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En Zhu

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48 papers
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48

AAAI Conference 2026 Conference Paper

DMCAR: Disentangled Mixture-of-Experts with Context-Aware Routing for Multi-View Clustering

  • Baili Xiao
  • Ke Liang
  • Jiaqi Jin
  • Jun Wang
  • Yinbo Xu
  • Siwei Wang
  • En Zhu

Multi-View Clustering (MVC) aims to enhance clustering performance by integrating multi-source complementary information. However, existing deep MVC methods face inherent challenges in balancing the learning of shared consensus representations with the preservation of view-specific information: independent encoders hinder effective cross-view collaboration, while a single shared encoder tends to sacrifice representation diversity. Although the recently introduced Mixture-of-Experts (MoE) model offers a novel approach to facilitating view collaboration, its flattened expert pool design often leads to entanglement between shared and specific information, and its routing mechanism limits collaboration potential by neglecting cross-view context. To address these challenges, this paper proposes a novel deep multi-view clustering framework—Decoupled Mixture-of-Experts with Context-Aware Routing for Multi-View Clustering (DMCAR-MVC). At its core is an innovative Decoupled MoE (D-MoE) architecture. We establish a public expert pool to learn cross-view shared representations while equipping each view with an independent private expert pool to capture its unique information, thereby structurally enforcing the decoupling of shared and specific representations. Building on this, we further design a Context-Aware Hierarchical Routing (CAHR) mechanism. When routing for the public expert pool, this mechanism introduces a global context vector to guide expert selection, enabling more efficient and globally informed cross-view collaboration. Finally, to optimize the model, we adopt a multi-level contrastive learning paradigm: on one hand, a cross-view alignment loss ensures semantic consistency in shared representations; on the other, an orthogonality constraint is imposed to further enhance separability between shared and specific representations. Extensive experiments on multiple benchmark datasets demonstrate that DMCAR-MVC significantly outperforms state-of-the-art methods across key clustering metrics. Additionally, comprehensive ablation studies thoroughly validate the effectiveness and necessity of each proposed component.

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AAAI Conference 2026 Conference Paper

Hierarchical Cross-View Alignment for Multi-View Clustering via Decoupled Information Distillation

  • Taichun Zhou
  • Siwei Wang
  • Zhibin Dong
  • Jiaqi Jin
  • Ke Liang
  • Baili Xiao
  • Miaomiao Li
  • Xinwang Liu

Multi-view clustering aims to uncover shared semantics and complementary information across different views. However, the inherent heterogeneity among views poses significant challenges to effective collaborative modeling and information integration. While recent studies have introduced distillation-based mechanisms to enhance cross-view consistency and alleviate heterogeneity, these approaches often rely on manually defined knowledge transfer paths or fixed fusion weights, which are inflexible in handling complex and dynamic view relationships in practice. To address this issue, we propose HOARD: a novel framework for Hierarchical crOss-view Alignment for multi-view clusteRing via Decoupled information distillation. HOARD structurally decouples multi-view representations into shared and specific components, and performs hierarchical alignment. Specifically, we introduce a granular-ball contrastive alignment to enhance the semantic consistency of shared features, and a prototype collaborative transmission alignment strategy to align specific features while preserving view-specific structural characteristics. Moreover, we design an information distillation unit to adaptively model cross-view knowledge transfer in both feature spaces. An attention mechanism is further employed to integrate shared and specific information. Extensive experiments on benchmark datasets demonstrate that HOARD significantly improves alignment quality and clustering performance, achieving state-of-the-art results.

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AAAI Conference 2026 Conference Paper

Sample-specific Modality Diagnosis and Cross-modal Enhancement for Incomplete Multimodal Representations

  • Junsong Chen
  • Jiyuan Liu
  • Suyuan Liu
  • Wei Zhang
  • Ao Li
  • En Zhu
  • Xinwang Liu

In multimodal sentiment analysis, modality missingness and quality degradation are common. Existing methods often rely on batch-level modality generation, generation but neglect sample-level missingness, hence their flexibility is limited severely in real-world scenarios. To address this, Sample-specific Modality Diagnosis and Cross-modal Enhancement for Incomplete Multimodal Representations (SMCIR) is proposed. Specifically, The Dynamic Multi-feature Fusion Detector (DMFD) is presented, which detects missingness and severity at the sample-level using indicators such as information entropy, modality similarity, and mutual information. Unlike batch-based methods, the DMFD provides fine-grained detection and adaptive responses, improving sensitivity to modality disturbances. Meanwhile, the Context-aware Modality Completion Generator (CMCG) is developed to restore missing modalities through context-guided reconstruction using multiscale feature fusion and cross-modal attention. In this way, the proposed CMCG method can avoid redundancy and inconsistency, enhancing the consistency and discriminativity of the fused representation. In CMCG, the text modality serves as a stable guide to improve context consistency. Experiments on the CMU-MOSI and CMU-MOSEI datasets show that SMCIR outperforms existing full-modal and non-recovery-based methods, well validating its efficacy and superiority in multimodal learning.

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ICML Conference 2025 Conference Paper

Automatically Identify and Rectify: Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios

  • Xihong Yang
  • Siwei Wang 0001
  • Fangdi Wang
  • Jiaqi Jin
  • Suyuan Liu
  • Yue Liu 0008
  • En Zhu
  • Xinwang Liu 0002

Leveraging the powerful representation learning capabilities, deep multi-view clustering methods have demonstrated reliable performance by effectively integrating multi-source information from diverse views in recent years. Most existing methods rely on the assumption of clean views. However, noise is pervasive in real-world scenarios, leading to a significant degradation in performance. To tackle this problem, we propose a novel multi-view clustering framework for the automatic identification and rectification of noisy data, termed AIRMVC. Specifically, we reformulate noisy identification as an anomaly identification problem using GMM. We then design a hybrid rectification strategy to mitigate the adverse effects of noisy data based on the identification results. Furthermore, we introduce a noise-robust contrastive mechanism to generate reliable representations. Additionally, we provide a theoretical proof demonstrating that these representations can discard noisy information, thereby improving the performance of downstream tasks. Extensive experiments on six benchmark datasets demonstrate that AIRMVC outperforms state-of-the-art algorithms in terms of robustness in noisy scenarios. The code of AIRMVC are available at https: //github. com/xihongyang1999/AIRMVC on Github.

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ICML Conference 2025 Conference Paper

Bifurcate then Alienate: Incomplete Multi-view Clustering via Coupled Distribution Learning with Linear Overhead

  • Shengju Yu
  • Yiu-ming Cheung
  • Siwei Wang 0001
  • Xinwang Liu 0002
  • En Zhu

Despite remarkable advances, existing incomplete multi-view clustering (IMC) methods typically leverage either perspective-shared or perspective-specific determinants to encode cluster representations. To address this limitation, we introduce a BACDL algorithm designed to explicitly capture both concurrently, thereby exploiting heterogeneous data more effectively. It chooses to bifurcate feature clusters and further alienate them to enlarge the discrimination. With distribution learning, it successfully couples view guidance into feature clusters to alleviate dimension inconsistency. Then, building on the principle that samples in one common cluster own similar marginal distribution and conditional distribution, it unifies the association between feature clusters and sample clusters to bridge all views. Thereafter, all incomplete sample clusters are reordered and mapped to a common one to formulate clustering embedding. Last, the overall linear overhead endows it with a resource-efficient characteristic.

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IJCAI Conference 2025 Conference Paper

Code-BT: A Code-Driven Approach to Behavior Tree Generation for Robot Tasks Planning with Large Language Models

  • Siyang Zhang
  • Bin Li
  • Jingtao Qi
  • Xueying Wang
  • Fu Li
  • Jianan Wang
  • En Zhu
  • Jinjing Sun

Behavior trees(BTs) provide a systematic and structured control architecture extensively employed in game AI and robotic behavior control, owing to their modularity, reactivity, and reusability. Nonetheless, manual BTs design requires significant expertise and becomes inefficient as task complexity increases. Recent automation technologies have avoided manual work, but often have high application barriers and face challenges in adapting to new tasks, making it difficult to easily configure them to specific requirements. Code-BT introduces a novel approach that utilizes large language models(LLMs) to automatically generate BTs, representing the task planning process as the process of coding and organizing sequences. By retrieving control flow information from the generated code, BTs can be efficiently constructed to address the complexity and diversity of task planning challenges. Rather than relying on manual design, Code-BT uses task instructions to guide the selection of relevant APIs, and then systematically assembles these APIs into modular code to align with the BTs structure. Finally, action sequences and control logic are extracted from the generated code to construct the BTs. Our approach not only ensures the automation of BTs generation but also guarantees the scalability and adaptability for long-term tasks. Experimental results demonstrate that Code-BT substantially improves LLM performance in BTs generation, achieving improvements ranging from16. 67% to 29. 17%.

