Graph clustering, which aims to divide nodes in the graph into several distinct clusters, is a fundamental yet challenging task. Benefiting from the powerful representation capability of deep learning, deep graph clustering methods have achieved great success in recent years. However, the corresponding survey paper is relatively scarce, and it is imminent to make a summary of this field. From this motivation, we conduct a comprehensive survey of deep graph clustering. Firstly, we introduce formulaic definition, evaluation, and development in this field. Secondly, the taxonomy of deep graph clustering methods is presented based on four different criteria, including graph type, network architecture, learning paradigm, and clustering method. Thirdly, we carefully analyze the existing methods via extensive experiments and summarize the challenges and opportunities from five perspectives, including graph data quality, stability, scalability, discriminative capability, and unknown cluster number. Besides, the applications of deep graph clustering methods in six domains, including computer vision, natural language processing, recommendation systems, social network analyses, bioinformatics, and medical science, are presented. Last but not least, this paper provides open resource supports, including 1) a collection (https://github.com/yueliu1999/Awesome-Deep-Graph-Clustering) of state-of-the-art deep graph clustering methods (papers, codes, and datasets) and 2) a flexible and extensible Python library (https://github.com/Marigoldwu/PyDGC) for deep graph clustering. We hope this work can serve as a quick guide and help researchers overcome challenges in this vibrant field.

Multi-hop Knowledge Base Question Answering (KBQA) aims to find answer entities in the knowledge base that are multiple hops away from the entities in the question. Information retrieval-based (IR-based) methods extract a pivotal subgraph from the entire KB to locate candidate answers and then evaluate their plausibility through semantic matching with the question. However, we observed that the extracted subgraphs often include nodes that are weakly related or irrelevant to the question. Without a proper node filtering mechanism, the number of irrelevant nodes grows as the number of hops increases, leading to excessive consumption of computational resources. To address these challenges, this study introduces an efficient LLM-based subgraph retrieval method for multi-hop knowledge base question answering, M-ER. The framework leverages Monte Carlo Tree Search (MCTS) to transform subgraph exploration into a tree-structured search process. During the MCTS selection phase, nodes that are highly relevant to the question are prioritized for inclusion in the subgraph, eliminating the need to traverse all nodes in the KB. The framework further incorporates a large language model (LLM) to refine the search direction, ensuring that exploration remains focused on nodes relevant to the question. In addition, selected nodes are quantitatively scored, and these scores are fed back into the node selection process to effectively filter out irrelevant candidates, thereby improving the quality of the subgraph. This mechanism not only narrows the search space but also enhances the overall efficiency of multi-hop KBQA. Experiments on the WebQSP benchmark demonstrate that M-ER achieves 78.88% on the Hits@1 metric, while also improving computational efficiency. These results not only validate the effectiveness of M-ER, but also offer a viable technical path to balance performance and computational efficiency.

The field of knowledge graph representation learning (KGRL) has been rapidly expanding. To effectively apply KGRL models to large real-world knowledge graphs (KGs), anchor-based methods have been proposed. These methods aim to reduce computational costs and parameter requirements by encoding entities using a small set of entity anchors. However, existing anchor selection approaches are often rudimentary and sometimes yield suboptimal results. In this article, we propose a scalable anchor-based KGRL method called SKIP. By leveraging prototype information, our method selects representative entities as anchors. The SKIP method consists of two main steps. First, pretraining models are employed to encode entities by utilizing the topological structure and textual information in KGs. Second, the prototype learning module (PLM) extracts entity prototypes, which are then used to sample entity anchors that contain valuable prototype information. These settings enable SKIP to identify representative and reasonable entity anchors, leading to improved performance while requiring fewer computational resources. Extensive experiments conducted on various downstream tasks using KGs of different scales demonstrate the superiority and effectiveness of SKIP. Particularly, on the large OGB WikiKG 2 dataset, our method achieves comparable performance while reducing running time by approximately 21.28% and requiring 21.43% fewer model parameters compared to the baseline. This indicates the superior scalability of SKIP.

Text-based knowledge graph completion methods take advantage of pre-trained language models (PLM) to enhance intrinsic semantic connections of raw triplets with detailed text descriptions. Typical methods in this branch map an input query (textual descriptions associated with an entity and a relation) and its candidate entities into feature vectors, respectively, and then maximize the probability of valid triples. These methods are gaining promising performance and increasing attention for the rapid development of large language models. According to the property of the language models, the more related and specific context information the input query provides, the more discriminative the resultant embedding will be. In this paper, through observation and validation, we find a neglected fact that the relation-aware neighbors of the head entities in queries could act as effective contexts for more precise link prediction. Driven by this finding, we propose a relation-aware anchor enhanced knowledge graph completion method (RAA-KGC). Specifically, in our method, to provide a reference of what might the target entity be like, we first generate anchor entities within the relation-aware neighborhood of the head entity. Then, by pulling the query embedding towards the neighborhoods of the anchors, it is tuned to be more discriminative for target entity matching. The results of our extensive experiments not only validate the efficacy of RAA-KGC but also reveal that by integrating our relation-aware anchor enhancement strategy, the performance of current leading methods can be notably enhanced without substantial modifications.

Chain-of-thought (CoT) distillation allows a large language model (LLM) to guide a small language model (SLM) in reasoning tasks.Existing methods train the SLM to learn the long rationale in one iteration, resulting in two issues: 1) Long rationales lead to a large tokenlevel batch size during training, making gradients of core reasoning tokens (i.e., the token will directly affect the correctness of subsequent reasoning) over-smoothed as they contribute a tiny fraction of the rationale.As a result, the SLM converges to sharp minima where it fails to grasp the reasoning logic.2) The response is slow, as the SLM must generate a long rationale before reaching the answer.Therefore, we propose chunk-wise training (CWT), which uses a heuristic search to divide the rationale into internal semantically coherent chunks and focuses SLM on learning from only one chunk per iteration.In this way, CWT naturally isolates non-reasoning chunks that do not involve the core reasoning token (e.g., summary and transitional chunks) from the SLM learning for reasoning chunks, making the fraction of the core reasoning token increase in the corresponding iteration.Based on CWT, skip-thinking training (STT) is proposed.STT makes the SLM automatically skip nonreasoning medium chunks to reach the answer, improving reasoning speed while maintaining accuracy.We validate our approach on a variety of SLMs and multiple reasoning tasks.

