s for a stable estimate. In this work, we assume instead the availability of a relevant feature vector $\\mathbf{f}_i$ per node $i$, from which we compute an optimal feature graph via optimization of a feature metric. Specifically, we alternately optimize the diagonal and off-diagonal entries of a Mahalanobis distance matrix $\\mathbf{M}$ by minimizing the graph Laplacian regularizer (GLR) $\\mathbf{z}^{\\top} \\mathbf{L} \\mathbf{z}$, where edge weight is $w_{i,j} = \\exp\\{-(\\mathbf{f}_i - \\mathbf{f}_j)^{\\top} \\mathbf{M} (\\mathbf{f}_i - \\mathbf{f}_j) \\}$, given a single observation $\\mathbf{z}$. We optimize diagonal entries via proximal gradient (PG), where we constrain $\\mathbf{M}$ to be positive definite (PD) via linear inequalities derived from the Gershgorin circle theorem. To optimize off-diagonal entries, we design a block descent algorithm that iteratively optimizes one row and column of $\\mathbf{M}$. To keep $\\mathbf{M}$ PD, we constrain the Schur complement of sub-matrix $\\mathbf{M}_{2,2}$ of $\\mathbf{M}$ to be PD when optimizing via PG. Our algorithm mitigates full eigen-decomposition of $\\mathbf{M}$, thus ensuring fast computation speed even when feature vector $\\mathbf{f}_i$ has high dimension. To validate its usefulness, we apply our feature graph learning algorithm to the problem of 3D point cloud denoising, resulting in state-of-the-art performance compared to competing schemes in extensive experiments. ","authors":[{"id":"5440fddbdabfae7f9b361238","name":"Hu Wei"},{"name":"Gao Xiang"},{"id":"5631bad745cedb3399f01eaf","name":"Cheung Gene"},{"id":"548a700ddabfaed7b5fa4167","name":"Guo Zongming"}],"doi":"10.1109\u002Ftsp.2020.2978617","flags":[{"flag":"affirm_author","person_id":"5440fddbdabfae7f9b361238"}],"id":"5d36dcc73a55ac954df90f36","num_citation":11,"order":0,"pages":{"end":"1","start":"1"},"pdf":"https:\u002F\u002Fstatic.aminer.cn\u002Fstorage\u002Fpdf\u002Farxiv\u002F19\u002F1907\u002F1907.09138.pdf","title":"Feature Graph Learning for 3D Point Cloud Denoising","urls":["https:\u002F\u002Farxiv.org\u002Fabs\u002F1907.09138","http:\u002F\u002Fdblp.uni-trier.de\u002Fdb\u002Fjournals\u002Fcorr\u002Fcorr1907.html#abs-1907-09138","http:\u002F\u002Farxiv.org\u002Fpdf\u002F1907.09138.pdf"],"venue":{"info":{"name":"Sport Psychologist"},"issue":"","volume":""},"versions":[{"id":"5d36dcc73a55ac954df90f36","sid":"1907.09138","src":"arxiv","year":2019},{"id":"5ea012619fced0a24b9bb7e0","sid":"3010078784","src":"mag","vsid":"116921146","year":2020}],"year":2020},{"abstract":"We propose a general projection-free metric learning framework, where the minimization objective is a convex differentiable function of the metric matrix M, and M resides in the set S of generalized graph Laplacian matrices for connected graphs with positive edge weights and node degrees. Unlike low-rank metric matrices common in the literature, S includes the important positivediagonal-only matrices as a special case in the limit. The key idea for fast optimization is to rewrite the positive definite cone constraint in S as signal-adaptive linear constraints via Gershgorin disc alignment, so that the alternating optimization of the diagonal and offdiagonal terms in M can be solved efficiently as linear programs via Frank-Wolfe iterations. We prove that left-ends of the Gershgorin discs can be aligned perfectly using the first eigenvector v of M, which we update iteratively using Locally Optimal Block …","authors":[{"id":"562d4d4f45cedb3398db8dfc","name":"Cheng Yang"},{"id":"5631bad745cedb3399f01eaf","name":"Gene Cheung"},{"id":"5440fddbdabfae7f9b361238","name":"Wei