edge-deleted complete graph \(K_n-e\) has \(\theta=n\). For \(n\ge 4\), we present all factors of \(K_n\) with \(\theta=n\) and next \(\theta=n-1\). Therein in case \(\theta=n-1\) and \(n\) odd only, we show that a specific extra structure, non-matching, is required.

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12

Verma, Vikas, Meng Qu, Kenji Kawaguchi, Alex Lamb, Yoshua Bengio, Juho Kannala, and Jian Tang. "GraphMix: Improved Training of GNNs for Semi-Supervised Learning." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 11 (May 18, 2021): 10024–32. http://dx.doi.org/10.1609/aaai.v35i11.17203.

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We present GraphMix, a regularization method for Graph Neural Network based semi-supervised object classification, whereby we propose to train a fully-connected network jointly with the graph neural network via parameter sharing and interpolation-based regularization. Further, we provide a theoretical analysis of how GraphMix improves the generalization bounds of the underlying graph neural network, without making any assumptions about the "aggregation" layer or the depth of the graph neural networks. We experimentally validate this analysis by applying GraphMix to various architectures such as Graph Convolutional Networks, Graph Attention Networks and Graph-U-Net. Despite its simplicity, we demonstrate that GraphMix can consistently improve or closely match state-of-the-art performance using even simpler architectures such as Graph Convolutional Networks, across three established graph benchmarks: Cora, Citeseer and Pubmed citation network datasets, as well as three newly proposed datasets: Cora-Full, Co-author-CS and Co-author-Physics.

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13

Tian, Xiuzhi, Chris H. Q. Ding, Sibao Chen, Bin Luo, and Xin Wang. "Regularization graph convolutional networks with data augmentation." Neurocomputing 436 (May 2021): 92–102. http://dx.doi.org/10.1016/j.neucom.2020.12.124.

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14

Yang, Maosheng, Mario Coutino, Geert Leus, and Elvin Isufi. "Node-Adaptive Regularization for Graph Signal Reconstruction." IEEE Open Journal of Signal Processing 2 (2021): 85–98. http://dx.doi.org/10.1109/ojsp.2021.3056897.

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15

Lian, Huiqiang, Huiying Xu, Siwei Wang, Miaomiao Li, Xinzhong Zhu, and Xinwang Liu. "Partial multiview clustering with locality graph regularization." International Journal of Intelligent Systems 36, no. 6 (March 15, 2021): 2991–3010. http://dx.doi.org/10.1002/int.22409.

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16

Li, Xuelong, Guosheng Cui, and Yongsheng Dong. "Refined-Graph Regularization-Based Nonnegative Matrix Factorization." ACM Transactions on Intelligent Systems and Technology 9, no. 1 (October 17, 2017): 1–21. http://dx.doi.org/10.1145/3090312.

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17

Śmieja, Marek, Oleksandr Myronov, and Jacek Tabor. "Semi-supervised discriminative clustering with graph regularization." Knowledge-Based Systems 151 (July 2018): 24–36. http://dx.doi.org/10.1016/j.knosys.2018.03.019.

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18

Wen, Jie, Xiaozhao Fang, Yong Xu, Chunwei Tian, and Lunke Fei. "Low-rank representation with adaptive graph regularization." Neural Networks 108 (December 2018): 83–96. http://dx.doi.org/10.1016/j.neunet.2018.08.007.

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19

Abernethy, Jacob, Olivier Chapelle, and Carlos Castillo. "Graph regularization methods for Web spam detection." Machine Learning 81, no. 2 (March 25, 2010): 207–25. http://dx.doi.org/10.1007/s10994-010-5171-1.

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20

Mann, R. B. "Regularization dependence of the superstring anomaly graph." Nuclear Physics B 303, no. 1 (June 1988): 99–134. http://dx.doi.org/10.1016/0550-3213(88)90219-2.

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21

Fu, Zhenyong, Zhiwu Lu, Horace Ip, Yuxin Peng, and Hongtao Lu. "Symmetric Graph Regularized Constraint Propagation." Proceedings of the AAAI Conference on Artificial Intelligence 25, no. 1 (August 4, 2011): 350–55. http://dx.doi.org/10.1609/aaai.v25i1.7897.