Reasoning paths are reliable information in knowledge graph completion (KGC) in which algorithms can find strong clues of the actual relation between entities. However, in real-world applications, it is difficult to guarantee that computationally affordable paths exist toward all candidate entities. According to our observation, the prediction accuracy drops significantly when paths are absent. To make the proposed algorithm more stable against the missing path circumstances, we introduce soft reasoning paths. Concretely, a specific learnable latent path embedding is concatenated to each relation to help better model the characteristics of the corresponding paths. The combination of the relation and the corresponding learnable embedding is termed a soft path in our paper. By aligning the soft paths with the reasoning paths, a learnable embedding is guided to learn a generalized path representation of the corresponding relation. In addition, we introduce a hierarchical ranking strategy to make full use of information about the entity, relation, path, and soft path to help improve both the efficiency and accuracy of the model. Extensive experimental results illustrate that our algorithm outperforms the compared state-of-the-art algorithms by a notable margin. Our code will be released at https://github.com/7HHHHH/SRP-KGC.

Incomplete multi-view deep clustering is an emerging research hot-pot to incorporate data information of multiple sources or modalities when parts of them are missing. Most of existing approaches encode the available data observations into multiple view-specific latent representations and subsequently integrate them for the next clustering task. However, they ignore that the latent representations are unique to a fixed set of data samples in all views. Meanwhile, the pair-wise similarities of missing data observations are also failed to utilize in latent representation learning sufficiently, leading to unsatisfactory clustering performance. To address these issues, we propose an incomplete multi-view deep clustering method with data imputation and alignment. Assuming that each data sample corresponds to a same latent representation among all views, it projects the latent representations into feature spaces with neural networks. As a result, not only the available data observations are reconstructed, but also the missing ones can be imputed accordingly. Moreover, a linear alignment measurement of linear complexity is defined to compute the pair-wise similarities of all data observations, especially including those of the missing. By executing the above two procedures iteratively, the discriminative latent representations can be learned and used to group the data into categories with off-the-shelf clustering algorithms. In experiment, the proposed method is validated on a set of benchmark datasets and achieves state-of-the-art performances.

Temporal Graph Clustering (TGC) is a new task with little attention, focusing on node clustering in temporal graphs. Compared with existing static graph clustering, it can find the balance between time requirement and space requirement (Time-Space Balance) through the interaction sequence-based batch-processing pattern. However, there are two major challenges that hinder the development of TGC, i.e., inapplicable clustering techniques and inapplicable datasets. To address these challenges, we propose a comprehensive benchmark, called BenchTGC. Specially, we design a BenchTGC Framework to illustrate the paradigm of temporal graph clustering and improve existing clustering techniques to fit temporal graphs. In addition, we also discuss problems with public temporal graph datasets and develop multiple datasets suitable for TGC task, called BenchTGC Datasets. According to extensive experiments, we not only verify the advantages of BenchTGC, but also demonstrate the necessity and importance of TGC task. We wish to point out that the dynamically changing and complex scenarios in real world are the foundation of temporal graph clustering.

Attribute-missing graph learning, a common yet challenging problem, has recently attracted considerable attention. Existing efforts have at least one of the following limitations: 1) lack a noise filtering and information enhancing scheme, resulting in less comprehensive data completion; 2) isolate the node attribute and graph structure encoding processes, introducing more parameters and failing to take full advantage of the two types of information; and 3) impose overly strict distribution assumptions on the latent variables, leading to biased or less discriminative node representations. To tackle the issues, based on the idea of introducing intimate information interaction between the two information sources, we propose Weight-sharing Attribute-missing Graph autoEncoder (WAGE) to boost the expressive capacity of node representations for high-quality missing attribute reconstruction. Specifically, three strategies have been conducted. Firstly, we entangle the attribute embedding and structure embedding by introducing a weight-sharing architecture to share the parameters learned by both processes, which allows the network training to benefit from more abundant and diverse information. Secondly, we introduce a $K$K-nearest neighbor-based dual non-local learning mechanism to improve the quality of data imputation by revealing unobserved high-confidence connections while filtering unreliable ones. Thirdly, we manually mask the connections on multiple adjacency matrices and force the structure-oriented embedding sub-network to recover the actual adjacency matrix, thus enforcing the resulting network to be able to selectively exploit more high-order discriminative features for data completion. Extensive experiments on six benchmark datasets demonstrate the effectiveness and superiority of WAGE against state-of-the-art competitors.

Knowledge graphs (KGs) represent known entities and their relationships using triplets, but this method cannot represent relationships between facts, limiting their expressiveness. Recently, the Bi-level Knowledge Graph (Bi-level KG) has addressed this issue by modeling facts as nodes and establishing relationships between these facts, introducing two new tasks: triplet prediction and conditional link prediction. Existing methods enhance triplets through data augmentation method and represent facts using entity representations. However, these methods do not address the isolated nodes at the structure level, nor do they effectively capture the information of facts at the feature level. To address these two issues, we design a data augmentation method that identifies islanded node by detecting anomalous structures and features in the graph. Subsequently, we perform similar subgraph matching for each isolated node to construct potential facts. To enrich the features of facts, we design a weighted combination initialization method for facts and introduce a new relation $\widetilde {R}$ , to connect facts with related entities. This approach allows for the co-training of fact and entity representations during the training process. Extensive experiments validate the effectiveness of our data augmentation and co-training methods. Our model achieves optimal performance in triplet prediction and conditional link prediction tasks.

Inductive relation prediction aims to predict missing connections between entities unseen during training. Recent approaches adopt binary (positive or negative) training labels, which indicate whether the query relation exists between the entities, as supervision to teach models recognizing the entity-independent relation patterns in the context (enclosed subgraph or connective path). However, we argue that in this kind of method, the trained models are guided to make relation predictions by remembering whether the query relation and its contextual relational pattern co-occur more frequently in positive or negative samples. This solution could introduce two major limitations: 1) the model struggles with long-tail combinations, i.e., the combination between query relation and the relational pattern rarely occurs during training; 2) when noisy relational patterns, which fail to provide evidence for predicting the query relation, frequently occur with the query relation in positive training samples, the model will be misled into considering the noisy relational patterns as a feature supporting the existence of the query relation. To solve these problems, we propose ToC (Thinking on Context). ToC first utilizes large language models (LLMs) to incorporate a chain of thought as an additional supervisory constraint, guiding the model to make relational predictions based on logical reasoning instead of co-occurrence frequency. Additionally, ToC employs the reasoning capabilities of LLMs to construct context-level negative samples, aiding the model in identifying and disregarding noisy relational patterns. Extensive experiments show that ToC significantly outperforms state-of-the-art methods across three widely used datasets in multiple inductive settingshttps://github.com/AI-Chen/ToC_KGC.