Hu"}],"doi":"10.1109\u002FICASSP40776.2020.9053552","id":"5ed858099e795e87fac5978a","lang":"en","num_citation":4,"order":2,"pages":{"end":"5534","start":"5530"},"title":"Graph Metric Learning via Gershgorin Disc Alignment","urls":["https:\u002F\u002Fscholar.google.com.hk\u002Fcitations?view_op=view_citation&hl=zh-CN&user=5oFf8Q4AAAAJ&pagesize=100&citation_for_view=5oFf8Q4AAAAJ:b0M2c_1WBrUC","https:\u002F\u002Fdblp.org\u002Frec\u002Fconf\u002Ficassp\u002FYangCH20","https:\u002F\u002Fdoi.org\u002F10.1109\u002FICASSP40776.2020.9053552"],"venue":{"info":{"name":"ICASSP"},"issue":"","volume":""},"versions":[{"id":"5ed858099e795e87fac5978a","sid":"5ed858099e795e87fac5978a","src":"user-5ebe287b4c775eda72abcdd8","year":2020},{"id":"5f1c035291e011e914125d19","sid":"conf\u002Ficassp\u002FYangCH20","src":"dblp","vsid":"conf\u002Ficassp","year":2020}],"year":2020},{"authors":[{"name":"Xiang Gao"},{"id":"5440fddbdabfae7f9b361238","name":"Wei Hu"},{"id":"563136d045cedb3399d0cc3f","name":"Zongming Guo"}],"doi":"10.1109\u002FICME46284.2020.9102726","id":"5fae6de6d4150a363cec6c32","num_citation":0,"order":1,"pages":{"end":"6","start":"1"},"title":"Exploring Structure-Adaptive Graph Learning for Robust Semi-Supervised Classification","urls":["http:\u002F\u002Fxplorestaging.ieee.org\u002Fielx7\u002F9099125\u002F9102711\u002F09102726.pdf?arnumber=9102726","https:\u002F\u002Fdblp.org\u002Frec\u002Fconf\u002Ficmcs\u002FGaoHG20","https:\u002F\u002Fdoi.org\u002F10.1109\u002FICME46284.2020.9102726"],"venue":{"info":{"name":"ICME"}},"versions":[{"id":"5fae6de6d4150a363cec6c32","sid":"3035467734","src":"mag","vsid":"1126322613","year":2020},{"id":"5ff8804a91e011c8326691e2","sid":"conf\u002Ficmcs\u002FGaoHG20","src":"dblp","vsid":"conf\u002Ficmcs","year":2020}],"year":2020},{"abstract":"We propose a general projection-free metric learning framework, where the minimization objective min(M is an element of S) Q(M) is a convex differentiable function of the metric matrix M, and M resides in the set S of generalized graph Laplacian matrices for connected graphs with positive edge weights and node degrees. Unlike low-rank metric matrices common in the literature, S includes the important positive-diagonal-only matrices as a special case in the limit. The key idea for fast optimization is to rewrite the positive definite cone constraint in S as signal-adaptive linear constraints via Gershgorin disc alignment, so that the alternating optimization of the diagonal and off-diagonal terms in M can be solved efficiently as linear programs via Frank-Wolfe iterations. We prove that left-ends of the Gershgorin discs can be aligned perfectly using the first eigenvector v of M, which we update iteratively using Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) with warm start as diagonal \u002F off-diagonal terms are optimized. Experiments show that our efficiently computed graph metric matrices outperform metrics learned using competing methods in terms of classification tasks.","authors":[{"id":"562d4d4f45cedb3398db8dfc","name":"Cheng Yang"},{"id":"5631bad745cedb3399f01eaf","name":"Gene Cheung"},{"id":"5440fddbdabfae7f9b361238","name":"Wei Hu"}],"id":"619b53a11c45e57ce99f1f2d","lang":"en","num_citation":0,"order":2,"pages":{"end":"5534","start":"5530"},"title":"Graph Metric Learning Via Gershgorin Disc Alignment","urls":["http:\u002F\u002Fwww.webofknowledge.com\u002F"],"venue":{"info":{"name":"2020 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING"}},"versions":[{"id":"619b53a11c45e57ce99f1f2d","sid":"WOS:000615970405158","src":"wos","vsid":"2020 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING","year":2020}],"year":2020},{"abstract":" We