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Xiao-ming Wu

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23 papers

1 author row

NeurIPS Conference 2025 Conference Paper

Can LLMs Outshine Conventional Recommenders? A Comparative Evaluation

Qijiong Liu
Jieming Zhu
Lu Fan
Kun Wang
Hengchang Hu
Wei Guo
Yong Liu
Xiao-ming Wu

Integrating large language models (LLMs) into recommender systems has created new opportunities for improving recommendation quality. However, a comprehensive benchmark is needed to thoroughly evaluate and compare the recommendation capabilities of LLMs with traditional recommender systems. In this paper, we introduce \recbench{}, which systematically investigates various item representation forms (including unique identifier, text, semantic embedding, and semantic identifier) and evaluates two primary recommendation tasks, i. e. , click-through rate prediction (CTR) and sequential recommendation (SeqRec). Our extensive experiments cover up to 17 large models and are conducted across five diverse datasets from fashion, news, video, books, and music domains. Our findings indicate that LLM-based recommenders outperform conventional recommenders, achieving up to a 5% AUC improvement in CTR and up to a 170% NDCG@10 improvement in SeqRec. However, these substantial performance gains come at the expense of significantly reduced inference efficiency, rendering LLMs impractical as real-time recommenders. We have released our code and data to enable other researchers to reproduce and build upon our experimental results.

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AAAI Conference 2025 Conference Paper

Dynamic Spectral Graph Anomaly Detection

Jianbo Zheng
Chao Yang
Tairui Zhang
Longbing Cao
Bin Jiang
Xuhui Fan
Xiao-ming Wu
Xianxun Zhu

Graph anomaly detection is crucial for identifying anomalous nodes within graphs and addressing applications like financial fraud detection and social spam detection. Recent spectral graph neural network methods advance graph anomaly detection by focusing on anomalies that notably affect the distribution of graph spectral energy. Such spectrum-based methods rely on two steps: graph wavelet extraction and feature fusion. However, both steps are hand-designed, capturing incomprehensive anomaly information of wavelet-specific features and resulting in their inconsistent feature fusion. To address these problems, we propose a dynamic spectral graph anomaly detection framework DSGAD to adaptively capture comprehensive anomaly information and perform consistent feature fusion. DSGAD introduces dynamic wavelets, consisting of trainable wavelets to adaptively learn anomalous patterns and capture wavelet-specific features with comprehensive anomaly information. Furthermore, the consistent fusion of wavelet-specific features achieves dynamic fusion by combining wavelet-specific feature extraction with energy difference and channel convolution fusion using location correlation. Experimental results on four datasets substantiate the efficacy of our DSGAD method, surpassing state-of-the-art methods in both homogeneous and heterogeneous graphs.

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JBHI Journal 2025 Journal Article

Video Object Segmentation with Optimal Frame Auto-selection Based on Prior Knowledge for Midbrain Assessment in Transcranial Ultrasound

Xinyi Wang
Sai Kit LAM
Hongyu KANG
Yu Sun
Chao HOU
Shuai Li
Xin Sun
Fangxian LI

Transcranial sonography (TCS) provides a non-invasive means of assessing movement disorders such as Parkinson's disease (PD). However, current TCS-based evaluations rely heavily on manual operation by experienced physicians, making the process time-consuming and physician-dependent. For the first time, we aimed to develop a hybrid pipeline for real-time video object segmentation (VOS) and automatic optimal frame selection. Eighty-three standardized TCS real-time data comprising 1, 992 midbrain frames from Beijing Tiantan Hospital were collected. We adopted three state-of-the-art VOS models (STCN, RDE-VOS, and XMEM) and incorporated anatomical priors to guide optimal frame selection. Specifically, we leveraged the anatomical trend of midbrain morphology to estimate the midbrain radius at the optimal frame and selected the frame where the VOS-segmented midbrain best matched this estimate. The XMEM-based pipeline achieved high segmentation performance (Jaccard: 0. 85, Boundary Accuracy: 0. 95, Dice: 0. 92) and optimal frame selection (Distance: 4. 87; Jaccard: 0. 92), with efficiency (51. 05 FPS, 0. 56 s/patient, 661. 55 MB). Subgroup analyses confirmed robustness across image quality and PD conditions. Assessment of a junior physician's selection suggests potential to reduce the expertise gap in optimal frame selection. The proposed hybrid pipeline offers an automated tool for midbrain assessment using TCS, which may help reduce physicians' workload and minimize subjectivity, particularly supporting junior physicians in mitigating the expertise-demanding nature of TCS. This approach may serve as a foundation for more promising TCS-based assessments in the future, contributing to broader adoption of non-invasive ultrasound techniques in PD evaluation.