The ubiquity of Graph Neural Networks (GNNs) emphasizes the imperative to assess their resilience against node injection attacks, a type of evasion attacks that impact victim models by injecting nodes with fabricated attributes and structures. However, prevailing attacks face two primary limitations: (1) Sequential construction of attributes and structures results in suboptimal outcomes as structure information is overlooked during attribute construction and vice versa. (2) In black-box scenarios, where attackers lack access to victim model architecture and parameters, reliance on surrogate models degrades performance due to architectural discrepancies. To overcome these limitations, we introduce GZOO, a black-box node injection attack that leverages an adversarial graph generator, compromising both attribute and structure sub-generators. This integration crafts optimal attributes and structures by considering their mutual information, enhancing their influence when aggregating information from injected nodes. Furthermore, GZOO proposes a zeroth-order optimization algorithm leveraging prediction results from victim models to estimate gradients for updating generator parameters, eliminating the necessity to train surrogate models. Across sixteen datasets, GZOO significantly outperforms state-of-the-art attacks, achieving remarkable effectiveness and robustness. Notably, on the Cora dataset with the GCN model, GZOO achieves an impressive 95.69% success rate, surpassing the maximum 66.01% achieved by baselines.

Site selection aims to select optimal locations for new stores, which is crucial in business management and urban computing. The early data-driven models heavily relied on feature engineering, which could not effectively model the complex relationships and diverse influences among different data. To alleviate such issues, the knowledge-driven paradigm is proposed based on urban knowledge graphs (KGs). However, the research on them is at an early stage. They omit extra multi-modal information corresponding to brands and stores due to two main challenges, i.e., (1) building available datasets, and (2) designing effective models. It constrains the expressive ability and practical value of previous models. To this end, we first construct new multi-modal urban KGs for site selection with three extra modal (i.e., visual, textual, and acoustic) attributes. Then, we propose a novel multi-modal knowledge-driven model (MGKsite). Concretely, a graph neural network (GNN) based fusion network is designed to fuse the features based on the attribute K-Nearest Neighbor (KNN) graph, which models both intra and inter-modal correlations among the features. The fused embeddings are further injected into the knowledge-driven backbones for learning and inference. Experiments prove promising capacities of MGKsite from five aspects, i.e., superiority, effectiveness, sensitivity, transferability and complexity.

Chain-of-thought distillation (CoT-distillation) aims to endow small language models (SLMs) with reasoning ability to improve their performance toward specific tasks by allowing them to imitate the reasoning procedure of large language models (LLMs) beyond simply predicting the answers. Most existing CoT-distillation methods adopt a pre-thinking mechanism, allowing the SLM to generate a rationale before answering. In this way, pre-thinking enables SLM to analyze questions but makes answer correctness sensitive to minor errors in rationale. Therefore, we propose a robust post-thinking mechanism to generate answers before the rationale. Thanks to this answer-first setting: 1) the answer can escape from the rationale-sensitive problem; 2) the rationale serves as an error amplifier, making SLM focus on learning hard samples; and 3) the inferring efficiency can also benefit. Although post-thinking brings many advantages, it may lose the ability to analyze complex questions compared to pre-thinking. Therefore, a plug-and-play adaptive-thinking mechanism is proposed to integrate the merits of pre-thinking and post-thinking, in which a perception module based on soft prompt tuning is introduced to prompt SLM to answer or think first according to the complexity of questions. Extensive experiments are conducted across 12 datasets and 2 language models to demonstrate the effectiveness of the proposed mechanism.

As an emerging task, temporal graph clustering (TGC) is committed to clustering nodes on temporal graphs through interaction sequence-based batch-processing patterns. These patterns allow for more flexibility in finding a balance between time and space requirements than adjacency matrix-based static graph clustering. However, as a new task, TGC still has important unresolved challenges, such as insufficient information. This challenge manifests itself in a variety of problems in real-world datasets, including missing features (eigenvalues are missing or even nonexistent), long-tail nodes (most inactive nodes have little interaction), and noisy data (data is subject to anomalies, errors, and sparsity). These problems occur before training, making it difficult for the model to train well with insufficient information. To solve the challenge, we propose a method that introduces multiview clustering (MVC) into TGC, called MVTGC. Our method aims to perform data augmentation on the temporal graph by constructing multiple views to increase the information richness. In particular, we utilize different techniques to model a certain part of the temporal graph to generate enhanced views focusing on different angles. These views are combined into training through early fusion and late fusion and ultimately enhance the model's receptive field and information richness. Comparative experiments and a case study on real-world datasets demonstrate the significance and effectiveness of MVTGC, which achieves at most 10.48% performance improvement. The code and data are available at https://github.com/MGitHubL/MVTGC.

Temporal graph learning aims to generate high-quality representations for graph-based tasks with dynamic information, which has recently garnered increasing attention. In contrast to static graphs, temporal graphs are typically organized as node interaction sequences over continuous time rather than an adjacency matrix. Most temporal graph learning methods model current interactions by incorporating historical neighborhood. However, such methods only consider first-order temporal information while disregarding crucial high-order structural information, resulting in suboptimal performance. To address this issue, we propose a self-supervised method called S2T for temporal graph learning, which extracts both temporal and structural information to learn more informative node representations. Notably, the initial node representations combine first-order temporal and high-order structural information differently to calculate two conditional intensities. An alignment loss is then introduced to optimize the node representations, narrowing the gap between the two intensities and making them more informative. Concretely, in addition to modeling temporal information using historical neighbor sequences, we further consider structural knowledge at both local and global levels. At the local level, we generate structural intensity by aggregating features from high-order neighbor sequences. At the global level, a global representation is generated based on all nodes to adjust the structural intensity according to the active statuses on different nodes. Extensive experiments demonstrate that the proposed model S2T achieves at most 10.13% performance improvement compared with the state-of-the-art competitors on several datasets.

Deep graph clustering, which aims to reveal the underlying graph structure and divide the nodes into different clusters without human annotations, is a fundamental yet challenging task. However, we observe that the existing methods suffer from the representation collapse problem and tend to encode samples with different classes into the same latent embedding. Consequently, the discriminative capability of nodes is limited, resulting in suboptimal clustering performance. To address this problem, we propose a novel deep graph clustering algorithm termed improved dual correlation reduction network (IDCRN) through improving the discriminative capability of samples. Specifically, by approximating the cross-view feature correlation matrix to an identity matrix, we reduce the redundancy between different dimensions of features, thus improving the discriminative capability of the latent space explicitly. Meanwhile, the cross-view sample correlation matrix is forced to approximate the designed clustering-refined adjacency matrix to guide the learned latent representation to recover the affinity matrix even across views, thus enhancing the discriminative capability of features implicitly. Moreover, we avoid the collapsed representation caused by the oversmoothing issue in graph convolutional networks (GCNs) through an introduced propagation regularization term, enabling IDCRN to capture the long-range information with the shallow network structure. Extensive experimental results on six benchmarks have demonstrated the effectiveness and efficiency of IDCRN compared with the existing state-of-the-art deep graph clustering algorithms. The code of IDCRN is released at IDCRN. Besides, we share a collection of deep graph clustering, including papers, codes, and datasets at ADGC.