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ICML Conference 2025 Conference Paper

COKE: Core Kernel for More Efficient Approximation of Kernel Weights in Multiple Kernel Clustering

  • Weixuan Liang
  • Xinwang Liu 0002
  • Ke Liang 0006
  • Jiyuan Liu 0003
  • En Zhu

Inspired by the well-known coreset in clustering algorithms, we introduce the definition of the core kernel for multiple kernel clustering (MKC) algorithms. The core kernel refers to running MKC algorithms on smaller-scale base kernel matrices to obtain kernel weights similar to those obtained from the original full-scale kernel matrices. Specifically, the core kernel refers to a set of kernel matrices of size $\widetilde{\mathcal{O}}(1/\varepsilon^2)$ that perform MKC algorithms on them can achieve a $(1+\varepsilon)$-approximation for the kernel weights. Subsequently, we can leverage approximated kernel weights to obtain a theoretically guaranteed large-scale extension of MKC algorithms. In this paper, we propose a core kernel construction method based on singular value decomposition and prove that it satisfies the definition of the core kernel for three mainstream MKC algorithms. Finally, we conduct experiments on several benchmark datasets to verify the correctness of theoretical results and the efficiency of the proposed method.

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ICLR Conference 2025 Conference Paper

DLEFT-MKC: Dynamic Late Fusion Multiple Kernel Clustering with Robust Tensor Learning via Min-Max Optimization

  • Yi Zhang 0104
  • Siwei Wang 0001
  • Jiyuan Liu 0003
  • Shengju Yu
  • Zhibin Dong
  • Suyuan Liu
  • Xinwang Liu 0002
  • En Zhu

Recent advancements in multiple kernel clustering (MKC) have highlighted the effectiveness of late fusion strategies, particularly in enhancing computational efficiency to near-linear complexity while achieving promising clustering performance. However, existing methods encounter three significant limitations: (1) reliance on fixed base partition matrices that do not adaptively optimize during the clustering process, thereby constraining their performance to the inherent representational capabilities of these matrices; (2) a focus on adjusting kernel weights to explore inter-view consistency and complementarity, which often neglects the intrinsic high-order correlations among views, thereby limiting the extraction of comprehensive multiple kernel information; (3) a lack of adaptive mechanisms to accommodate varying distributions within the data, which limits robustness and generalization. To address these challenges, this paper proposes a novel algorithm termed Dynamic Late Fusion Multiple Kernel Clustering with Robust {Tensor Learning via min-max optimization (DLEFT-MKC), which effectively overcomes the representational bottleneck of base partition matrices and facilitates the learning of meaningful high-order cross-view information. Specifically, it is the first to incorporate a min-max optimization paradigm into tensor-based MKC, enhancing algorithm robustness and generalization. Additionally, it dynamically reconstructs decision layers to enhance representation capabilities and subsequently stacks the reconstructed representations for tensor learning that promotes the capture of high-order associations and cluster structures across views, ultimately yielding consensus clustering partitions. To solve the resultant optimization problem, we innovatively design a strategy that combines reduced gradient descent with the alternating direction method of multipliers, ensuring convergence to local optima while maintaining high computational efficiency. Extensive experimental results across various benchmark datasets validate the superior effectiveness and efficiency of the proposed DLEFT-MKC.

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ICML Conference 2025 Conference Paper

Efficient Federated Incomplete Multi-View Clustering

  • Suyuan Liu
  • Hao Yu 0017
  • Hao Tan
  • Ke Liang 0006
  • Siwei Wang 0001
  • Shengju Yu
  • En Zhu
  • Xinwang Liu 0002

Multi-view clustering (MVC) leverages complementary information from diverse data sources to enhance clustering performance. However, its practical deployment in distributed and privacy-sensitive scenarios remains challenging. Federated multi-view clustering (FMVC) has emerged as a potential solution, but existing approaches suffer from substantial limitations, including excessive communication overhead, insufficient privacy protection, and inadequate handling of missing views. To address these issues, we propose Efficient Federated Incomplete Multi-View Clustering (EFIMVC), a novel framework that introduces a localized optimization strategy to significantly reduce communication costs while ensuring theoretical convergence. EFIMVC employs both view-specific and shared anchor graphs as communication variables, thereby enhancing privacy by avoiding the transmission of sensitive embeddings. Moreover, EFIMVC seamlessly extends to scenarios with missing views, making it a practical and scalable solution for real-world applications. Extensive experiments on benchmark datasets demonstrate the superiority of EFIMVC in clustering accuracy, communication efficiency, and privacy preservation. Our code is publicly available at https: //github. com/Tracesource/EFIMVC.

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AAAI Conference 2025 Conference Paper

Max-Mahalanobis Anchors Guidance for Multi-View Clustering

  • Pei Zhang
  • Yuangang Pan
  • Siwei Wang
  • Shengju Yu
  • Huiying Xu
  • En Zhu
  • Xinwang Liu
  • Ivor Tsang

Anchor selection or learning has become a critical component in large-scale multi-view clustering. Existing anchor-based methods, which either select-then-fix or initialize-then-optimize with orthogonality, yield promising performance. However, these methods still suffer from instability of initialization or insufficient depiction of data distribution. Moreover, the desired properties of anchors in multi-view clustering remain unspecified. To address these issues, this paper first formalizes the desired characteristics of anchors, namely Diversity, Balance and Compactness. We then devise and mathematically validate anchors that satisfy these properties by maximizing the Mahalanobis distance between anchors. Furthermore, we introduce a novel method called Max-Mahalanobis Anchors Guidance for multi-view Clustering (MAGIC), which guides the cross-view representations to progressively align with our well-defined anchors. This process yields highly discriminative and compact representations, significantly enhancing the performance of multi-view clustering. Experimental results show that our meticulously designed strategy significantly outperforms existing anchor-based methods in enhancing anchor efficacy, leading to substantial improvement in multi-view clustering performance.

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AAAI Conference 2024 Conference Paper

A Non-parametric Graph Clustering Framework for Multi-View Data

  • Shengju Yu
  • Siwei Wang
  • Zhibin Dong
  • Wenxuan Tu
  • Suyuan Liu
  • Zhao Lv
  • Pan Li
  • Miao Wang

Multi-view graph clustering (MVGC) derives encouraging grouping results by seamlessly integrating abundant information inside heterogeneous data, and has captured surging focus recently. Nevertheless, the majority of current MVGC works involve at least one hyper-parameter, which not only requires additional efforts for tuning, but also leads to a complicated solving procedure, largely harming the flexibility and scalability of corresponding algorithms. To this end, in the article we are devoted to getting rid of hyper-parameters, and devise a non-parametric graph clustering (NpGC) framework to more practically partition multi-view data. To be specific, we hold that hyper-parameters play a role in balancing error item and regularization item so as to form high-quality clustering representations. Therefore, under without the assistance of hyper-parameters, how to acquire high-quality representations becomes the key. Inspired by this, we adopt two types of anchors, view-related and view-unrelated, to concurrently mine exclusive characteristics and common characteristics among views. Then, all anchors' information is gathered together via a consensus bipartite graph. By such ways, NpGC extracts both complementary and consistent multi-view features, thereby obtaining superior clustering results. Also, linear complexities enable it to handle datasets with over 120000 samples. Numerous experiments reveal NpGC's strong points compared to lots of classical approaches.