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This paper presents a novel symmetric graph regularization framework for pairwise constraint propagation. We first decompose the challenging problem of pairwise constraint propagation into a series of two-class label propagation subproblems and then deal with these subproblems by quadratic optimization with symmetric graph regularization. More importantly, we clearly show that pairwise constraint propagation is actually equivalent to solving a Lyapunov matrix equation, which is widely used in Control Theory as a standard continuous-time equation. Different from most previous constraint propagation methods that suffer from severe limitations, our method can directly be applied to multi-class problem and also can effectively exploit both must-link and cannot-link constraints. The propagated constraints are further used to adjust the similarity between data points so that they can be incorporated into subsequent clustering. The proposed method has been tested in clustering tasks on six real-life data sets and then shown to achieve significant improvements with respect to the state of the arts.

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22

Chen, Lin, Li Zeng, Jin Peng, Junren Ming, and Xianghui Zhu. "Regularity Index of Uncertain Random Graph." Symmetry 15, no. 1 (January 3, 2023): 137. http://dx.doi.org/10.3390/sym15010137.

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A graph containing some edges with probability measures and other edges with uncertain measures is referred to as an uncertain random graph. Numerous real-world problems in social networks and transportation networks can be boiled down to optimization problems in uncertain random graphs. Actually, information in optimization problems in uncertain random graphs is always asymmetric. Regularization is a common optimization problem in graph theory, and the regularity index is a fundamentally measurable indicator of graphs. Therefore, this paper investigates the regularity index of an uncertain random graph within the framework of chance theory and information asymmetry theory. The concepts of k-regularity index and regularity index of the uncertain random graph are first presented on the basis of the chance theory. Then, in order to compute the k-regularity index and the regularity index of the uncertain random graph, a simple and straightforward calculating approach is presented and discussed. Furthermore, we discuss the relationship between the regularity index and the k-regularity index of the uncertain random graph. Additionally, an adjacency matrix-based algorithm that can compute the k-regularity index of the uncertain random graph is provided. Some specific examples are given to illustrate the proposed method and algorithm. Finally, we conclude by highlighting some potential applications of uncertain random graphs in social networks and transportation networks, as well as the future vision of its combination with symmetry.

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23

Cariou, Claude, Steven Le Moan, and Kacem Chehdi. "Improving K-Nearest Neighbor Approaches for Density-Based Pixel Clustering in Hyperspectral Remote Sensing Images." Remote Sensing 12, no. 22 (November 14, 2020): 3745. http://dx.doi.org/10.3390/rs12223745.

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We investigated nearest-neighbor density-based clustering for hyperspectral image analysis. Four existing techniques were considered that rely on a K-nearest neighbor (KNN) graph to estimate local density and to propagate labels through algorithm-specific labeling decisions. We first improved two of these techniques, a KNN variant of the density peaks clustering method dpc, and a weighted-mode variant of knnclust, so the four methods use the same input KNN graph and only differ by their labeling rules. We propose two regularization schemes for hyperspectral image analysis: (i) a graph regularization based on mutual nearest neighbors (MNN) prior to clustering to improve cluster discovery in high dimensions; (ii) a spatial regularization to account for correlation between neighboring pixels. We demonstrate the relevance of the proposed methods on synthetic data and hyperspectral images, and show they achieve superior overall performances in most cases, outperforming the state-of-the-art methods by up to 20% in kappa index on real hyperspectral images.

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24

Liu, Hongyi, Wen Jiang, Yuchen Zha, and Zhihui Wei. "Coupled Tensor Block Term Decomposition with Superpixel-Based Graph Laplacian Regularization for Hyperspectral Super-Resolution." Remote Sensing 14, no. 18 (September 9, 2022): 4520. http://dx.doi.org/10.3390/rs14184520.

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Hyperspectral image (HSI) super-resolution aims at improving the spatial resolution of HSI by fusing a high spatial resolution multispectral image (MSI). To preserve local submanifold structures in HSI super-resolution, a novel superpixel graph-based super-resolution method is proposed. Firstly, the MSI is segmented into superpixel blocks to form two-directional feature tensors, then two graphs are created using spectral–spatial distance between the unfolded feature tensors. Secondly, two graph Laplacian terms involving underlying BTD factors of high-resolution HSI are developed, which ensures the inheritance of the spatial geometric structures. Finally, by incorporating graph Laplacian priors with the coupled BTD degradation model, a HSI super-resolution model is established. Experimental results demonstrate that the proposed method achieves better fused results compared with other advanced super-resolution methods, especially on the improvement of the spatial structure.