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NeurIPS Conference 2024 Conference Paper

Classic GNNs are Strong Baselines: Reassessing GNNs for Node Classification

Yuankai Luo
Lei Shi
Xiao-ming Wu

Graph Transformers (GTs) have recently emerged as popular alternatives to traditional message-passing Graph Neural Networks (GNNs), due to their theoretically superior expressiveness and impressive performance reported on standard node classification benchmarks, often significantly outperforming GNNs. In this paper, we conduct a thorough empirical analysis to reevaluate the performance of three classic GNN models (GCN, GAT, and GraphSAGE) against GTs. Our findings suggest that the previously reported superiority of GTs may have been overstated due to suboptimal hyperparameter configurations in GNNs. Remarkably, with slight hyperparameter tuning, these classic GNN models achieve state-of-the-art performance, matching or even exceeding that of recent GTs across 17 out of the 18 diverse datasets examined. Additionally, we conduct detailed ablation studies to investigate the influence of various GNN configurations—such as normalization, dropout, residual connections, and network depth—on node classification performance. Our study aims to promote a higher standard of empirical rigor in the field of graph machine learning, encouraging more accurate comparisons and evaluations of model capabilities. Our implementation is available at https: //github. com/LUOyk1999/tunedGNN.

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AAAI Conference 2024 Conference Paper

Correlation Matching Transformation Transformers for UHD Image Restoration

Cong Wang
Jinshan Pan
Wei Wang
Gang Fu
Siyuan Liang
Mengzhu Wang
Xiao-ming Wu
Jun Liu

This paper proposes UHDformer, a general Transformer for Ultra-High-Definition (UHD) image restoration. UHDformer contains two learning spaces: (a) learning in high-resolution space and (b) learning in low-resolution space. The former learns multi-level high-resolution features and fuses low-high features and reconstructs the residual images, while the latter explores more representative features learning from the high-resolution ones to facilitate better restoration. To better improve feature representation in low-resolution space, we propose to build feature transformation from the high-resolution space to the low-resolution one. To that end, we propose two new modules: Dual-path Correlation Matching Transformation module (DualCMT) and Adaptive Channel Modulator (ACM). The DualCMT selects top C/r (r is greater or equal to 1 which controls the squeezing level) correlation channels from the max-pooling/mean-pooling high-resolution features to replace low-resolution ones in Transformers, which can effectively squeeze useless content to improve the feature representation in low-resolution space to facilitate better recovery. The ACM is exploited to adaptively modulate multi-level high-resolution features, enabling to provide more useful features to low-resolution space for better learning. Experimental results show that our UHDformer reduces about ninety-seven percent model sizes compared with most state-of-the-art methods while significantly improving performance under different training sets on 3 UHD image restoration tasks, including low-light image enhancement, image dehazing, and image deblurring. The source codes will be made available at https://github.com/supersupercong/UHDformer.