Few-shot relation reasoning on knowledge graphs (FS-KGR) is an important and practical problem that aims to infer long-tail relations and has drawn increasing attention these years. Among all the proposed methods, self-supervised learning (SSL) methods, which effectively extract the hidden essential inductive patterns relying only on the support sets, have achieved promising performance. However, the existing SSL methods simply cut down connections between high-frequency and long-tail relations, which ignores the fact, i.e., the two kinds of information could be highly related to each other. Specifically, we observe that relations with similar contextual meanings, called aliasing relations (ARs), may have similar attributes. In other words, the ARs of the target long-tail relation could be in high-frequency, and leveraging such attributes can largely improve the reasoning performance. Based on the interesting observation above, we proposed a novel Self-supervised learning model by leveraging Aliasing Relations to assist FS-KGR, termed SARF. Specifically, we propose a graph neural network (GNN)-based AR-assist module to encode the ARs. Besides, we further provide two fusion strategies, i.e., simple summation and learnable fusion, to fuse the generated representations, which contain extra abundant information underlying the ARs, into the self-supervised reasoning backbone for performance enhancement. Extensive experiments on three few-shot benchmarks demonstrate that SARF achieves state-of-the-art (SOTA) performance compared with other methods in most cases.

With the development of various applications, such as recommendation systems and social network analysis, graph data have been ubiquitous in the real world. However, graphs usually suffer from being absent during data collection due to copyright restrictions or privacy-protecting policies. The graph absence could be roughly grouped into attribute-incomplete and attribute-missing cases. Specifically, attribute-incomplete indicates that a portion of the attribute vectors of all nodes are incomplete, while attribute-missing indicates that all attribute vectors of partial nodes are missing. Although various graph imputation methods have been proposed, none of them is custom-designed for a common situation where both types of graph absence exist simultaneously. To fill this gap, we develop a novel graph imputation network termed revisiting initializing then refining (RITR), where both attribute-incomplete and attribute-missing samples are completed under the guidance of a novel initializing-then-refining imputation criterion. Specifically, to complete attribute-incomplete samples, we first initialize the incomplete attributes using Gaussian noise before network learning, and then introduce a structure-attribute consistency constraint to refine incomplete values by approximating a structure-attribute correlation matrix to a high-order structure matrix. To complete attribute-missing samples, we first adopt structure embeddings of attribute-missing samples as the embedding initialization, and then refine these initial values by adaptively aggregating the reliable information of attribute-incomplete samples according to a dynamic affinity structure. To the best of our knowledge, this newly designed method is the first end-to-end unsupervised framework dedicated to handling hybrid-absent graphs. Extensive experiments on six datasets have verified that our methods consistently outperform the existing state-of-the-art competitors. Our source code is available at https://github.com/WxTu/RITR.

Crime prediction is a crucial yet challenging task within urban computing, which benefits public safety and resource optimization. Over the years, various models have been proposed, and spatial-temporal hypergraph learning models have recently shown outstanding performances. However, three correlations underlying crime are ignored, thus hindering the performance of previous models. Specifically, there are two spatial correlations and one temporal correlation, i.e., (1) co-occurrence of different types of crimes (type spatial correlation), (2) the closer to the crime center, the more dangerous it is around the neighborhood area (neighbor spatial correlation), and (3) the closer between two timestamps, the more relevant events are (hawkes temporal correlation). To this end, we propose Hawkes-enhanced Spatial-Temporal Hypergraph Contrastive Learning framework (HCL), which mines the aforementioned correlations via two specific strategies. Concretely, contrastive learning strategies are designed for two spatial correlations, and hawkes process modeling is adopted for temporal correlations. Extensive experiments demonstrate the promising capacities of HCL from four aspects, i.e., superiority, transferability, effectiveness, and sensitivity.

GraIL and its variants have shown their promising capacities for inductive relation reasoning on knowledge graphs. However, the uni-directional message-passing mechanism hinders such models from exploiting hidden mutual relations between entities in directed graphs. Besides, the enclosing subgraph extraction in most GraIL-based models restricts the model from extracting enough discriminative information for reasoning. Consequently, the expressive ability of these models is limited. To address the problems, we propose a novel GraIL-based framework, termed MINES, by introducing a Message Intercommunication mechanism on the Neighbor-Enhanced Subgraph. Concretely, the message intercommunication mechanism is designed to capture the omitted hidden mutual information. It introduces bi-directed information interactions between connected entities by inserting an undirected/bi-directed GCN layer between uni-directed RGCN layers. Moreover, inspired by the success of involving more neighbors in other graph-based tasks, we extend the neighborhood area beyond the enclosing subgraph to enhance the information collection for inductive relation reasoning. Extensive experiments prove the promising capacity of the proposed MINES from various aspects, especially for the superiority, effectiveness, and transfer ability.

Deep clustering with attribute-missing graphs, where only a subset of nodes possesses complete attributes while those of others are missing, is an important yet challenging topic in various practical applications. It has become a prevalent learning paradigm in existing studies to perform data imputation first and subsequently conduct clustering using the imputed information. However, these ``two-stage" methods disconnect the clustering and imputation processes, preventing the model from effectively learning clustering-friendly graph embedding. Furthermore, they are not tailored for clustering tasks, leading to inferior clustering results. To solve these issues, we propose a novel Attribute-Missing Graph Clustering (AMGC) method to alternately promote clustering and imputation in a unified framework, where we iteratively produce the clustering-enhanced nearest neighbor information to conduct the data imputation process and utilize the imputed information to implicitly refine the clustering distribution through model optimization. Specifically, in the imputation step, we take the learned clustering information as imputation prompts to help each attribute-missing sample gather highly correlated features within its clusters for data completion, such that the intra-class compactness can be improved. Moreover, to support reliable clustering, we maximize inter-class separability by conducting cost-efficient dual non-contrastive learning over the imputed latent features, which in turn promotes greater graph encoding capability for clustering sub-network. Extensive experiments on five datasets have verified the superiority of AMGC against competitors.