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25

Dai, Na. "Building Contextual Anchor Text Representation using Graph Regularization." Proceedings of the AAAI Conference on Artificial Intelligence 26, no. 1 (September 20, 2021): 24–30. http://dx.doi.org/10.1609/aaai.v26i1.8123.

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Anchor texts are useful complementary description for target pages, widely applied to improve search relevance. The benefits come from the additional information introduced into document representation and the intelligent ways of estimating their relative importance. Previous work on anchor importance estimation treated anchor text independently without considering its context. As a result, the lack of constraints from such context fails to guarantee a stable anchor text representation. We propose an anchor graph regularization approach to incorporate constraints from such context into anchor text weighting process, casting the task into a convex quadratic optimization problem. The constraints draw from the estimation of anchor-anchor, anchor-page, and page-page similarity. Based on any estimators, our approach operates as a post process of refining the estimated anchor weights, making it a plug and play component in search infrastructure. Comparable experiments on standard data sets (TREC 2009 and 2010) demonstrate the efficacy of our approach.

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26

Zhang, Xiaoxia, Degang Chen, Hong Yu, Guoyin Wang, Houjun Tang, and Kesheng Wu. "Improving nonnegative matrix factorization with advanced graph regularization." Information Sciences 597 (June 2022): 125–43. http://dx.doi.org/10.1016/j.ins.2022.03.008.

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27

Young, Sean I., Aous T. Naman, and David Taubman. "Graph Laplacian Regularization for Robust Optical Flow Estimation." IEEE Transactions on Image Processing 29 (2020): 3970–83. http://dx.doi.org/10.1109/tip.2019.2945653.

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Dinesh, Chinthaka, Gene Cheung, and Ivan V. Bajic. "Point Cloud Denoising via Feature Graph Laplacian Regularization." IEEE Transactions on Image Processing 29 (2020): 4143–58. http://dx.doi.org/10.1109/tip.2020.2969052.

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29

Gong, Bo, Benjamin Schullcke, Sabine Krueger-Ziolek, Marko Vauhkonen, Gerhard Wolf, Ullrich Mueller-Lisse, and Knut Moeller. "EIT Imaging Regularization Based on Spectral Graph Wavelets." IEEE Transactions on Medical Imaging 36, no. 9 (September 2017): 1832–44. http://dx.doi.org/10.1109/tmi.2017.2716825.

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Chen, Yi-Lei, and Chiou-Ting Hsu. "Multilinear Graph Embedding: Representation and Regularization for Images." IEEE Transactions on Image Processing 23, no. 2 (February 2014): 741–54. http://dx.doi.org/10.1109/tip.2013.2292303.

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31

Freschi, Valerio. "Improved Biological Network Reconstruction Using Graph Laplacian Regularization." Journal of Computational Biology 18, no. 8 (August 2011): 987–96. http://dx.doi.org/10.1089/cmb.2010.0232.

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32

Shao, Yuanlong, Yuan Zhou, and Deng Cai. "Variational inference with graph regularization for image annotation." ACM Transactions on Intelligent Systems and Technology 2, no. 2 (February 2011): 1–21. http://dx.doi.org/10.1145/1899412.1899415.

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33

Tuo, Qianjuan, Hong Zhao, and Qinghua Hu. "Hierarchical feature selection with subtree based graph regularization." Knowledge-Based Systems 163 (January 2019): 996–1008. http://dx.doi.org/10.1016/j.knosys.2018.10.023.

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Wang, Yunyun, Yan Meng, Yun Li, Songcan Chen, Zhenyong Fu, and Hui Xue. "Semi-supervised manifold regularization with adaptive graph construction." Pattern Recognition Letters 98 (October 2017): 90–95. http://dx.doi.org/10.1016/j.patrec.2017.09.004.