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NeurIPS Conference 2024 Conference Paper

Enhancing Graph Transformers with Hierarchical Distance Structural Encoding

Yuankai Luo
Hongkang Li
Lei Shi
Xiao-ming Wu

Graph transformers need strong inductive biases to derive meaningful attention scores. Yet, current methods often fall short in capturing longer ranges, hierarchical structures, or community structures, which are common in various graphs such as molecules, social networks, and citation networks. This paper presents a Hierarchical Distance Structural Encoding (HDSE) method to model node distances in a graph, focusing on its multi-level, hierarchical nature. We introduce a novel framework to seamlessly integrate HDSE into the attention mechanism of existing graph transformers, allowing for simultaneous application with other positional encodings. To apply graph transformers with HDSE to large-scale graphs, we further propose a high-level HDSE that effectively biases the linear transformers towards graph hierarchies. We theoretically prove the superiority of HDSE in terms of expressivity and generalization. Empirically, we demonstrate that graph transformers with HDSE excel in graph classification, regression on 7 graph-level datasets, and node classification on 11 large-scale graphs.

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NeurIPS Conference 2024 Conference Paper

Grasp as You Say: Language-guided Dexterous Grasp Generation

Yi-Lin Wei
Jian-Jian Jiang
Chengyi Xing
Xian-Tuo Tan
Xiao-ming Wu
Hao Li
Mark Cutkosky
Wei-Shi Zheng

This paper explores a novel task "Dexterous Grasp as You Say'' (DexGYS), enabling robots to perform dexterous grasping based on human commands expressed in natural language. However, the development of this field is hindered by the lack of datasets with natural human guidance; thus, we propose a language-guided dexterous grasp dataset, named DexGYSNet, offering high-quality dexterous grasp annotations along with flexible and fine-grained human language guidance. Our dataset construction is cost-efficient, with the carefully-design hand-object interaction retargeting strategy, and the LLM-assisted language guidance annotation system. Equipped with this dataset, we introduce the DexGYSGrasp framework for generating dexterous grasps based on human language instructions, with the capability of producing grasps that are intent-aligned, high quality and diversity. To achieve this capability, our framework decomposes the complex learning process into two manageable progressive objectives and introduce two components to realize them. The first component learns the grasp distribution focusing on intention alignment and generation diversity. And the second component refines the grasp quality while maintaining intention consistency. Extensive experiments are conducted on DexGYSNet and real world environments for validation.

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TMLR Journal 2024 Journal Article

HiFE: Hierarchical Feature Ensemble Framework for Few-shot Hypotheses Adaptation

Yongfeng Zhong
Haoang Chi
Feng Liu
Xiao-ming Wu
Bo Han

The process of transferring knowledge from a source domain to a target domain in the absence of source data constitutes a formidable obstacle within the field of source-free domain adaptation, often termed hypothesis adaptation. Conventional methodologies have been dependent on a robustly trained (strong) source hypothesis to encapsulate the knowledge pertinent to the source domain. However, this strong hypothesis is prone to overfitting the source domain, resulting in diminished generalization performance when applied to the target domain. To mitigate this issue, we advocate for the augmentation of transferable source knowledge via the integration of multiple (weak) source models that are underfitting. Furthermore, we propose a novel architectural framework, designated as the Hierarchical Feature Ensemble (HiFE) framework for Few-Shot Hypotheses Adaptation, which amalgamates features from both the strong and intentionally underfit source models. Empirical evidence from our experiments indicates that these weaker models, while not optimal within the source domain context, contribute to an enhanced generalization capacity of the resultant model for the target domain. Moreover, the HiFE framework we introduce demonstrates superior performance, surpassing other leading baselines across a spectrum of few-shot hypothesis adaptation scenarios.

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AAAI Conference 2024 Conference Paper