In recent years, anchor-based methods have achieved promising progress in multi-view clustering. The performances of these methods are significantly affected by the quality of the anchors. However, the anchors generated by previous works solely rely on single-view information, ig-noring the correlation among different views. In particular, we observe that similar patterns are more likely to exist between similar views so such correlation information can be leveraged to enhance the quality of the anchors, which is also omitted. To this end, we propose a novel plug-and-play anchor enhancement strategy through view correlation for multi-view clustering. Specifically, we construct a view graph based on aligned initial anchor graphs to explore inter-view correlations. By learning from view correlation, we enhance the anchors of the current view using the relationships between anchors and samples on neighboring views, thereby narrowing the spatial distribution of anchors on similar views. Experimental results on seven datasets demonstrate the superiority of our proposed method over other existing methods. Furthermore, extensive comparative experiments validate the effectiveness of the proposed anchor enhancement module when applied to various anchor-based methods.

Late fusion multi-view clustering (LFMVC) has become a rapidly growing class of methods in the multi-view clustering (MVC) field, owing to its excellent computational speed and clustering performance. One bottleneck faced by existing late fusion methods is that they are usually aligned to the average kernel function, which makes the clustering performance highly dependent on the quality of datasets. Another problem is that they require subsequent k-means clustering after obtaining the consensus partition matrix to get the final discrete labels, and the resulting separation of the label learning and cluster structure optimization processes limits the integrity of these models. To address the above issues, we propose an integrated framework named One-Step Late Fusion Multi-view Clustering with Compressed Subspace (OS-LFMVC-CS). Specifically, we use the consensus subspace to align the partition matrix while optimizing the partition fusion, and utilize the fused partition matrix to guide the learning of discrete labels. A six-step iterative optimization approach with verified convergence is proposed. Sufficient experiments on multiple datasets validate the effectiveness and efficiency of our proposed method.

Deep graph clustering has recently received significant attention due to its ability to enhance the representation learning capabilities of models in unsupervised scenarios. Nevertheless, deep clustering for temporal graphs, which could capture crucial dynamic interaction information, has not been fully explored. It means that in many clustering-oriented real-world scenarios, temporal graphs can only be processed as static graphs. This not only causes the loss of dynamic information but also triggers huge computational consumption. To solve the problem, we propose a general framework for deep Temporal Graph Clustering called TGC, which introduces deep clustering techniques to suit the interaction sequence-based batch-processing pattern of temporal graphs. In addition, we discuss differences between temporal graph clustering and static graph clustering from several levels. To verify the superiority of the proposed framework TGC, we conduct extensive experiments. The experimental results show that temporal graph clustering enables more flexibility in finding a balance between time and space requirements, and our framework can effectively improve the performance of existing temporal graph learning methods. The code is released: https://github.com/MGitHubL/Deep-Temporal-Graph-Clustering.

Various information in different modalities in an intuitive way in multi-modal knowledge graphs (MKGs), which are utilized in different downstream tasks, like recommendation. However, most MKGs are still far from complete, which motivates the flourishing of MKG reasoning models. Recently, with the development of general artificial intelligence, pre-trained transformers have drawn increasing attention, especially in multi-modal scenarios. However, the research of multi-modal pre-trained transformers (MPT) for knowledge graph reasoning (KGR) is still at an early stage. As the biggest difference between MKG and other multi-modal data, the rich structural information underlying the MKG is still not fully utilized in previous MPT. Most of them only use the graph structure as a retrieval map for matching images and texts connected with the same entity, which hinders their reasoning performances. To this end, the graph Structure Guided Multi-modal Pre-trained Transformer is proposed for knowledge graph reasoning (SGMPT). Specifically, the graph structure encoder is adopted for structural feature encoding. Then, a structure-guided fusion module with two simple yet effective strategies, i.e., weighted summation and alignment constraint, is designed to inject the structural information into both the textual and visual features. To the best of our knowledge, SGMPT is the first MPT for multi-modal KGR, which mines structural information underlying MKGs. Extensive experiments on FB15k-237-IMG and WN18-IMG, demonstrate that our SGMPT outperforms existing state-of-the-art models, and proves the effectiveness of the designed strategies.

Contrastive deep graph clustering (CDGC) leverages the power of contrastive learning to group nodes into different clusters. The quality of contrastive samples is crucial for achieving better performance, making augmentation techniques a key factor in the process. However, the augmentation samples in existing methods are always predefined by human experiences, and agnostic from the downstream task clustering, thus leading to high human resource costs and poor performance. To overcome these limitations, we propose a Graph Node Clustering with Fully Learnable Augmentation, termed GraphLearner. It introduces learnable augmentors to generate high-quality and task-specific augmented samples for CDGC. GraphLearner incorporates two learnable augmentors specifically designed for capturing attribute and structural information. Moreover, we introduce two refinement matrices, including the high-confidence pseudo-label matrix and the cross-view sample similarity matrix, to enhance the reliability of the learned affinity matrix. During the training procedure, we notice the distinct optimization goals for training learnable augmentors and contrastive learning networks. In other words, we should both guarantee the consistency of the embeddings as well as the diversity of the augmented samples. To address this challenge, we propose an adversarial learning mechanism within our method. Besides, we leverage a two-stage training strategy to refine the high-confidence matrices. Extensive experimental results on six benchmark datasets validate the effectiveness of GraphLearner.The code and appendix of GraphLearner are available at https://github.com/xihongyang1999/GraphLearner on Github.

Traditional knowledge graph embedding (KGE) models map entities and relations to unique embedding vectors in a shallow lookup manner. As the scale of data becomes larger, this manner will raise unaffordable computational costs. Anchor-based strategies have been treated as effective ways to alleviate such efficiency problems by propagation on representative entities instead of the whole graph. However, most existing anchor-based KGE models select the anchors in a primitive manner, which limits their performance. To this end, we propose a novel anchor-based strategy for KGE, i.e., a relational clustering-based anchor selection strategy (RecPiece), where two characteristics are leveraged, i.e., (1) representative ability of the cluster centroids and (2) descriptive ability of relation types in KGs. Specifically, we first perform clustering over features of factual triplets instead of entities, where cluster number is naturally set as number of relation types since each fact can be characterized by its relation in KGs. Then, representative triplets are selected around the clustering centroids, further mapped into corresponding anchor entities. Extensive experiments on six datasets show that RecPiece achieves higher performances but comparable or even fewer parameters compared to previous anchor-based KGE models, indicating that our model can select better anchors in a more scalable way.