propose a fast general projection-free metric learning framework, where the minimization objective $\\min_{\\M \\in \\cS} Q(\\M)$ is a convex differentiable function of the metric matrix $\\M$, and $\\M$ resides in the set $\\cS$ of generalized graph Laplacian matrices for connected graphs with positive edge weights and node degrees. Unlike low-rank metric matrices common in the literature, $\\cS$ includes the important positive-diagonal-only matrices as a special case in the limit. The key idea for fast optimization is to rewrite the positive definite cone constraint in $\\cS$ as signal-adaptive linear constraints via Gershgorin disc alignment, so that the alternating optimization of the diagonal and off-diagonal terms in $\\M$ can be solved efficiently as linear programs via Frank-Wolfe iterations. We prove that the Gershgorin discs can be aligned perfectly using the first eigenvector $\\v$ of $\\M$, which we update iteratively using Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) with warm start as diagonal \u002F off-diagonal terms are optimized. Experiments show that our efficiently computed graph metric matrices outperform metrics learned using competing methods in terms of classification tasks. ","authors":[{"name":"Yang Cheng"},{"id":"5631bad745cedb3399f01eaf","name":"Cheung Gene"},{"id":"5440fddbdabfae7f9b361238","name":"Hu Wei"}],"doi":"10.1109\u002Ficassp40776.2020.9053552","flags":[{"flag":"affirm_author","person_id":"5440fddbdabfae7f9b361238"}],"id":"5e3158db3a55ac24c97a23e4","num_citation":0,"order":2,"pages":{"end":"","start":""},"pdf":"https:\u002F\u002Fstatic.aminer.cn\u002Fstorage\u002Fpdf\u002Farxiv\u002F20\u002F2001\u002F2001.10485.pdf","title":"Fast Graph Metric Learning via Gershgorin Disc Alignment","urls":["https:\u002F\u002Farxiv.org\u002Fabs\u002F2001.10485"],"venue":{"info":{"name":"international conference on acoustics speech and signal processing"},"issue":"","volume":""},"versions":[{"id":"5e3158db3a55ac24c97a23e4","sid":"2001.10485","src":"arxiv","year":2020},{"id":"5ecbc5e39fced0a24b4ec7b3","sid":"3015921871","src":"mag","vsid":"1121227772","year":2020}],"year":2020},{"abstract":" This paper addresses the problem of 3D hand pose estimation from a monocular RGB image. We are the first to propose a graph-based generative adversarial learning framework regularized by a hand model, aiming at realistic 3D hand pose estimation. Our model consists of a 3D hand pose generator and a multi-source discriminator. Taking one monocular RGB image as the input, the generator is essentially a residual graph convolution module with a parametric deformable hand model as prior for pose refinement. Further, we design a multi-source discriminator with hand poses, bones and the input image as input to capture intrinsic features, which distinguishes the predicted 3D hand pose from the ground-truth and leads to anthropomorphically valid hand poses. In addition, we propose two novel bone-constrained loss functions, which characterize the morphable structure of hand poses explicitly. Extensive experiments demonstrate that our model sets new state-of-the-art performances in 3D hand pose estimation from a monocular image on standard benchmarks. ","authors":[{"name":"He Yiming"},{"id":"5440fddbdabfae7f9b361238","name":"Hu Wei"},{"name":"Yang Siyuan"},{"name":"Qu Xiaochao"},{"name":"Wan Pengfei"},{"name":"Guo Zongming"}],"flags":[{"flag":"affirm_author","person_id":"5440fddbdabfae7f9b361238"}],"id":"5de8d54c3a55ac9c42291809","num_citation":0,"order":1,"pdf":"https:\u002F\u002Fstatic.aminer.cn\u002Fstorage\u002Fpdf\u002Farxiv\u002F19\u002F1912\u002F1912.01875.pdf","title":"GraphPoseGAN: 