SelfPromer: Self-Prompt Dehazing Transformers with Depth-Consistency

Cong Wang
Jinshan Pan
Wanyu Lin
Jiangxin Dong
Wei Wang
Xiao-ming Wu

This work presents an effective depth-consistency Self-Prompt Transformer, terms as SelfPromer, for image dehazing. It is motivated by an observation that the estimated depths of an image with haze residuals and its clear counterpart vary. Enforcing the depth consistency of dehazed images with clear ones, therefore, is essential for dehazing. For this purpose, we develop a prompt based on the features of depth differences between the hazy input images and corresponding clear counterparts that can guide dehazing models for better restoration. Specifically, we first apply deep features extracted from the input images to the depth difference features for generating the prompt that contains the haze residual information in the input. Then we propose a prompt embedding module that is designed to perceive the haze residuals, by linearly adding the prompt to the deep features. Further, we develop an effective prompt attention module to pay more attention to haze residuals for better removal. By incorporating the prompt, prompt embedding, and prompt attention into an encoder-decoder network based on VQGAN, we can achieve better perception quality. As the depths of clear images are not available at inference, and the dehazed images with one-time feed-forward execution may still contain a portion of haze residuals, we propose a new continuous self-prompt inference that can iteratively correct the dehazing model towards better haze-free image generation. Extensive experiments show that our SelfPromer performs favorably against the state-of-the-art approaches on both synthetic and real-world datasets in terms of perception metrics including NIQE, PI, and PIQE. The source codes will be made available at https://github.com/supersupercong/SelfPromer.

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AAAI Conference 2023 Conference Paper

Boosting Few-Shot Text Classification via Distribution Estimation

Han Liu
Feng Zhang
Xiaotong Zhang
Siyang Zhao
Fenglong Ma
Xiao-ming Wu
Hongyang Chen
Hong Yu

Distribution estimation has been demonstrated as one of the most effective approaches in dealing with few-shot image classification, as the low-level patterns and underlying representations can be easily transferred across different tasks in computer vision domain. However, directly applying this approach to few-shot text classification is challenging, since leveraging the statistics of known classes with sufficient samples to calibrate the distributions of novel classes may cause negative effects due to serious category difference in text domain. To alleviate this issue, we propose two simple yet effective strategies to estimate the distributions of the novel classes by utilizing unlabeled query samples, thus avoiding the potential negative transfer issue. Specifically, we first assume a class or sample follows the Gaussian distribution, and use the original support set and the nearest few query samples to estimate the corresponding mean and covariance. Then, we augment the labeled samples by sampling from the estimated distribution, which can provide sufficient supervision for training the classification model. Extensive experiments on eight few-shot text classification datasets show that the proposed method outperforms state-of-the-art baselines significantly.

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AAAI Conference 2023 Conference Paper

Continual Graph Convolutional Network for Text Classification

Tiandeng Wu
Qijiong Liu
Yi Cao
Yao Huang
Xiao-ming Wu
Jiandong Ding

Graph convolutional network (GCN) has been successfully applied to capture global non-consecutive and long-distance semantic information for text classification. However, while GCN-based methods have shown promising results in offline evaluations, they commonly follow a seen-token-seen-document paradigm by constructing a fixed document-token graph and cannot make inferences on new documents. It is a challenge to deploy them in online systems to infer steaming text data. In this work, we present a continual GCN model (ContGCN) to generalize inferences from observed documents to unobserved documents. Concretely, we propose a new all-token-any-document paradigm to dynamically update the document-token graph in every batch during both the training and testing phases of an online system. Moreover, we design an occurrence memory module and a self-supervised contrastive learning objective to update ContGCN in a label-free manner. A 3-month A/B test on Huawei public opinion analysis system shows ContGCN achieves 8.86% performance gain compared with state-of-the-art methods. Offline experiments on five public datasets also show ContGCN can improve inference quality. The source code will be released at https://github.com/Jyonn/ContGCN.

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NeurIPS Conference 2023 Conference Paper

Real-World Image Super-Resolution as Multi-Task Learning

Wenlong Zhang
Xiaohui Li
Guangyuan SHI
Xiangyu Chen
Yu Qiao
Xiaoyun Zhang
Xiao-ming Wu
Chao Dong

In this paper, we take a new look at real-world image super-resolution (real-SR) from a multi-task learning perspective. We demonstrate that the conventional formulation of real-SR can be viewed as solving multiple distinct degradation tasks using a single shared model. This poses a challenge known as task competition or task conflict in multi-task learning, where certain tasks dominate the learning process, resulting in poor performance on other tasks. This problem is exacerbated in the case of real-SR, due to the involvement of numerous degradation tasks. To address the issue of task competition in real-SR, we propose a task grouping approach. Our approach efficiently identifies the degradation tasks where a real-SR model falls short and groups these unsatisfactory tasks into multiple task groups. We then utilize the task groups to fine-tune the real-SR model in a simple way, which effectively mitigates task competition and facilitates knowledge transfer. Extensive experiments demonstrate our method achieves significantly enhanced performance across a wide range of degradation scenarios.