Knowledge graph reasoning (KGR), aiming to deduce new facts from existing facts based on mined logic rules underlying knowledge graphs (KGs), has become a fast-growing research direction. It has been proven to significantly benefit the usage of KGs in many AI applications, such as question answering, recommendation systems, and etc. According to the graph types, existing KGR models can be roughly divided into three categories, i.e., static models, temporal models, and multi-modal models. Early works in this domain mainly focus on static KGR, and recent works try to leverage the temporal and multi-modal information, which are more practical and closer to real-world. However, no survey papers and open-source repositories comprehensively summarize and discuss models in this important direction. To fill the gap, we conduct a first survey for knowledge graph reasoning tracing from static to temporal and then to multi-modal KGs. Concretely, the models are reviewed based on bi-level taxonomy, i.e., top-level (graph types) and base-level (techniques and scenarios). Besides, the performances, as well as datasets, are summarized and presented. Moreover, we point out the challenges and potential opportunities to enlighten the readers.

Graph Neural Networks (GNNs) have achieved promising performance in semi-supervised node classification in recent years. However, the problem of insufficient supervision, together with representation collapse, largely limits the performance of the GNNs in this field. To alleviate the collapse of node representations in semi-supervised scenario, we propose a novel graph contrastive learning method, termed M ixed G raph C ontrastive N etwork (MGCN). In our method, we improve the discriminative capability of the latent embeddings by an interpolation-based augmentation strategy and a correlation reduction mechanism. Specifically, we first conduct the interpolation-based augmentation in the latent space and then force the prediction model to change linearly between samples. Second, we enable the learned network to tell apart samples across two interpolation-perturbed views through forcing the correlation matrix across views to approximate an identity matrix. By combining the two settings, we extract rich supervision information from both the abundant unlabeled nodes and the rare yet valuable labeled nodes for discriminative representation learning. Extensive experimental results on six datasets demonstrate the effectiveness and the generality of MGCN compared to the existing state-of-the-art methods. The code of MGCN is available at https://github.com/xihongyang1999/MGCN on Github.

Knowledge graph embedding (KGE) aims at learning powerful representations to benefit various artificial intelligence applications. Meanwhile, contrastive learning has been widely leveraged in graph learning as an effective mechanism to enhance the discriminative capacity of the learned representations. However, the complex structures of KG make it hard to construct appropriate contrastive pairs. Only a few attempts have integrated contrastive learning strategies with KGE. But, most of them rely on language models (e.g.,Bert) for contrastive pair construction instead of fully mining information underlying the graph structure, hindering expressive ability. Surprisingly, we find that the entities within a relational symmetrical structure are usually similar and correlated. To this end, we propose a knowledge graph contrastive learning framework based on relation-symmetrical structure, KGE-SymCL, which mines symmetrical structure information in KGs to enhance the discriminative ability of KGE models. Concretely, a plug-and-play approach is proposed by taking entities in the relation-symmetrical positions as positive pairs. Besides, a self-supervised alignment loss is designed to pull together positive pairs. Experimental results on link prediction and entity classification datasets demonstrate that our KGE-SymCL can be easily adopted to various KGE models for performance improvements. Moreover, extensive experiments show that our model could outperform other state-of-the-art baselines.

Federated knowledge graph reasoning (FedKGR) aims to perform reasoning over different clients while protecting data privacy, drawing increasing attention to its high practical value. Previous works primarily focus on data heterogeneity, ignoring challenges from limited data scale and primitive negative sample strategies, i.e., random entity replacement, which yield low-quality negatives and zero loss issues. Meanwhile, generative adversarial networks (GANs) are widely used in different fields to generate high-quality negative samples, but no work has been developed for FedKGR. To this end, we propose a plug-and-playEntity-awareAdversarialNegative sampling strategy for FedKGR, termed FedEAN. Specifically, we are the first to adopt GANs to generate high-quality negative samples in different clients. It takes the target triplet in each batch as input and outputs high-quality negative samples, which guaranteed by the joint training of the generator and discriminator. Moreover, we design an entity-aware adaptive negative sampling mechanism based on the similarity of entity representations before and after server aggregation, which can persevere the entity global consistency across clients during training. Extensive experiments demonstrate that FedEAN excels with various FedKGR backbones, demonstrating its ability to construct high-quality negative samples and address the zero-loss issue.

Masked graph autoencoder (MGAE) has emerged as a promising self-supervised graph pre-training (SGP) paradigm due to its simplicity and effectiveness. However, existing efforts perform the mask-then-reconstruct operation in the raw data space as is done in computer vision (CV) and natural language processing (NLP) areas, while neglecting the important non-Euclidean property of graph data. As a result, the highly unstable local structures largely increase the uncertainty in inferring masked data and decrease the reliability of the exploited self-supervision signals, leading to inferior representations for downstream evaluations. To address this issue, we propose a novel SGP method termed Robust mAsked gRaph autoEncoder (RARE) to improve the certainty in inferring masked data and the reliability of the self-supervision mechanism by further masking and reconstructing node samples in the high-order latent feature space. Through both theoretical and empirical analyses, we have discovered that performing a joint mask-then-reconstruct strategy in both latent feature and raw data spaces could yield improved stability and performance. To this end, we elaborately design a masked latent feature completion scheme, which predicts latent features of masked nodes under the guidance of high-order sample correlations that are hard to be observed from the raw data perspective. Specifically, we first adopt a latent feature predictor to predict the masked latent features from the visible ones. Next, we encode the raw data of masked samples with a momentum graph encoder and subsequently employ the resulting representations to improve the predicted results through latent feature matching. Extensive experiments on seventeen datasets have demonstrated the effectiveness and robustness of RARE against state-of-the-art (SOTA) competitors across three downstream tasks. Our source code is available athttps://github.com/WxTu/RARE.

Deep clustering, which can elegantly exploit data representation to seek a partition of the samples, has attracted intensive attention. Recently, combining auto-encoder (AE) with graph neural networks (GNNs) has accomplished excellent performance by introducing structural information implied among data in clustering tasks. However, we observe that there are some limitations of most existing works: 1) in practical graph datasets, there exist some noisy or inaccurate connections among nodes, which would confuse network learning and cause biased representations, thus leading to unsatisfied clustering performance; 2) lacking dynamic information fusion module to carefully combine and refine the node attributes and the graph structural information to learn more consistent representations; and 3) failing to exploit the two separated views' information for generating a more robust target distribution. To solve these problems, we propose a novel method termed deep fusion clustering network with reliable structure preservation (DFCN-RSP). Specifically, the random walk mechanism is introduced to boost the reliability of the original graph structure by measuring localized structure similarities among nodes. It can simultaneously filter out noisy connections and supplement reliable connections in the original graph. Moreover, we provide a transformer-based graph auto-encoder (TGAE) that can use a self-attention mechanism with the localized structure similarity information to fine-tune the fused topology structure among nodes layer by layer. Furthermore, we provide a dynamic cross-modality fusion strategy to combine the representations learned from both TGAE and AE. Also, we design a triplet self-supervision strategy and a target distribution generation measure to explore the cross-modality information. The experimental results on five public benchmark datasets reflect that DFCN-RSP is more competitive than the state-of-the-art deep clustering algorithms. The corresponding code is available at https://github.com/gongleii/DFCN-RSP.