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NeurIPS Conference 2024 Conference Paper

Alleviate Anchor-Shift: Explore Blind Spots with Cross-View Reconstruction for Incomplete Multi-View Clustering

  • Suyuan Liu
  • Siwei Wang
  • Ke Liang
  • Junpu Zhang
  • Zhibin Dong
  • Tianrui Liu
  • En Zhu
  • Kunlun He

Incomplete multi-view clustering aims to learn complete correlations among samples by leveraging complementary information across multiple views for clustering. Anchor-based methods further establish sample-level similarities for representative anchor generation, effectively addressing scalability issues in large-scale scenarios. Despite efficiency improvements, existing methods overlook the misguidance in anchors learning induced by partial missing samples, i. e. , the absence of samples results in shift of learned anchors, further leading to sub-optimal clustering performance. To conquer the challenges, our solution involves a cross-view reconstruction strategy that not only alleviate the anchor shift problem through a carefully designed cross-view learning process, but also reconstructs missing samples in a way that transcends the limitations imposed by convex combinations. By employing affine combinations, our method explores areas beyond the convex hull defined by anchors, thereby illuminating blind spots in the reconstruction of missing samples. Experimental results on four benchmark datasets and three large-scale datasets validate the effectiveness of our proposed method.

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ICML Conference 2024 Conference Paper

Decouple then Classify: A Dynamic Multi-view Labeling Strategy with Shared and Specific Information

  • Xinhang Wan
  • Jiyuan Liu 0003
  • Xinwang Liu 0002
  • Yi Wen 0001
  • Hao Yu 0017
  • Siwei Wang 0001
  • Shengju Yu
  • Tianjiao Wan

Sample labeling is the most primary and fundamental step of semi-supervised learning. In literature, most existing methods randomly label samples with a given ratio, but achieve unpromising and unstable results due to the randomness, especially in multi-view settings. To address this issue, we propose a Dynamic Multi-view Labeling Strategy with Shared and Specific Information. To be brief, by building two classifiers with existing labels to utilize decoupled shared and specific information, we select the samples of low classification confidence and label them in high priorities. The newly generated labels are also integrated to update the classifiers adaptively. The two processes are executed alternatively until a satisfying classification performance. To validate the effectiveness of the proposed method, we conduct extensive experiments on popular benchmarks, achieving promising performance. The code is publicly available at https: //github. com/wanxinhang/ICML2024_decouple_then_classify.

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AAAI Conference 2024 Conference Paper

DVSAI: Diverse View-Shared Anchors Based Incomplete Multi-View Clustering

  • Shengju Yu
  • Siwei Wang
  • Pei Zhang
  • Miao Wang
  • Ziming Wang
  • Zhe Liu
  • Liming Fang
  • En Zhu

In numerous real-world applications, it is quite common that sample information is partially available for some views due to machine breakdown or sensor failure, causing the problem of incomplete multi-view clustering (IMVC). While several IMVC approaches using view-shared anchors have successfully achieved pleasing performance improvement, (1) they generally construct anchors with only one dimension, which could deteriorate the multi-view diversity, bringing about serious information loss; (2) the constructed anchors are typically with a single size, which could not sufficiently characterize the distribution of the whole samples, leading to limited clustering performance. For generating view-shared anchors with multi-dimension and multi-size for IMVC, we design a novel framework called Diverse View-Shared Anchors based Incomplete multi-view clustering (DVSAI). Concretely, we associate each partial view with several potential spaces. In each space, we enable anchors to communicate among views and generate the view-shared anchors with space-specific dimension and size. Consequently, spaces with various scales make the generated view-shared anchors enjoy diverse dimensions and sizes. Subsequently, we devise an integration scheme with linear computational and memory expenditures to integrate the outputted multi-scale unified anchor graphs such that running spectral algorithm generates the spectral embedding. Afterwards, we theoretically demonstrate that DVSAI owns linear time and space costs, thus well-suited for tackling large-size datasets. Finally, comprehensive experiments confirm the effectiveness and advantages of DVSAI.

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NeurIPS Conference 2024 Conference Paper

Evaluate then Cooperate: Shapley-based View Cooperation Enhancement for Multi-view Clustering

  • Fangdi Wang
  • Jiaqi Jin
  • Jingtao Hu
  • Suyuan Liu
  • Xihong Yang
  • Siwei Wang
  • Xinwang Liu
  • En Zhu

The fundamental goal of deep multi-view clustering is to achieve preferable task performance through inter-view cooperation. Although numerous DMVC approaches have been proposed, the collaboration role of individual views have not been well investigated in existing literature. Moreover, how to further enhance view cooperation for better fusion still needs to be explored. In this paper, we firstly consider DMVC as an unsupervised cooperative game where each view can be regarded as a participant. Then, we introduce the Shapley value and propose a novel MVC framework termed Shapley-based Cooperation Enhancing Multi-view Clustering (SCE-MVC), which evaluates view cooperation with game theory. Specially, we employ the optimal transport distance between fused cluster distributions and single view component as the utility function for computing shapley values. Afterwards, we apply shapley values to assess the contribution of each view and utilize these contributions to promote view cooperation. Comprehensive experimental results well support the effectiveness of our framework adopting to existing DMVC frameworks, demonstrating the importance and necessity of enhancing the cooperation among views.

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AAAI Conference 2024 Conference Paper

Sample-Level Cross-View Similarity Learning for Incomplete Multi-View Clustering

  • Suyuan Liu
  • Junpu Zhang
  • Yi Wen
  • Xihong Yang
  • Siwei Wang
  • Yi Zhang
  • En Zhu
  • Chang Tang

Incomplete multi-view clustering has attracted much attention due to its ability to handle partial multi-view data. Recently, similarity-based methods have been developed to explore the complete relationship among incomplete multi-view data. Although widely applied to partial scenarios, most of the existing approaches are still faced with two limitations. Firstly, fusing similarities constructed individually on each view fails to yield a complete unified similarity. Moreover, incomplete similarity generation may lead to anomalous similarity values with column sum constraints, affecting the final clustering results. To solve the above challenging issues, we propose a Sample-level Cross-view Similarity Learning (SCSL) method for Incomplete Multi-view Clustering. Specifically, we project all samples to the same dimension and simultaneously construct a complete similarity matrix across views based on the inter-view sample relationship and the intra-view sample relationship. In addition, a simultaneously learning consensus representation ensures the validity of the projection, which further enhances the quality of the similarity matrix through the graph Laplacian regularization. Experimental results on six benchmark datasets demonstrate the ability of SCSL in processing incomplete multi-view clustering tasks. Our code is publicly available at https://github.com/Tracesource/SCSL.

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ICML Conference 2024 Conference Paper

Scalable Multiple Kernel Clustering: Learning Clustering Structure from Expectation

  • Weixuan Liang
  • En Zhu
  • Shengju Yu
  • Huiying Xu
  • Xinzhong Zhu
  • Xinwang Liu 0002

In this paper, we derive an upper bound of the difference between a kernel matrix and its expectation under a mild assumption. Specifically, we assume that the true distribution of the training data is an unknown isotropic Gaussian distribution. When the kernel function is a Gaussian kernel, and the mean of each cluster is sufficiently separated, we find that the expectation of a kernel matrix can be close to a rank-$k$ matrix, where $k$ is the cluster number. Moreover, we prove that the normalized kernel matrix of the training set deviates (w. r. t. Frobenius norm) from its expectation in the order of $\widetilde{\mathcal{O}}(1/\sqrt{d})$, where $d$ is the dimension of samples. Based on the above theoretical results, we propose a novel multiple kernel clustering framework which attempts to learn the information of the expectation kernel matrices. First, we aim to minimize the distance between each base kernel and a rank-$k$ matrix, which is a proxy of the expectation kernel. Then, we fuse these rank-$k$ matrices into a consensus rank-$k$ matrix to find the clustering structure. Using an anchor-based method, the proposed framework is flexible with the sizes of input kernel matrices and able to handle large-scale datasets. We also provide the approximation guarantee by deriving two non-asymptotic bounds for the consensus kernel and clustering indicator matrices. Finally, we conduct extensive experiments to verify the clustering performance of the proposed method and the correctness of the proposed theoretical results.