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AAAI Conference 2022 Conference Paper

Online Enhanced Semantic Hashing: Towards Effective and Efficient Retrieval for Streaming Multi-Modal Data

Xiao-ming Wu
Xin Luo
Yu-Wei Zhan
Chen-Lu Ding
Zhen-Duo Chen
Xin-Shun Xu

With the vigorous development of multimedia equipments and applications, efficient retrieval of large-scale multi-modal data has become a trendy research topic. Thereinto, hashing has become a prevalent choice due to its retrieval efficiency and low storage cost. Although multi-modal hashing has drawn lots of attention in recent years, there still remain some problems. The first point is that existing methods are mainly designed in batch mode and not able to efficiently handle streaming multi-modal data. The second point is that all existing online multi-modal hashing methods fail to effectively handle unseen new classes which come continuously with streaming data chunks. In this paper, we propose a new model, termed Online enhAnced SemantIc haShing (OASIS). We design novel semantic-enhanced representation for data, which could help handle the new coming classes, and thereby construct the enhanced semantic objective function. An efficient and effective discrete online optimization algorithm is further proposed for OASIS. Extensive experiments show that our method can exceed the state-of-the-art models. For good reproducibility and benefiting the community, our code and data are already publicly available.

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AAAI Conference 2022 Conference Paper

Online-Updated High-Order Collaborative Networks for Single Image Deraining

Cong Wang
Jinshan Pan
Xiao-ming Wu

Single image deraining is an important and challenging task for some downstream artificial intelligence applications such as video surveillance and self-driving systems. Most of the existing deep-learning-based methods constrain the network to generate derained images but few of them explore features from intermediate layers, different levels, and different modules which are beneficial for rain streaks removal. In this paper, we propose a high-order collaborative network with multi-scale compact constraints and a bidirectional scale-content similarity mining module to exploit features from deep networks externally and internally for rain streaks removal. Externally, we design a deraining framework with three sub-networks trained in a collaborative manner, where the bottom network transmits intermediate features to the middle network which also receives shallower rainy features from the top network and sends back features to the bottom network. Internally, we enforce multi-scale compact constraints on the intermediate layers of deep networks to learn useful features via a Laplacian pyramid. Further, we develop a bidirectional scale-content similarity mining module to explore features at different scales in a down-to-up and up-to-down manner. To improve the model performance on real-world images, we propose an online-update learning approach, which uses real-world rainy images to finetune the network and update the deraining results in a selfsupervised manner. Extensive experiments demonstrate that our proposed method performs favorably against eleven stateof-the-art methods on five public synthetic datasets and one real-world dataset.

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NeurIPS Conference 2021 Conference Paper

Overcoming Catastrophic Forgetting in Incremental Few-Shot Learning by Finding Flat Minima

Guangyuan SHI
Jiaxin Chen
Wenlong Zhang
Li-ming Zhan
Xiao-ming Wu

This paper considers incremental few-shot learning, which requires a model to continually recognize new categories with only a few examples provided. Our study shows that existing methods severely suffer from catastrophic forgetting, a well-known problem in incremental learning, which is aggravated due to data scarcity and imbalance in the few-shot setting. Our analysis further suggests that to prevent catastrophic forgetting, actions need to be taken in the primitive stage -- the training of base classes instead of later few-shot learning sessions. Therefore, we propose to search for flat local minima of the base training objective function and then fine-tune the model parameters within the flat region on new tasks. In this way, the model can efficiently learn new classes while preserving the old ones. Comprehensive experimental results demonstrate that our approach outperforms all prior state-of-the-art methods and is very close to the approximate upper bound. The source code is available at https: //github. com/moukamisama/F2M.