Contrastive learning has recently attracted plenty of attention in deep graph clustering due to its promising performance. However, complicated data augmentations and time-consuming graph convolutional operations undermine the efficiency of these methods. To solve this problem, we propose a simple contrastive graph clustering (SCGC) algorithm to improve the existing methods from the perspectives of network architecture, data augmentation, and objective function. As to the architecture, our network includes two main parts, that is, preprocessing and network backbone. A simple low-pass denoising operation conducts neighbor information aggregation as an independent preprocessing, and only two multilayer perceptrons (MLPs) are included as the backbone. For data augmentation, instead of introducing complex operations over graphs, we construct two augmented views of the same vertex by designing parameter unshared Siamese encoders and perturbing the node embeddings directly. Finally, as to the objective function, to further improve the clustering performance, a novel cross-view structural consistency objective function is designed to enhance the discriminative capability of the learned network. Extensive experimental results on seven benchmark datasets validate our proposed algorithm's effectiveness and superiority. Significantly, our algorithm outperforms the recent contrastive deep clustering competitors with at least seven times speedup on average. The code of SCGC is released at SCGC. Besides, we share a collection of deep graph clustering, including papers, codes, and datasets at ADGC.

Anomaly detection (AD), which models a given normal class and distinguishes it from the rest of abnormal classes, has been a long-standing topic with ubiquitous applications. As modern scenarios often deal with massive high-dimensional complex data spawned by multiple sources, it is natural to consider AD from the perspective of multiview deep learning. However, it has not been formally discussed by the literature and remains underexplored. Motivated by this blank, this article makes fourfold contributions: First, to the best of our knowledge, this is the first work that formally identifies and formulates the multiview deep AD problem. Second, we take recent advances in relevant areas into account and systematically devise various baseline solutions, which lays the foundation for multiview deep AD research. Third, to remedy the problem that limited benchmark datasets are available for multiview deep AD, we extensively collect the existing public data and process them into more than 30 multiview benchmark datasets via multiple means, so as to provide a better evaluation platform for multiview deep AD. Finally, by comprehensively evaluating the devised solutions on different types of multiview deep AD benchmark datasets, we conduct a thorough analysis on the effectiveness of the designed baselines and hopefully provide other researchers with beneficial guidance and insight into the new multiview deep AD topic.

Semi-supervised learning (SSL) has long been proved to be an effective technique to construct powerful models with limited labels. In the existing literature, consistency regularization-based methods, which force the perturbed samples to have similar predictions with the original ones have attracted much attention for their promising accuracy. However, we observe that the performance of such methods decreases drastically when the labels get extremely limited, e.g., 2 or 3 labels for each category. Our empirical study finds that the main problem lies with the drift of semantic information in the procedure of data augmentation. The problem can be alleviated when enough supervision is provided. However, when little guidance is available, the incorrect regularization would mislead the network and undermine the performance of the algorithm. To tackle the problem, we: 1) propose an interpolation-based method to construct more reliable positive sample pairs and 2) design a novel contrastive loss to guide the embedding of the learned network to change linearly between samples so as to improve the discriminative capability of the network by enlarging the margin decision boundaries. Since no destructive regularization is introduced, the performance of our proposed algorithm is largely improved. Specifically, the proposed algorithm outperforms the second best algorithm (Comatch) with 5.3% by achieving 88.73% classification accuracy when only two labels are available for each class on the CIFAR-10 dataset. Moreover, we further prove the generality of the proposed method by improving the performance of the existing state-of-the-art algorithms considerably with our proposed strategy. The corresponding code is available at https://github.com/xihongyang1999/ICL_SSL.

A weakness of the existing metric-based few-shot classification method is that task-unrelated objects or backgrounds may mislead the model since the small number of samples in the support set is insufficient to reveal the task-related targets. An essential cue of human wisdom in the few-shot classification task is that they can recognize the task-related targets by a glimpse of support images without being distracted by task-unrelated things. Thus, we propose to explicitly learn task-related saliency features and make use of them in the metric-based few-shot learning schema. We divide the tackling of the task into three phases, namely, the modeling, the analyzing, and the matching. In the modeling phase, we introduce a saliency sensitive module (SSM), which is an inexact supervision task jointly trained with a standard multiclass classification task. SSM not only enhances the fine-grained representation of feature embedding but also can locate the task-related saliency features. Meanwhile, we propose a self-training-based task-related saliency network (TRSN) which is a lightweight network to distill task-related salience produced by SSM. In the analyzing phase, we freeze TRSN and use it to handle novel tasks. TRSN extracts task-relevant features while suppressing the disturbing task-unrelated features. We, therefore, can discriminate samples accurately in the matching phase by strengthening the task-related features. We conduct extensive experiments on five-way 1-shot and 5-shot settings to evaluate the proposed method. Results show that our method achieves a consistent performance gain on benchmarks and achieves the state-of-the-art.

Contrastive deep graph clustering, which aims to divide nodes into disjoint groups via contrastive mechanisms, is a challenging research spot. Among the recent works, hard sample mining-based algorithms have achieved great attention for their promising performance. However, we find that the existing hard sample mining methods have two problems as follows. 1) In the hardness measurement, the important structural information is overlooked for similarity calculation, degrading the representativeness of the selected hard negative samples. 2) Previous works merely focus on the hard negative sample pairs while neglecting the hard positive sample pairs. Nevertheless, samples within the same cluster but with low similarity should also be carefully learned. To solve the problems, we propose a novel contrastive deep graph clustering method dubbed Hard Sample Aware Network (HSAN) by introducing a comprehensive similarity measure criterion and a general dynamic sample weighing strategy. Concretely, in our algorithm, the similarities between samples are calculated by considering both the attribute embeddings and the structure embeddings, better revealing sample relationships and assisting hardness measurement. Moreover, under the guidance of the carefully collected high-confidence clustering information, our proposed weight modulating function will first recognize the positive and negative samples and then dynamically up-weight the hard sample pairs while down-weighting the easy ones. In this way, our method can mine not only the hard negative samples but also the hard positive sample, thus improving the discriminative capability of the samples further. Extensive experiments and analyses demonstrate the superiority and effectiveness of our proposed method. The source code of HSAN is shared at https://github.com/yueliu1999/HSAN and a collection (papers, codes and, datasets) of deep graph clustering is shared at https://github.com/yueliu1999/Awesome-Deep-Graph-Clustering on Github.