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Liu, Bo, Liping Jing, Jian Yu, and Jia Li. "Robust graph learning via constrained elastic-net regularization." Neurocomputing 171 (January 2016): 299–312. http://dx.doi.org/10.1016/j.neucom.2015.06.059.

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Zhang, Yuan, Fei Sun, Xiaoyong Yang, Chen Xu, Wenwu Ou, and Yan Zhang. "Graph-based Regularization on Embedding Layers for Recommendation." ACM Transactions on Information Systems 39, no. 1 (January 5, 2021): 1–27. http://dx.doi.org/10.1145/3414067.

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Kawano, Shuichi, Toshihiro Misumi, and Sadanori Konishi. "Semi-Supervised Logistic Discrimination Via Graph-Based Regularization." Neural Processing Letters 36, no. 3 (May 29, 2012): 203–16. http://dx.doi.org/10.1007/s11063-012-9231-3.

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38

Gong, Bo, Benjamin Schullcke, Sabine Krueger-Ziolek, and Knut Moeller. "Regularization of EIT reconstruction based on multi-scales wavelet transforms." Current Directions in Biomedical Engineering 2, no. 1 (September 1, 2016): 423–26. http://dx.doi.org/10.1515/cdbme-2016-0094.

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AbstractElectrical Impedance Tomography (EIT) intends to obtain the conductivity distribution of a domain from the electrical boundary conditions. This is an ill-posed inverse problem usually solved on finite element meshes. Wavelet transforms are widely used for medical image reconstruction. However, because of the irregular form of the finite element meshes, the canonical wavelet transforms is impossible to perform on meshes. In this article, we present a framework that combines multi-scales wavelet transforms and finite element meshes by viewing meshes as undirected graphs and applying spectral graph wavelet transform on the meshes.

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Deutsch, Shay, Andrea Bertozzi, and Stefano Soatto. "Zero Shot Learning with the Isoperimetric Loss." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 07 (April 3, 2020): 10704–12. http://dx.doi.org/10.1609/aaai.v34i07.6698.

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We introduce the isoperimetric loss as a regularization criterion for learning the map from a visual representation to a semantic embedding, to be used to transfer knowledge to unknown classes in a zero-shot learning setting. We use a pre-trained deep neural network model as a visual representation of image data, a Word2Vec embedding of class labels, and linear maps between the visual and semantic embedding spaces. However, the spaces themselves are not linear, and we postulate the sample embedding to be populated by noisy samples near otherwise smooth manifolds. We exploit the graph structure defined by the sample points to regularize the estimates of the manifolds by inferring the graph connectivity using a generalization of the isoperimetric inequalities from Riemannian geometry to graphs. Surprisingly, this regularization alone, paired with the simplest baseline model, outperforms the state-of-the-art among fully automated methods in zero-shot learning benchmarks such as AwA and CUB. This improvement is achieved solely by learning the structure of the underlying spaces by imposing regularity.

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40

Hořejší, J., J. Novotný, and O. I. Zavialov. "Dimensional regularization of the VVA triangle graph as a continuous superposition of Pauli-Villars regularizations." Physics Letters B 213, no. 2 (October 1988): 173–76. http://dx.doi.org/10.1016/0370-2693(88)91020-9.

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Wang, Dengwei. "A Markov Random Field and Adaptive Regularization Embedded Level Set Segmentation Model Solving by Graph Cuts." Journal of Electrical and Computer Engineering 2019 (January 14, 2019): 1–13. http://dx.doi.org/10.1155/2019/8747385.

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This paper presents a novel Markov random field (MRF) and adaptive regularization embedded level set model for robust image segmentation and uses graph cuts optimization to numerically solve it. Firstly, a special MRF-based energy term in the form of level set formulation is constructed for strong local neighborhood modeling. Secondly, a regularization constraint with adaptive properties is imposed onto the proposed model with the following purposes: reduce the influence of noise, force the power exponent of the regularization process to change adaptively with image coordinates, and ensure the active contour does not pass through the weak object boundaries. Thirdly, graph cuts optimization is used to implement the numerical solution of the proposed model to obtain extremely fast convergence performance. The extensive and promising experimental results on wide variety of images demonstrate the excellent performance of the proposed method in both segmentation accuracy and convergence rate.