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AAAI Conference 2023 Conference Paper

Auto-Weighted Multi-View Clustering for Large-Scale Data

  • Xinhang Wan
  • Xinwang Liu
  • Jiyuan Liu
  • Siwei Wang
  • Yi Wen
  • Weixuan Liang
  • En Zhu
  • Zhe Liu

Multi-view clustering has gained broad attention owing to its capacity to exploit complementary information across multiple data views. Although existing methods demonstrate delightful clustering performance, most of them are of high time complexity and cannot handle large-scale data. Matrix factorization-based models are a representative of solving this problem. However, they assume that the views share a dimension-fixed consensus coefficient matrix and view-specific base matrices, limiting their representability. Moreover, a series of large-scale algorithms that bear one or more hyperparameters are impractical in real-world applications. To address the two issues, we propose an auto-weighted multi-view clustering (AWMVC) algorithm. Specifically, AWMVC first learns coefficient matrices from corresponding base matrices of different dimensions, then fuses them to obtain an optimal consensus matrix. By mapping original features into distinctive low-dimensional spaces, we can attain more comprehensive knowledge, thus obtaining better clustering results. Moreover, we design a six-step alternative optimization algorithm proven to be convergent theoretically. Also, AWMVC shows excellent performance on various benchmark datasets compared with existing ones. The code of AWMVC is publicly available at https://github.com/wanxinhang/AAAI-2023-AWMVC.

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AAAI Conference 2023 Conference Paper

Cluster-Guided Contrastive Graph Clustering Network

  • Xihong Yang
  • Yue Liu
  • Sihang Zhou
  • Siwei Wang
  • Wenxuan Tu
  • Qun Zheng
  • Xinwang Liu
  • Liming Fang

Benefiting from the intrinsic supervision information exploitation capability, contrastive learning has achieved promising performance in the field of deep graph clustering recently. However, we observe that two drawbacks of the positive and negative sample construction mechanisms limit the performance of existing algorithms from further improvement. 1) The quality of positive samples heavily depends on the carefully designed data augmentations, while inappropriate data augmentations would easily lead to the semantic drift and indiscriminative positive samples. 2) The constructed negative samples are not reliable for ignoring important clustering information. To solve these problems, we propose a Cluster-guided Contrastive deep Graph Clustering network (CCGC) by mining the intrinsic supervision information in the high-confidence clustering results. Specifically, instead of conducting complex node or edge perturbation, we construct two views of the graph by designing special Siamese encoders whose weights are not shared between the sibling sub-networks. Then, guided by the high-confidence clustering information, we carefully select and construct the positive samples from the same high-confidence cluster in two views. Moreover, to construct semantic meaningful negative sample pairs, we regard the centers of different high-confidence clusters as negative samples, thus improving the discriminative capability and reliability of the constructed sample pairs. Lastly, we design an objective function to pull close the samples from the same cluster while pushing away those from other clusters by maximizing and minimizing the cross-view cosine similarity between positive and negative samples. Extensive experimental results on six datasets demonstrate the effectiveness of CCGC compared with the existing state-of-the-art algorithms. The code of CCGC is available at https://github.com/xihongyang1999/CCGC on Github.

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ICML Conference 2023 Conference Paper

Consistency of Multiple Kernel Clustering

  • Weixuan Liang
  • Xinwang Liu 0002
  • Yong Liu 0018
  • Chuan Ma 0001
  • Yunping Zhao
  • Zhe Liu 0001
  • En Zhu

Consistency plays an important role in learning theory. However, in multiple kernel clustering (MKC), the consistency of kernel weights has not been sufficiently investigated. In this work, we fill this gap with a non-asymptotic analysis on the consistency of kernel weights of a novel method termed SimpleMKKM. Under the assumptions of the eigenvalue gap, we give an infinity norm bound as $\widetilde{\mathcal{O}}(k/\sqrt{n})$, where $k$ is the number of clusters and $n$ is the number of samples. On this basis, we establish an upper bound for the excess clustering risk. Moreover, we study the difference of the kernel weights learned from $n$ samples and $r$ points sampled without replacement, and derive its upper bound as $\widetilde{\mathcal{O}}(k\cdot\sqrt{1/r-1/n})$. Based on the above results, we propose a novel strategy with Nyström method to enable SimpleMKKM to handle large-scale datasets with a theoretical learning guarantee. Finally, extensive experiments are conducted to verify the theoretical results and the effectiveness of the proposed large-scale strategy.

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AAAI Conference 2023 Conference Paper

Graph Anomaly Detection via Multi-Scale Contrastive Learning Networks with Augmented View

  • Jingcan Duan
  • Siwei Wang
  • Pei Zhang
  • En Zhu
  • Jingtao Hu
  • Hu Jin
  • Yue Liu
  • Zhibin Dong

Graph anomaly detection (GAD) is a vital task in graph-based machine learning and has been widely applied in many real-world applications. The primary goal of GAD is to capture anomalous nodes from graph datasets, which evidently deviate from the majority of nodes. Recent methods have paid attention to various scales of contrastive strategies for GAD, i.e., node-subgraph and node-node contrasts. However, they neglect the subgraph-subgraph comparison information which the normal and abnormal subgraph pairs behave differently in terms of embeddings and structures in GAD, resulting in sub-optimal task performance. In this paper, we fulfill the above idea in the proposed multi-view multi-scale contrastive learning framework with subgraph-subgraph contrast for the first practice. To be specific, we regard the original input graph as the first view and generate the second view by graph augmentation with edge modifications. With the guidance of maximizing the similarity of the subgraph pairs, the proposed subgraph-subgraph contrast contributes to more robust subgraph embeddings despite of the structure variation. Moreover, the introduced subgraph-subgraph contrast cooperates well with the widely-adopted node-subgraph and node-node contrastive counterparts for mutual GAD performance promotions. Besides, we also conduct sufficient experiments to investigate the impact of different graph augmentation approaches on detection performance. The comprehensive experimental results well demonstrate the superiority of our method compared with the state-of-the-art approaches and the effectiveness of the multi-view subgraph pair contrastive strategy for the GAD task. The source code is released at https://github.com/FelixDJC/GRADATE.

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AAAI Conference 2023 Conference Paper

Let the Data Choose: Flexible and Diverse Anchor Graph Fusion for Scalable Multi-View Clustering

  • Pei Zhang
  • Siwei Wang
  • Liang Li
  • Changwang Zhang
  • Xinwang Liu
  • En Zhu
  • Zhe Liu
  • Lu Zhou

In the past few years, numerous multi-view graph clustering algorithms have been proposed to enhance the clustering performance by exploring information from multiple views. Despite the superior performance, the high time and space expenditures limit their scalability. Accordingly, anchor graph learning has been introduced to alleviate the computational complexity. However, existing approaches can be further improved by the following considerations: (i) Existing anchor-based methods share the same number of anchors across views. This strategy violates the diversity and flexibility of multi-view data distribution. (ii) Searching for the optimal anchor number within hyper-parameters takes much extra tuning time, which makes existing methods impractical. (iii) How to flexibly fuse multi-view anchor graphs of diverse sizes has not been well explored in existing literature. To address the above issues, we propose a novel anchor-based method termed Flexible and Diverse Anchor Graph Fusion for Scalable Multi-view Clustering (FDAGF) in this paper. Instead of manually tuning optimal anchor with massive hyper-parameters, we propose to optimize the contribution weights of a group of pre-defined anchor numbers to avoid extra time expenditure among views. Most importantly, we propose a novel hybrid fusion strategy for multi-size anchor graphs with theoretical proof, which allows flexible and diverse anchor graph fusion. Then, an efficient linear optimization algorithm is proposed to solve the resultant problem. Comprehensive experimental results demonstrate the effectiveness and efficiency of our proposed framework. The source code is available at https://github.com/Jeaninezpp/FDAGF.