3D Hand Pose Estimation from a Monocular RGB Image via Adversarial Learning on Graphs","urls":["https:\u002F\u002Farxiv.org\u002Fabs\u002F1912.01875"],"versions":[{"id":"5de8d54c3a55ac9c42291809","sid":"1912.01875","src":"arxiv","year":2019}],"year":2019},{"abstract":" Graph Convolutional Neural Networks (GCNNs) extend classical CNNs to graph data domain, such as brain networks, social networks and 3D point clouds. It is critical to identify an appropriate graph for the subsequent graph convolution. Existing methods manually construct or learn one fixed graph for all the layers of a GCNN. In order to adapt to the underlying structure of node features in different layers, we propose dynamic learning of graphs and node features jointly in GCNNs. In particular, we cast the graph optimization problem as distance metric learning to capture pairwise similarities of features in each layer. We deploy the Mahalanobis distance metric and further decompose the metric matrix into a low-dimensional matrix, which converts graph learning to the optimization of a low-dimensional matrix for efficient implementation. Extensive experiments on point clouds and citation network datasets demonstrate the superiority of the proposed method in terms of both accuracies and robustness. ","authors":[{"name":"Tang Jiaxiang"},{"id":"5440fddbdabfae7f9b361238","name":"Hu Wei"},{"name":"Gao Xiang"},{"id":"548a700ddabfaed7b5fa4167","name":"Guo Zongming"}],"flags":[{"flag":"affirm_author","person_id":"5440fddbdabfae7f9b361238"}],"id":"5d79a4f43a55ac5af95ae2c7","num_citation":0,"order":1,"pdf":"https:\u002F\u002Fstatic.aminer.cn\u002Fstorage\u002Fpdf\u002Farxiv\u002F19\u002F1909\u002F1909.04931.pdf","title":"Joint Learning of Graph Representation and Node Features in Graph Convolutional Neural Networks","urls":["https:\u002F\u002Farxiv.org\u002Fabs\u002F1909.04931"],"versions":[{"id":"5d79a4f43a55ac5af95ae2c7","sid":"1909.04931","src":"arxiv","year":2019}],"year":2019},{"abstract":"With the prevalence of depth sensors and 3D scanning devices, point clouds have attracted increasing attention as a format for 3D object representation, with applications in various fields such as tele-presence, navigation for autonomous driving and heritage reconstruction. However, point clouds usually exhibit holes of missing data, mainly due to the limitation of acquisition techniques and complicated structure. Hence, we propose an efficient inpainting method for the attribute (e.g., color) of point clouds, exploiting non-local selfsimilarity in graph spectral domain. Specifically, we represent irregular point clouds naturally on graphs, and split a point cloud into fixed-sized cubes as the processing unit. We then globally search for the most similar cubes to the target cube with holes inside, and compute the graph Fourier transform (GFT) basis from the similar cubes, which will be leveraged for the GFT representation of the target patch. We then formulate attribute inpainting as a sparse coding problem, imposing sparsity on the GFT representation of the attribute for hole filling. Experimental results demonstrate the superiority of our method.","authors":[{"id":"53f430cbdabfaec22ba4398a","name":"Ju He"},{"name":"Zeqing Fu"},{"id":"5440fddbdabfae7f9b361238","name":"Wei Hu"},{"id":"548a700ddabfaed7b5fa4167","name":"Zongming Guo"}],"id":"619b52891c45e57ce98f8cbe","lang":"en","num_citation":0,"order":2,"pages":{"end":"4389","start":"4385"},"title":"Point Cloud Attribute Inpainting In Graph Spectral Domain","urls":["http:\u002F\u002Fwww.webofknowledge.com\u002F"],"venue":{"info":{"name":"2019 IEEE INTERNATIONAL CONFERENCE ON IMAGE