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NeurIPS Conference 2020 Conference Paper

A Closer Look at the Training Strategy for Modern Meta-Learning

Jiaxin Chen
Xiao-ming Wu
Yanke Li
Qimai Li
Li-ming Zhan
Fu-lai Chung

The support/query (S/Q) episodic training strategy has been widely used in modern meta-learning algorithms and is believed to improve their generalization ability to test environments. This paper conducts a theoretical investigation of this training strategy on generalization. From a stability perspective, we analyze the generalization error bound of generic meta-learning algorithms trained with such strategy. We show that the S/Q episodic training strategy naturally leads to a counterintuitive generalization bound of $O(1/\sqrt{n})$, which only depends on the task number $n$ but independent of the inner-task sample size $m$. Under the common assumption $m<<n$ for few-shot learning, the bound of $O(1/\sqrt{n})$ implies strong generalization guarantees for modern meta-learning algorithms in the few-shot regime. To further explore the influence of training strategies on generalization, we propose a leave-one-out (LOO) training strategy for meta-learning and compare it with S/Q training. Experiments on standard few-shot regression and classification tasks with popular meta-learning algorithms validate our analysis.

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AAAI Conference 2020 Conference Paper

Variational Metric Scaling for Metric-Based Meta-Learning

Jiaxin Chen
Li-ming Zhan
Xiao-ming Wu
Fu-lai Chung

Metric-based meta-learning has attracted a lot of attention due to its effectiveness and efficiency in few-shot learning. Recent studies show that metric scaling plays a crucial role in the performance of metric-based meta-learning algorithms. However, there still lacks a principled method for learning the metric scaling parameter automatically. In this paper, we recast metric-based meta-learning from a Bayesian perspective and develop a variational metric scaling framework for learning a proper metric scaling parameter. Firstly, we propose a stochastic variational method to learn a single global scaling parameter. To better fit the embedding space to a given data distribution, we extend our method to learn a dimensional scaling vector to transform the embedding space. Furthermore, to learn task-specific embeddings, we generate task-dependent dimensional scaling vectors with amortized variational inference. Our method is end-to-end without any pre-training and can be used as a simple plug-and-play module for existing metric-based meta-algorithms. Experiments on miniImageNet show that our methods can be used to consistently improve the performance of existing metric-based meta-algorithms including prototypical networks and TADAM.

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IJCAI Conference 2019 Conference Paper

Attributed Graph Clustering via Adaptive Graph Convolution

Xiaotong Zhang
Han Liu
Qimai Li
Xiao-ming Wu

Attributed graph clustering is challenging as it requires joint modelling of graph structures and node attributes. Recent progress on graph convolutional networks has proved that graph convolution is effective in combining structural and content information, and several recent methods based on it have achieved promising clustering performance on some real attributed networks. However, there is limited understanding of how graph convolution affects clustering performance and how to properly use it to optimize performance for different graphs. Existing methods essentially use graph convolution of a fixed and low order that only takes into account neighbours within a few hops of each node, which underutilizes node relations and ignores the diversity of graphs. In this paper, we propose an adaptive graph convolution method for attributed graph clustering that exploits high-order graph convolution to capture global cluster structure and adaptively selects the appropriate order for different graphs. We establish the validity of our method by theoretical analysis and extensive experiments on benchmark datasets. Empirical results show that our method compares favourably with state-of-the-art methods.

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AAAI Conference 2018 Conference Paper

Deeper Insights Into Graph Convolutional Networks for Semi-Supervised Learning

Qimai Li
Zhichao Han
Xiao-ming Wu

Many interesting problems in machine learning are being revisited with new deep learning tools. For graph-based semisupervised learning, a recent important development is graph convolutional networks (GCNs), which nicely integrate local vertex features and graph topology in the convolutional layers. Although the GCN model compares favorably with other state-of-the-art methods, its mechanisms are not clear and it still requires considerable amount of labeled data for validation and model selection. In this paper, we develop deeper insights into the GCN model and address its fundamental limits. First, we show that the graph convolution of the GCN model is actually a special form of Laplacian smoothing, which is the key reason why GCNs work, but it also brings potential concerns of oversmoothing with many convolutional layers. Second, to overcome the limits of the GCN model with shallow architectures, we propose both co-training and self-training approaches to train GCNs. Our approaches signiﬁcantly improve GCNs in learning with very few labels, and exempt them from requiring additional labels for validation. Extensive experiments on benchmarks have veriﬁed our theory and proposals.