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NeurIPS Conference 2022 Conference Paper

Align then Fusion: Generalized Large-scale Multi-view Clustering with Anchor Matching Correspondences

  • Siwei Wang
  • Xinwang Liu
  • Suyuan Liu
  • Jiaqi Jin
  • Wenxuan Tu
  • Xinzhong Zhu
  • En Zhu

Multi-view anchor graph clustering selects representative anchors to avoid full pair-wise similarities and therefore reduce the complexity of graph methods. Although widely applied in large-scale applications, existing approaches do not pay sufficient attention to establishing correct correspondences between the anchor sets across views. To be specific, anchor graphs obtained from different views are not aligned column-wisely. Such an Anchor-Unaligned Problem (AUP) would cause inaccurate graph fusion and degrade the clustering performance. Under multi-view scenarios, generating correct correspondences could be extremely difficult since anchors are not consistent in feature dimensions. To solve this challenging issue, we propose the first study of the generalized and flexible anchor graph fusion framework termed Fast Multi-View Anchor-Correspondence Clustering (FMVACC). Specifically, we show how to find anchor correspondence with both feature and structure information, after which anchor graph fusion is performed column-wisely. Moreover, we theoretically show the connection between FMVACC and existing multi-view late fusion and partial view-aligned clustering, which further demonstrates our generality. Extensive experiments on seven benchmark datasets demonstrate the effectiveness and efficiency of our proposed method. Moreover, the proposed alignment module also shows significant performance improvement applying to existing multi-view anchor graph competitors indicating the importance of anchor alignment. Our code is available at \url{https: //github. com/wangsiwei2010/NeurIPS22-FMVACC}.

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AAAI Conference 2022 Conference Paper

Deep Graph Clustering via Dual Correlation Reduction

  • Yue Liu
  • Wenxuan Tu
  • Sihang Zhou
  • Xinwang Liu
  • Linxuan Song
  • Xihong Yang
  • En Zhu

Deep graph clustering, which aims to reveal the underlying graph structure and divide the nodes into different groups, has attracted intensive attention in recent years. However, we observe that, in the process of node encoding, existing methods suffer from representation collapse which tends to map all data into the same representation. Consequently, the discriminative capability of the node representation is limited, leading to unsatisfied clustering performance. To address this issue, we propose a novel self-supervised deep graph clustering method termed Dual Correlation Reduction Network (DCRN) by reducing information correlation in a dual manner. Specifically, in our method, we first design a siamese network to encode samples. Then by forcing the cross-view sample correlation matrix and cross-view feature correlation matrix to approximate two identity matrices, respectively, we reduce the information correlation in the dual-level, thus improving the discriminative capability of the resulting features. Moreover, in order to alleviate representation collapse caused by over-smoothing in GCN, we introduce a propagation regularization term to enable the network to gain long-distance information with the shallow network structure. Extensive experimental results on six benchmark datasets demonstrate the effectiveness of the proposed DCRN against the existing state-of-the-art methods. The code of DCRN is available at https: //github. com/yueliu1999/DCRN and a collection (papers, codes and, datasets) of deep graph clustering is shared at https: //github. com/yueliu1999/Awesome-Deep- Graph-Clustering on Github.

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AAAI Conference 2022 Conference Paper

Fusion Multiple Kernel K-means

  • Yi Zhang
  • Xinwang Liu
  • Jiyuan Liu
  • Sisi Dai
  • Changwang Zhang
  • Kai Xu
  • En Zhu

Multiple kernel clustering aims to seek an appropriate combination of base kernels to mine inherent non-linear information for optimal clustering. Late fusion algorithms generate base partitions independently and integrate them in the following clustering procedure, improving the overall efficiency. However, the separate base partition generation leads to inadequate negotiation with the clustering procedure and a great loss of beneficial information in corresponding kernel matrices, which negatively affects the clustering performance. To address this issue, we propose a novel algorithm, termed as Fusion Multiple Kernel k-means (FMKKM), which unifies base partition learning and late fusion clustering into one single objective function, and adopts early fusion technique to capture more sufficient information in kernel matrices. Specifically, the early fusion helps base partitions keep more beneficial kernel details, and the base partitions learning further guides the generation of consensus partition in the late fusion stage, while the late fusion provides positive feedback on two former procedures. The close collaboration of three procedures results in a promising performance improvement. Subsequently, an alternate optimization method with promising convergence is developed to solve the resultant optimization problem. Comprehensive experimental results demonstrate that our proposed algorithm achieves stateof-the-art performance on multiple public datasets, validating its effectiveness. The code of this work is publicly available at https: //github. com/ethan-yizhang/Fusion-Multiple-Kernel- K-means.

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IJCAI Conference 2022 Conference Paper

Initializing Then Refining: A Simple Graph Attribute Imputation Network

  • Wenxuan Tu
  • Sihang Zhou
  • Xinwang Liu
  • Yue Liu
  • Zhiping Cai
  • En Zhu
  • Changwang Zhang
  • Jieren Cheng

Representation learning on the attribute-missing graphs, whose connection information is complete while the attribute information of some nodes is missing, is an important yet challenging task. To impute the missing attributes, existing methods isolate the learning processes of attribute and structure information embeddings, and force both resultant representations to align with a common in-discriminative normal distribution, leading to inaccurate imputation. To tackle these issues, we propose a novel graph-oriented imputation framework called initializing then refining (ITR), where we first employ the structure information for initial imputation, and then leverage observed attribute and structure information to adaptively refine the imputed latent variables. Specifically, we first adopt the structure embeddings of attribute-missing samples as the embedding initialization, and then refine these initial values by aggregating the reliable and informative embeddings of attribute-observed samples according to the affinity structure. Specially, in our refining process, the affinity structure is adaptively updated through iterations by calculating the sample-wise correlations upon the recomposed embeddings. Extensive experiments on four benchmark datasets verify the superiority of ITR against state-of-the-art methods.

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AAAI Conference 2022 Conference Paper

Robust Graph-Based Multi-View Clustering

  • Weixuan Liang
  • Xinwang Liu
  • Sihang Zhou
  • Jiyuan Liu
  • Siwei Wang
  • En Zhu

Graph-based multi-view clustering (G-MVC) constructs a graphical representation of each view and then fuses them to a unified graph for clustering. Though demonstrating promising clustering performance in various applications, we observe that their formulations are usually non-convex, leading to a local optimum. In this paper, we propose a novel MVC algorithm termed robust graph-based multi-view clustering (RG-MVC) to address this issue. In particular, we define a min-max formulation for robust learning and then rewrite it as a convex and differentiable objective function whose convexity and differentiability are carefully proved. Thus, we can efficiently solve the resultant problem using a reduced gradient descent algorithm, and the corresponding solution is guaranteed to be globally optimal. As a consequence, although our algorithm is free of hyper-parameters, it has shown good robustness against noisy views. Extensive experiments on benchmark datasets verify the superiority of the proposed method against the compared state-of-the-art algorithms. Our codes and appendix are available at https: //github. com/wxliang/RG-MVC.

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NeurIPS Conference 2022 Conference Paper

Stability and Generalization of Kernel Clustering: from Single Kernel to Multiple Kernel

  • Weixuan Liang
  • Xinwang Liu
  • Yong Liu
  • Sihang Zhou
  • Jun-Jie Huang
  • Siwei Wang
  • Jiyuan Liu
  • Yi Zhang

Multiple kernel clustering (MKC) is an important research topic that has been widely studied for decades. However, current methods still face two problems: inefficient when handling out-of-sample data points and lack of theoretical study of the stability and generalization of clustering. In this paper, we propose a novel method that can efficiently compute the embedding of out-of-sample data with a solid generalization guarantee. Specifically, we approximate the eigen functions of the integral operator associated with the linear combination of base kernel functions to construct low-dimensional embeddings of out-of-sample points for efficient multiple kernel clustering. In addition, we, for the first time, theoretically study the stability of clustering algorithms and prove that the single-view version of the proposed method has uniform stability as $\mathcal{O}\left(Kn^{-3/2}\right)$ and establish an upper bound of excess risk as $\widetilde{\mathcal{O}}\left(Kn^{-3/2}+n^{-1/2}\right)$, where $K$ is the cluster number and $n$ is the number of samples. We then extend the theoretical results to multiple kernel scenarios and find that the stability of MKC depends on kernel weights. As an example, we apply our method to a novel MKC algorithm termed SimpleMKKM and derive the upper bound of its excess clustering risk, which is tighter than the current results. Extensive experimental results validate the effectiveness and efficiency of the proposed method.