PROCESSING (ICIP)"}},"versions":[{"id":"619b52891c45e57ce98f8cbe","sid":"WOS:000521828604095","src":"wos","vsid":"2019 IEEE INTERNATIONAL CONFERENCE ON IMAGE PROCESSING (ICIP)","year":2019}],"year":2019},{"abstract":"This paper addresses the problem of 3D hand pose estimation from a monocular RGB image. While previous methods have shown their success, the structure of hands has not been exploited explicitly, which is critical in pose estimation. To this end, we propose a hand-model regularized graph refinement paradigm under an adversarial learning framework, aiming to explicitly capture structural inter-dependencies of hand joints for the learning of intrinsic patterns. We estimate an initial hand pose from a parametric hand model as a prior of hand structure, and refine the structure by learning the deformation of the prior pose via residual graph convolution. To optimize the hand structure further, we propose two bone-constrained loss functions, which characterize the morphable structure of hand poses explicitly. Also, we introduce an adversarial learning framework with a multi-source discriminator to capture structural …","authors":[{"name":"Yiming He"},{"id":"5440fddbdabfae7f9b361238","name":"Wei Hu"},{"name":"Siyuan Yang"},{"name":"Xiaochao Qu"},{"name":"Pengfei Wan"},{"name":"Zongming Guo"}],"id":"5ed858099e795e87fac5978b","lang":"en","num_citation":0,"order":1,"pages":{"end":"","start":"arXiv: 1912.01875"},"title":"3D Hand Pose Estimation in the Wild via Graph Refinement under Adversarial Learning","urls":["https:\u002F\u002Fscholar.google.com.hk\u002Fcitations?view_op=view_citation&hl=zh-CN&user=5oFf8Q4AAAAJ&pagesize=100&citation_for_view=5oFf8Q4AAAAJ:NhqRSupF_l8C"],"venue":{"info":{"name":"arXiv"},"issue":"","volume":""},"versions":[{"id":"5ed858099e795e87fac5978b","sid":"5ed858099e795e87fac5978b","src":"user-5ebe287b4c775eda72abcdd8","year":2019}],"year":2019},{"authors":[{"id":"53f430cbdabfaec22ba4398a","name":"Ju He"},{"name":"Zeqing Fu"},{"id":"5440fddbdabfae7f9b361238","name":"Wei Hu"},{"id":"548a700ddabfaed7b5fa4167","name":"Zongming Guo"}],"doi":"10.1109\u002Ficip.2019.8803497","flags":[{"flag":"affirm_author","person_id":"5440fddbdabfae7f9b361238"}],"id":"5db92a2447c8f76646201155","num_citation":1,"order":2,"pages":{"end":"4389","start":"4385"},"title":"Point Cloud Attribute Inpainting in Graph Spectral Domain","venue":{"info":{"name":"international conference on image processing"},"issue":"","volume":""},"versions":[{"id":"5db92a2447c8f76646201155","sid":"2971302076","src":"mag","vsid":"1163163559","year":2019},{"id":"5df362513a55aced4508faf8","sid":"conf\u002Ficip\u002FHeF0G19","src":"dblp","vsid":"conf\u002Ficip","year":2019}],"year":2019}],"profilePubsTotal":61,"profilePatentsPage":1,"profilePatents":[{"state":"","affiliation":{},"public_date":0,"patentees":[],"app_number":"","applicants":[{"city":"","name":"MA SIWEI","state":"","country":"","alias":[],"id":""},{"city":"","name":"XU YIQUN","state":"","country":"","alias":[],"id":""},{"city":"","name":"WANG SHANSHE","state":"","country":"","alias":[],"id":""},{"city":"","name":"LI JUNRU","state":"","country":"","alias":[],"id":""},{"city":"","name":"HU WEI","state":"","country":"","alias":[],"id":""}],"country":"","pub_date":0,"id":"60bde2adca25408ec8b69caa","status":"","title":"Fourier graph transformation-based point cloud intraframe coding method and apparatus","lang":"","type":0,"public_number":"","title_zh":"种基于傅里叶图变换的点云帧内编码方法及装置","app_date":20171213}],"profilePatentsTotal":1,"profilePatentsEnd":true,"profileProjectsPage":0,"profileProjects":null,"profileProjectsTotal":null,"newInfo":null,"checkDelPubs":[]}};