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NeurIPS Conference 2013 Conference Paper

Analyzing the Harmonic Structure in Graph-Based Learning

Xiao-ming Wu
Zhenguo Li
Shih-Fu Chang

We show that either explicitly or implicitly, various well-known graph-based models exhibit a common significant \emph{harmonic} structure in its target function -- the value of a vertex is approximately the weighted average of the values of its adjacent neighbors. Understanding of such structure and analysis of the loss defined over such structure help reveal important properties of the target function over a graph. In this paper, we show that the variation of the target function across a cut can be upper and lower bounded by the ratio of its harmonic loss and the cut cost. We use this to develop an analytical tool and analyze 5 popular models in graph-based learning: absorbing random walks, partially absorbing random walks, hitting times, pseudo-inverse of graph Laplacian, and eigenvectors of the Laplacian matrices. Our analysis well explains several open questions of these models reported in the literature. Furthermore, it provides theoretical justifications and guidelines for their practical use. Simulations on synthetic and real datasets support our analysis.

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NeurIPS Conference 2012 Conference Paper

Learning with Partially Absorbing Random Walks

Xiao-ming Wu
Zhenguo Li
Anthony So
John Wright
Shih-Fu Chang

We propose a novel stochastic process that is with probability $\alpha_i$ being absorbed at current state $i$, and with probability $1-\alpha_i$ follows a random edge out of it. We analyze its properties and show its potential for exploring graph structures. We prove that under proper absorption rates, a random walk starting from a set $\mathcal{S}$ of low conductance will be mostly absorbed in $\mathcal{S}$. Moreover, the absorption probabilities vary slowly inside $\mathcal{S}$, while dropping sharply outside $\mathcal{S}$, thus implementing the desirable cluster assumption for graph-based learning. Remarkably, the partially absorbing process unifies many popular models arising in a variety of contexts, provides new insights into them, and makes it possible for transferring findings from one paradigm to another. Simulation results demonstrate its promising applications in graph-based learning.

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NeurIPS Conference 2009 Conference Paper

Fast Graph Laplacian Regularized Kernel Learning via Semidefinite–Quadratic–Linear Programming

Xiao-ming Wu
Anthony So
Zhenguo Li
Shuo-yen Li

Kernel learning is a powerful framework for nonlinear data modeling. Using the kernel trick, a number of problems have been formulated as semidefinite programs (SDPs). These include Maximum Variance Unfolding (MVU) (Weinberger et al. , 2004) in nonlinear dimensionality reduction, and Pairwise Constraint Propagation (PCP) (Li et al. , 2008) in constrained clustering. Although in theory SDPs can be efficiently solved, the high computational complexity incurred in numerically processing the huge linear matrix inequality constraints has rendered the SDP approach unscalable. In this paper, we show that a large class of kernel learning problems can be reformulated as semidefinite-quadratic-linear programs (SQLPs), which only contain a simple positive semidefinite constraint, a second-order cone constraint and a number of linear constraints. These constraints are much easier to process numerically, and the gain in speedup over previous approaches is at least of the order $m^{2. 5}$, where m is the matrix dimension. Experimental results are also presented to show the superb computational efficiency of our approach.

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NeurIPS Conference 2008 Conference Paper

Convergence and Rate of Convergence of a Manifold-Based Dimension Reduction Algorithm

Andrew Smith
Hongyuan Zha
Xiao-ming Wu

We study the convergence and the rate of convergence of a local manifold learning algorithm: LTSA [13]. The main technical tool is the perturbation analysis on the linear invariant subspace that corresponds to the solution of LTSA. We derive a worst-case upper bound of errors for LTSA which naturally leads to a convergence result. We then derive the rate of convergence for LTSA in a special case.

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