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AAAI Conference 2021 Conference Paper

Deep Fusion Clustering Network

  • Wenxuan Tu
  • Sihang Zhou
  • Xinwang Liu
  • Xifeng Guo
  • Zhiping Cai
  • En Zhu
  • Jieren Cheng

Deep clustering is a fundamental yet challenging task for data analysis. Recently we witness a strong tendency of combining autoencoder and graph neural networks to exploit structure information for clustering performance enhancement. However, we observe that existing literature 1) lacks a dynamic fusion mechanism to selectively integrate and refine the information of graph structure and node attributes for consensus representation learning; 2) fails to extract information from both sides for robust target distribution (i. e. , “groundtruth” soft labels) generation. To tackle the above issues, we propose a Deep Fusion Clustering Network (DFCN). Specifically, in our network, an interdependency learning-based Structure and Attribute Information Fusion (SAIF) module is proposed to explicitly merge the representations learned by an autoencoder and a graph autoencoder for consensus representation learning. Also, a reliable target distribution generation measure and a triplet self-supervision strategy, which facilitate cross-modality information exploitation, are designed for network training. Extensive experiments on six benchmark datasets have demonstrated that the proposed DFCN consistently outperforms the state-of-the-art deep clustering methods. Our code is publicly available at https: //github. com/WxTu/DFCN.

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IJCAI Conference 2021 Conference Paper

Hyperspectral Band Selection via Spatial-Spectral Weighted Region-wise Multiple Graph Fusion-Based Spectral Clustering

  • Chang Tang
  • Xinwang Liu
  • En Zhu
  • Lizhe Wang
  • Albert Zomaya

In this paper, we propose a hyperspectral band selection method via spatial-spectral weighted region-wise multiple graph fusion-based spectral clustering, referred to as RMGF briefly. Considering that different objects have different reflection characteristics, we use a superpixel segmentation algorithm to segment the first principal component of original hyperspectral image cube into homogeneous regions. For each superpixel, we construct a corresponding similarity graph to reflect the similarity between band pairs. Then, a multiple graph diffusion strategy with theoretical convergence guarantee is designed to learn a unified graph for partitioning the whole hyperspectral cube into several subcubes via spectral clustering. During the graph diffusion process, the spatial and spectral information of each superpixel are embedded to make spatial/spectral similar superpixels contribute more to each other. Finally, the band containing minimum noise in each subcube is selected to represent the whole subcube. Extensive experiments are conducted on three public datasets to validate the superiority of the proposed method when compared with other state-of-the-art ones.

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ICML Conference 2021 Conference Paper

One Pass Late Fusion Multi-view Clustering

  • Xinwang Liu 0002
  • Li Liu 0002
  • Qing Liao 0001
  • Siwei Wang 0001
  • Yi Zhang 0104
  • Wenxuan Tu
  • Chang Tang
  • Jiyuan Liu 0003

Existing late fusion multi-view clustering (LFMVC) optimally integrates a group of pre-specified base partition matrices to learn a consensus one. It is then taken as the input of the widely used k-means to generate the cluster labels. As observed, the learning of the consensus partition matrix and the generation of cluster labels are separately done. These two procedures lack necessary negotiation and can not best serve for each other, which may adversely affect the clustering performance. To address this issue, we propose to unify the aforementioned two learning procedures into a single optimization, in which the consensus partition matrix can better serve for the generation of cluster labels, and the latter is able to guide the learning of the former. To optimize the resultant optimization problem, we develop a four-step alternate algorithm with proved convergence. We theoretically analyze the clustering generalization error of the proposed algorithm on unseen data. Comprehensive experiments on multiple benchmark datasets demonstrate the superiority of our algorithm in terms of both clustering accuracy and computational efficiency. It is expected that the simplicity and effectiveness of our algorithm will make it a good option to be considered for practical multi-view clustering applications.

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TIST Journal 2020 Journal Article

A Theoretical Revisit to Linear Convergence for Saddle Point Problems

  • Wendi Wu
  • Yawei Zhao
  • En Zhu
  • Xinwang Liu
  • Xingxing Zhang
  • Lailong Luo
  • Shixiong Wang
  • Jianping Yin

Recently, convex-concave bilinear Saddle Point Problems (SPP) is widely used in lasso problems, Support Vector Machines, game theory, and so on. Previous researches have proposed many methods to solve SPP, and present their convergence rate theoretically. To achieve linear convergence, analysis in those previouse studies requires strong convexity of φ( z ). But, we find the linear convergence can also be achieved even for a general convex but not strongly convex φ( z ). In the article, by exploiting the strong duality of SPP, we propose a new method to solve SPP, and achieve the linear convergence. We present a new general sufficient condition to achieve linear convergence, but do not require the strong convexity of φ( z ). Furthermore, a more efficient method is also proposed, and its convergence rate is analyzed in theoretical. Our analysis shows that the well conditioned φ( z ) is necessary to improve the efficiency of our method. Finally, we conduct extensive empirical studies to evaluate the convergence performance of our methods.

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AAAI Conference 2020 Conference Paper

CGD: Multi-View Clustering via Cross-View Graph Diffusion

  • Chang Tang
  • Xinwang Liu
  • Xinzhong Zhu
  • En Zhu
  • Zhigang Luo
  • Lizhe Wang
  • Wen Gao

Graph based multi-view clustering has been paid great attention by exploring the neighborhood relationship among data points from multiple views. Though achieving great success in various applications, we observe that most of previous methods learn a consensus graph by building certain data representation models, which at least bears the following drawbacks. First, their clustering performance highly depends on the data representation capability of the model. Second, solving these resultant optimization models usually results in high computational complexity. Third, there are often some hyperparameters in these models need to tune for obtaining the optimal results. In this work, we propose a general, effective and parameter-free method with convergence guarantee to learn a unified graph for multi-view data clustering via cross-view graph diffusion (CGD), which is the first attempt to employ diffusion process for multi-view clustering. The proposed CGD takes the traditional predefined graph matrices of different views as input, and learns an improved graph for each single view via an iterative cross diffusion process by 1) capturing the underlying manifold geometry structure of original data points, and 2) leveraging the complementary information among multiple graphs. The final unified graph used for clustering is obtained by averaging the improved view associated graphs. Extensive experiments on several benchmark datasets are conducted to demonstrate the effectiveness of the proposed method in terms of seven clustering evaluation metrics.

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AAAI Conference 2020 Conference Paper

Multi-View Spectral Clustering with Optimal Neighborhood Laplacian Matrix

  • Sihang Zhou
  • Xinwang Liu
  • Jiyuan Liu
  • Xifeng Guo
  • Yawei Zhao
  • En Zhu
  • Yongping Zhai
  • Jianping Yin

Multi-view spectral clustering aims to group data into different categories by optimally exploring complementary information from multiple Laplacian matrices. However, existing methods usually linearly combine a group of pre-specified first-order Laplacian matrices to construct an optimal Laplacian matrix, which may result in limited representation capability and insufficient information exploitation. In this paper, we propose a novel optimal neighborhood multi-view spectral clustering (ONMSC) algorithm to address these issues. Specifically, the proposed algorithm generates an optimal Laplacian matrix by searching the neighborhood of both the linear combination of the first-order and high-order base Laplacian matrices simultaneously. This design enhances the representative capacity of the optimal Laplacian and better utilizes the hidden high-order connection information, leading to improved clustering performance. An efficient algorithm with proved convergence is designed to solve the resultant optimization problem. Extensive experimental results on 9 datasets demonstrate the superiority of our algorithm against state-of-the-art methods, which verifies the effectiveness and advantages of the proposed ONMSC.