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Zhu, Linli, Yu Pan, Mohammad Reza Farahani, and Wei Gao. "Graph Laplacian Based Ontology Regularization Distance Framework for Ontology Similarity Measuring and Ontology Mapping." Journal of Computational Mathematica 1, no. 1 (June 30, 2017): 88–98. http://dx.doi.org/10.26524/cm6.

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Fedorchenko, Ludmila, and Sergey Baranov. "Equivalent Transformations and Regularization in Context-Free Grammars." Cybernetics and Information Technologies 14, no. 4 (January 31, 2015): 29–44. http://dx.doi.org/10.1515/cait-2014-0003.

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Abstract Regularization of translational context-free grammar via equivalent transformations is a mandatory step in developing a reliable processor of a formal language defined by this grammar. In the 1970-ies, the multi-component oriented graphs with basic equivalent transformations were proposed to represent a formal grammar of ALGOL-68 in a compiler for IBM/360 compatibles. This paper describes a method of grammar regularization with the help of an algorithm of eliminating the left/right-hand side recursion of nonterminals which ultimately converts a context-free grammar into a regular one. The algorithm is based on special equivalent transformations of the grammar syntactic graph: elimination of recursions and insertion of iterations. When implemented in the system SynGT, it has demonstrated over 25% reduction of the memory size required to store the respective intermediate control tables, compared to the algorithm used in Flex/Bison parsers.

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Liu, Zhao-Yang, Shao-Yuan Li, Songcan Chen, Yao Hu, and Sheng-Jun Huang. "Uncertainty Aware Graph Gaussian Process for Semi-Supervised Learning." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 4957–64. http://dx.doi.org/10.1609/aaai.v34i04.5934.

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Graph-based semi-supervised learning (GSSL) studies the problem where in addition to a set of data points with few available labels, there also exists a graph structure that describes the underlying relationship between data items. In practice, structure uncertainty often occurs in graphs when edges exist between data with different labels, which may further results in prediction uncertainty of labels. Considering that Gaussian process generalizes well with few labels and can naturally model uncertainty, in this paper, we propose an Uncertainty aware Graph Gaussian Process based approach (UaGGP) for GSSL. UaGGP exploits the prediction uncertainty and label smooth regularization to guide each other during learning. To further subdue the effect of irrelevant neighbors, UaGGP also aggregates the clean representation in the original space and the learned representation. Experiments on benchmarks demonstrate the effectiveness of the proposed approach.

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Zhang, Guifang, and Jiaxin Chen. "Non-negative matrix factorization via adaptive sparse graph regularization." Multimedia Tools and Applications 80, no. 8 (January 12, 2021): 12507–24. http://dx.doi.org/10.1007/s11042-020-10247-3.

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Pilavc, Yusuf, Pierre-Olivier Amblard, Simon Barthelme, and Nicolas Tremblay. "Graph Tikhonov Regularization and Interpolation Via Random Spanning Forests." IEEE Transactions on Signal and Information Processing over Networks 7 (2021): 359–74. http://dx.doi.org/10.1109/tsipn.2021.3084879.

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Miao, Jianyu, Tiejun Yang, Junwei Jin, and Lingfeng Niu. "Graph-Based Clustering via Group Sparsity and Manifold Regularization." IEEE Access 7 (2019): 172123–35. http://dx.doi.org/10.1109/access.2019.2955971.

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Wang, Meng, Weijie Fu, Shijie Hao, Dacheng Tao, and Xindong Wu. "Scalable Semi-Supervised Learning by Efficient Anchor Graph Regularization." IEEE Transactions on Knowledge and Data Engineering 28, no. 7 (July 1, 2016): 1864–77. http://dx.doi.org/10.1109/tkde.2016.2535367.

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Hu, Juncheng, Yonghao Li, Wanfu Gao, and Ping Zhang. "Robust multi-label feature selection with dual-graph regularization." Knowledge-Based Systems 203 (September 2020): 106126. http://dx.doi.org/10.1016/j.knosys.2020.106126.

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Fan, Baojie, and Yang Cong. "Consistent multi-layer subtask tracker via hyper-graph regularization." Pattern Recognition 67 (July 2017): 299–312. http://dx.doi.org/10.1016/j.patcog.2017.02.008.

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