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AAAI Conference 2020 Conference Paper

R²MRF: Defocus Blur Detection via Recurrently Refining Multi-Scale Residual Features

  • Chang Tang
  • Xinwang Liu
  • Xinzhong Zhu
  • En Zhu
  • Kun Sun
  • Pichao Wang
  • Lizhe Wang
  • Albert Zomaya

Defocus blur detection aims to separate the in-focus and out-of-focus regions in an image. Although attracting more and more attention due to its remarkable potential applications, there are still several challenges for accurate defocus blur detection, such as the interference of background clutter, sensitivity to scales and missing boundary details of defocus blur regions. In order to address these issues, we propose a deep neural network which Recurrently Refines Multi-scale Residual Features (R2MRF) for defocus blur detection. We firstly extract multi-scale deep features by utilizing a fully convolutional network. For each layer, we design a novel recurrent residual refinement branch embedded with multiple residual refinement modules (RRMs) to more accurately detect blur regions from the input image. Considering that the features from bottom layers are able to capture rich low-level features for details preservation while the features from top layers are capable of characterizing the semantic information for locating blur regions, we aggregate the deep features from different layers to learn the residual between the intermediate prediction and the ground truth for each recurrent step in each residual refinement branch. Since the defocus degree is sensitive to image scales, we finally fuse the side output of each branch to obtain the final blur detection map. We evaluate the proposed network on two commonly used defocus blur detection benchmark datasets by comparing it with other 11 state-of-the-art methods. Extensive experimental results with ablation studies demonstrate that R2MRF consistently and significantly outperforms the competitors in terms of both efficiency and accuracy.

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TIST Journal 2020 Journal Article

Understand Dynamic Regret with Switching Cost for Online Decision Making

  • Yawei Zhao
  • Qian Zhao
  • Xingxing Zhang
  • En Zhu
  • Xinwang Liu
  • Jianping Yin

As a metric to measure the performance of an online method, dynamic regret with switching cost has drawn much attention for online decision making problems. Although the sublinear regret has been provided in much previous research, we still have little knowledge about the relation between the dynamic regret and the switching cost. In the article, we investigate the relation for two classic online settings: Online Algorithms (OA) and Online Convex Optimization (OCO). We provide a new theoretical analysis framework that shows an interesting observation; that is, the relation between the switching cost and the dynamic regret is different for settings of OA and OCO. Specifically, the switching cost has significant impact on the dynamic regret in the setting of OA. But it does not have an impact on the dynamic regret in the setting of OCO. Furthermore, we provide a lower bound of regret for the setting of OCO, which is same with the lower bound in the case of no switching cost. It shows that the switching cost does not change the difficulty of online decision making problems in the setting of OCO.

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IJCAI Conference 2019 Conference Paper

Affine Equivariant Autoencoder

  • Xifeng Guo
  • En Zhu
  • Xinwang Liu
  • Jianping Yin

Existing deep neural networks mainly focus on learning transformation invariant features. However, it is the equivariant features that are more adequate for general purpose tasks. Unfortunately, few work has been devoted to learning equivariant features. To fill this gap, in this paper, we propose an affine equivariant autoencoder to learn features that are equivariant to the affine transformation in an unsupervised manner. The objective consists of the self-reconstruction of the original example and affine transformed example, and the approximation of the affine transformation function, where the reconstruction makes the encoder a valid feature extractor and the approximation encourages the equivariance. Extensive experiments are conducted to validate the equivariance and discriminative ability of the features learned by our affine equivariant autoencoder.

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NeurIPS Conference 2019 Conference Paper

Effective End-to-end Unsupervised Outlier Detection via Inlier Priority of Discriminative Network

  • Siqi Wang
  • Yijie Zeng
  • Xinwang Liu
  • En Zhu
  • Jianping Yin
  • Chuanfu Xu
  • Marius Kloft

Despite the wide success of deep neural networks (DNN), little progress has been made on end-to-end unsupervised outlier detection (UOD) from high dimensional data like raw images. In this paper, we propose a framework named E^3Outlier, which can perform UOD in a both effective and end-to-end manner: First, instead of the commonly-used autoencoders in previous end-to-end UOD methods, E^3Outlier for the first time leverages a discriminative DNN for better representation learning, by using surrogate supervision to create multiple pseudo classes from original unlabelled data. Next, unlike classic UOD that utilizes data characteristics like density or proximity, we exploit a novel property named inlier priority to enable end-to-end UOD by discriminative DNN. We demonstrate theoretically and empirically that the intrinsic class imbalance of inliers/outliers will make the network prioritize minimizing inliers' loss when inliers/outliers are indiscriminately fed into the network for training, which enables us to differentiate outliers directly from DNN's outputs. Finally, based on inlier priority, we propose the negative entropy based score as a simple and effective outlierness measure. Extensive evaluations show that E^3Outlier significantly advances UOD performance by up to 30% AUROC against state-of-the-art counterparts, especially on relatively difficult benchmarks.

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AAAI Conference 2019 Conference Paper

Efficient and Effective Incomplete Multi-View Clustering

  • Xinwang Liu
  • Xinzhong Zhu
  • Miaomiao Li
  • Chang Tang
  • En Zhu
  • Jianping Yin
  • Wen Gao

Incomplete multi-view clustering (IMVC) optimally fuses multiple pre-specified incomplete views to improve clustering performance. Among various excellent solutions, the recently proposed multiple kernel k-means with incomplete kernels (MKKM-IK) forms a benchmark, which redefines IMVC as a joint optimization problem where the clustering and kernel matrix imputation tasks are alternately performed until convergence. Though demonstrating promising performance in various applications, we observe that the manner of kernel matrix imputation in MKKM-IK would incur intensive computational and storage complexities, overcomplicated optimization and limitedly improved clustering performance. In this paper, we propose an Efficient and Effective Incomplete Multi-view Clustering (EE-IMVC) algorithm to address these issues. Instead of completing the incomplete kernel matrices, EE-IMVC proposes to impute each incomplete base matrix generated by incomplete views with a learned consensus clustering matrix. We carefully develop a three-step iterative algorithm to solve the resultant optimization problem with linear computational complexity and theoretically prove its convergence. Further, we conduct comprehensive experiments to study the proposed EE-IMVC in terms of clustering accuracy, running time, evolution of the learned consensus clustering matrix and the convergence. As indicated, our algorithm significantly and consistently outperforms some state-of-the-art algorithms with much less running time and memory.

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IJCAI Conference 2019 Conference Paper

Multi-view Clustering via Late Fusion Alignment Maximization

  • Siwei Wang
  • Xinwang Liu
  • En Zhu
  • Chang Tang
  • Jiyuan Liu
  • Jingtao Hu
  • Jingyuan Xia
  • Jianping Yin

Multi-view clustering (MVC) optimally integrates complementary information from different views to improve clustering performance. Although demonstrating promising performance in many applications, we observe that most of existing methods directly combine multiple views to learn an optimal similarity for clustering. These methods would cause intensive computational complexity and over-complicated optimization. In this paper, we theoretically uncover the connection between existing k-means clustering and the alignment between base partitions and consensus partition. Based on this observation, we propose a simple but effective multi-view algorithm termed {Multi-view Clustering via Late Fusion Alignment Maximization (MVC-LFA)}. In specific, MVC-LFA proposes to maximally align the consensus partition with the weighted base partitions. Such a criterion is beneficial to significantly reduce the computational complexity and simplify the optimization procedure. Furthermore, we design a three-step iterative algorithm to solve the new resultant optimization problem with theoretically guaranteed convergence. Extensive experiments on five multi-view benchmark datasets demonstrate the effectiveness and efficiency of the proposed MVC-LFA.

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AAAI Conference 2019 Conference Paper

Robustness Can Be Cheap: A Highly Efficient Approach to Discover Outliers under High Outlier Ratios

  • Siqi Wang
  • En Zhu
  • Xiping Hu
  • Xinwang Liu
  • Qiang Liu
  • Jianping Yin
  • Fei Wang

Efficient detection of outliers from massive data with a high outlier ratio is challenging but not explicitly discussed yet. In such a case, existing methods either suffer from poor robustness or require expensive computations. This paper proposes a Low-rank based Efficient Outlier Detection (LEOD) framework to achieve favorable robustness against high outlier ratios with much cheaper computations. Specifically, it is worth highlighting the following aspects of LEOD: (1) Our framework exploits the low-rank structure embedded in the similarity matrix and considers inliers/outliers equally based on this low-rank structure, which facilitates us to encourage satisfying robustness with low computational cost later; (2) A novel re-weighting algorithm is derived as a new general solution to the constrained eigenvalue problem, which is a major bottleneck for the optimization process. Instead of the high space and time complexity (O((2n)2 )/O((2n)3 )) required by the classic solution, our algorithm enjoys O(n) space complexity and a faster optimization speed in the experiments; (3) A new alternative formulation is proposed for further acceleration of the solution process, where a cheap closed-form solution can be obtained. Experiments show that LEOD achieves strong robustness under an outlier ratio from 20% to 60%, while it is at most 100 times more memory efficient and 1000 times faster than its previous counterpart that attains comparable performance. The codes of LEOD are publicly available at https: //github. com/demonzyj56/LEOD.

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AAAI Conference 2018 Short Paper

Deep Embedding for Determining the Number of Clusters

  • Yiqi Wang
  • Zhan Shi
  • Xifeng Guo
  • Xinwang Liu
  • En Zhu
  • Jianping Yin

Determining the number of clusters is important but challenging, especially for data of high dimension. In this paper, we propose Deep Embedding Determination (DED), a method that can solve jointly for the unknown number of clusters and feature extraction. DED first combines the virtues of the convolutional autoencoder and the t-SNE technique to extract low dimensional embedded features. Then it determines the number of clusters using an improved density-based clustering algorithm. Our experimental evaluation on image datasets shows significant improvement over state-of-the-art methods and robustness with respect to hyperparameter settings.

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IJCAI Conference 2018 Conference Paper

Localized Incomplete Multiple Kernel k-means

  • Xinzhong Zhu
  • Xinwang Liu
  • Miaomiao Li
  • En Zhu
  • Li Liu
  • Zhiping Cai
  • Jianping Yin
  • Wen Gao

The recently proposed multiple kernel k-means with incomplete kernels (MKKM-IK) optimally integrates a group of pre-specified incomplete kernel matrices to improve clustering performance. Though it demonstrates promising performance in various applications, we observe that it does not \emph{sufficiently consider the local structure among data and indiscriminately forces all pairwise sample similarity to equally align with their ideal similarity values}. This could make the incomplete kernels less effectively imputed, and in turn adversely affect the clustering performance. In this paper, we propose a novel localized incomplete multiple kernel k-means (LI-MKKM) algorithm to address this issue. Different from existing MKKM-IK, LI-MKKM only requires the similarity of a sample to its k-nearest neighbors to align with their ideal similarity values. This helps the clustering algorithm to focus on closer sample pairs that shall stay together and avoids involving unreliable similarity evaluation for farther sample pairs. We carefully design a three-step iterative algorithm to solve the resultant optimization problem and theoretically prove its convergence. Comprehensive experiments on eight benchmark datasets demonstrate that our algorithm significantly outperforms the state-of-the-art comparable algorithms proposed in the recent literature, verifying the advantage of considering local structure.

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AAAI Conference 2018 Short Paper

Variance Reduced K-Means Clustering

  • Yawei Zhao
  • Yuewei Ming
  • Xinwang Liu
  • En Zhu
  • Jianping Yin

It is challenging to perform k-means clustering on a large scale dataset efficiently. One of the reasons is that k-means needs to scan a batch of training data to update the cluster centers at every iteration, which is time-consuming. In the paper, we propose a variance reduced k-mean VRKM, which outperforms the state-of-the-art method, and obtain 4× speedup for large-scale clustering. The source code is available on https://github.com/YaweiZhao/VRKM_sofia-ml.

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AAAI Conference 2017 Conference Paper

Multiple Kernel k-Means with Incomplete Kernels

  • Xinwang Liu
  • Miaomiao Li
  • Lei Wang
  • Yong Dou
  • Jianping Yin
  • En Zhu

Multiple kernel clustering (MKC) algorithms optimally combine a group of pre-specified base kernels to improve clustering performance. However, existing MKC algorithms cannot efficiently address the situation where some rows and columns of base kernels are absent. This paper proposes a simple while effective algorithm to address this issue. Different from existing approaches where incomplete kernels are firstly imputed and a standard MKC algorithm is applied to the imputed kernels, our algorithm integrates imputation and clustering into a unified learning procedure. Specifically, we perform multiple kernel clustering directly with the presence of incomplete kernels, which are treated as auxiliary variables to be jointly optimized. Our algorithm does not require that there be at least one complete base kernel over all the samples. Also, it adaptively imputes incomplete kernels and combines them to best serve clustering. A three-step iterative algorithm with proved convergence is designed to solve the resultant optimization problem. Extensive experiments are conducted on four benchmark data sets to compare the proposed algorithm with existing imputation-based methods. Our algorithm consistently achieves superior performance and the improvement becomes more significant with increasing missing ratio, verifying the effectiveness and advantages of the proposed joint imputation and clustering.

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AAAI Conference 2017 Conference Paper

Optimal Neighborhood Kernel Clustering with Multiple Kernels

  • Xinwang Liu
  • Sihang Zhou
  • Yueqing Wang
  • Miaomiao Li
  • Yong Dou
  • En Zhu
  • Jianping Yin

Multiple kernel k-means (MKKM) aims to improve clustering performance by learning an optimal kernel, which is usually assumed to be a linear combination of a group of prespecified base kernels. However, we observe that this assumption could: i) cause limited kernel representation capability; and ii) not sufficiently consider the negotiation between the process of learning the optimal kernel and that of clustering, leading to unsatisfying clustering performance. To address these issues, we propose an optimal neighborhood kernel clustering (ONKC) algorithm to enhance the representability of the optimal kernel and strengthen the negotiation between kernel learning and clustering. We theoretically justify this ONKC by revealing its connection with existing MKKM algorithms. Furthermore, this justification shows that existing MKKM algorithms can be viewed as a special case of our approach and indicates the extendability of the proposed ONKC for designing better clustering algorithms. An efficient algorithm with proved convergence is designed to solve the resultant optimization problem. Extensive experiments have been conducted to evaluate the clustering performance of the proposed algorithm. As demonstrated, our algorithm significantly outperforms the state-of-the-art ones in the literature, verifying the effectiveness and advantages of ONKC.

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IJCAI Conference 2016 Conference Paper

Multiple Kernel Clustering with Local Kernel Alignment Maximization

  • Miaomiao Li
  • Xinwang Liu
  • Lei Wang
  • Yong Dou
  • Jianping Yin
  • En Zhu

Kernel alignment has recently been employed for multiple kernel clustering (MKC). However, we find that most of existing works implement this alignment in a global manner, which: i) indiscriminately forces all sample pairs to be equally aligned with the same ideal similarity; and ii) is inconsistent with a well-established concept that the similarity evaluated for two farther samples in a high dimensional space is less reliable. To address these issues, this paper proposes a novel MKC algorithm with a "local" kernel alignment, which only requires that the similarity of a sample to its k-nearest neighbours be aligned with the ideal similarity matrix. Such an alignment helps the clustering algorithm to focus on closer sample pairs that shall stay together and avoids involving unreliable similarity evaluation for farther sample pairs. We derive a new optimization problem to implement this idea, and design a two-step algorithm to efficiently solve it. As experimentally demonstrated on six challenging multiple kernel learning benchmark data sets, our algorithm significantly outperforms the state-of-the-art comparable methods in the recent literature, verifying the effectiveness and superiority of maximizing local kernel alignment.

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AAAI Conference 2016 Conference Paper

Multiple Kernel k -Means Clustering with Matrix-Induced Regularization

  • Xinwang Liu
  • Yong Dou
  • Jianping Yin
  • Lei Wang
  • En Zhu

Multiple kernel k-means (MKKM) clustering aims to optimally combine a group of pre-specified kernels to improve clustering performance. However, we observe that existing MKKM algorithms do not sufficiently consider the correlation among these kernels. This could result in selecting mutually redundant kernels and affect the diversity of information sources utilized for clustering, which finally hurts the clustering performance. To address this issue, this paper proposes an MKKM clustering with a novel, effective matrix-induced regularization to reduce such redundancy and enhance the diversity of the selected kernels. We theoretically justify this matrix-induced regularization by revealing its connection with the commonly used kernel alignment criterion. Furthermore, this justification shows that maximizing the kernel alignment for clustering can be viewed as a special case of our approach and indicates the extendability of the proposed matrix-induced regularization for designing better clustering algorithms. As experimentally demonstrated on five challenging MKL benchmark data sets, our algorithm significantly improves existing MKKM and consistently outperforms the state-of-the-art ones in the literature, verifying the effectiveness and advantages of incorporating the proposed matrix-induced regularization.

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