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.

Multi-view clustering has attracted increasing attention in data mining communities. Despite superior clustering performance, we observe that existing multi-view subspace clustering methods directly fuse multi-view information in the similarity level by merging noisy affinity matrices; and isolate the processes of affinity learning, multiple information fusion and clustering. Both factors may cause insufficient utilization of multi-view information, leading to unsatisfying clustering performance. This paper proposes a novel consensus one-step multi-view subspace clustering (COMVSC) method to address these issues. Instead of directly fusing affinity matrices, COMVSC optimally integrates discriminative partition-level information, which is helpful in eliminating noise among data. Moreover, the affinity matrices, consensus representation and final clustering labels are learned simultaneously in a unified framework. Extensive experiment results on benchmark datasets demonstrate the superiority of our method over other state-of-the-art approaches.

Deep graph clustering, which aims to group the nodes of a graph into disjoint clusters with deep neural networks, has achieved promising progress in recent years. However, the existing methods fail to scale to the large graph with million nodes. To solve this problem, a scalable deep graph clustering method (Dink-Net) is proposed with the idea of dilation and shrink. Firstly, by discriminating nodes, whether being corrupted by augmentations, representations are learned in a self-supervised manner. Meanwhile, the cluster centers are initialized as learnable neural parameters. Subsequently, the clustering distribution is optimized by minimizing the proposed cluster dilation loss and cluster shrink loss in an adversarial manner. By these settings, we unify the two-step clustering, i.e., representation learning and clustering optimization, into an end-to-end framework, guiding the network to learn clustering-friendly features. Besides, Dink-Net scales well to large graphs since the designed loss functions adopt the mini-batch data to optimize the clustering distribution even without performance drops. Both experimental results and theoretical analyses demonstrate the superiority of our method. Compared to the runner-up, Dink-Net achieves $9.62%$ NMI improvement on the ogbn-papers100M dataset with 111 million nodes and 1.6 billion edges. The source code is released: https://github.com/yueliu1999/Dink-Net. Besides, a collection (papers, codes, and datasets) of deep graph clustering is shared on GitHub https://github.com/yueliu1999/Awesome-Deep-Graph-Clustering.

Audiovisual data is everywhere in this digital age, which raises higher requirements for the deep learning models developed on them. To well handle the information of the multi-modal data is the key to a better audiovisual modal. We observe that these audiovisual data naturally have temporal attributes, such as the time information for each frame in the video. More concretely, such data is inherently multi-modal according to both audio and visual cues, which proceed in a strict chronological order. It indicates that temporal information is important in multi-modal acoustic event modeling for both intra- and inter-modal. However, existing methods deal with each modal feature independently and simply fuse them together, which neglects the mining of temporal relation and thus leads to sub-optimal performance. With this motivation, we propose a Temporal Multi-modal graph learning method for Acoustic event Classification, called TMac, by modeling such temporal information via graph learning techniques. In particular, we construct a temporal graph for each acoustic event, dividing its audio data and video data into multiple segments. Each segment can be considered as a node, and the temporal relationships between nodes can be considered as timestamps on their edges. In this case, we can smoothly capture the dynamic information in intra-modal and inter-modal. Several experiments are conducted to demonstrate TMac outperforms other SOTA models in performance. Our code is available at https://github.com/MGitHubL/TMac.

Deep graph clustering, which aims to group nodes into disjoint clusters by neural networks in an unsupervised manner, has attracted great attention in recent years. Although the performance has been largely improved, the excellent performance of the existing methods heavily relies on an accurately predefined cluster number, which is not always available in the real-world scenario. To enable the deep graph clustering algorithms to work without the guidance of the predefined cluster number, we propose a new deep graph clustering method termed Reinforcement Graph Clustering (RGC). In our proposed method, cluster number determination and unsupervised representation learning are unified into a uniform framework by the reinforcement learning mechanism. Concretely, the discriminative node representations are first learned with the contrastive pretext task. Then, to capture the clustering state accurately with both local and global information in the graph, both node and cluster states are considered. Subsequently, at each state, the qualities of different cluster numbers are evaluated by the quality network, and the greedy action is executed to determine the cluster number. In order to conduct feedback actions, the clustering-oriented reward function is proposed to enhance the cohesion of the same clusters and separate the different clusters. Extensive experiments demonstrate the effectiveness and efficiency of our proposed method. The source code of RGC is shared at https://github.com/yueliu1999/RGC and a collection (papers, codes and, datasets) of deep graph clustering is shared at https://github.com/yueliu1999/Awesome-Deep-Graph-Clustering on Github.

Benefiting from the strong view-consistent information mining capacity, multi-view contrastive clustering has attracted plenty of attention in recent years. However, we observe the following drawback, which limits the clustering performance from further improvement. The existing multi-view models mainly focus on the consistency of the same samples in different views while ignoring the circumstance of similar but different samples in cross-view scenarios. To solve this problem, we propose a novel Dual contrastive calibration network for Multi-View Clustering (DealMVC). Specifically, we first design a fusion mechanism to obtain a global cross-view feature. Then, a global contrastive calibration loss is proposed by aligning the view feature similarity graph and the high-confidence pseudo-label graph. Moreover, to utilize the diversity of multi-view information, we propose a local contrastive calibration loss to constrain the consistency of pair-wise view features. The feature structure is regularized by reliable class information, thus guaranteeing similar samples have similar features in different views. During the training procedure, the interacted cross-view feature is jointly optimized at both local and global levels. In comparison with other state-of-the-art approaches, the comprehensive experimental results obtained from eight benchmark datasets provide substantial validation of the effectiveness and superiority of our algorithm. We release the code of DealMVC at https://github.com/xihongyang1999/DealMVC on GitHub.

Contrastive graph node clustering via learnable data augmentation is a hot research spot in the field of unsupervised graph learning. The existing methods learn the sampling distribution of a pre-defined augmentation to generate data-driven augmentations automatically. Although promising clustering performance has been achieved, we observe that these strategies still rely on pre-defined augmentations, the semantics of the augmented graph can easily drift. The reliability of the augmented view semantics for contrastive learning can not be guaranteed, thus limiting the model performance. To address these problems, we propose a novel CONtrastiVe Graph ClustEring network with Reliable AugmenTation (COVERT). Specifically, in our method, the data augmentations are processed by the proposed reversible perturb-recover network. It distills reliable semantic information by recovering the perturbed latent embeddings. Moreover, to further guarantee the reliability of semantics, a novel semantic loss is presented to constrain the network via quantifying the perturbation and recovery. Lastly, a label-matching mechanism is designed to guide the model by clustering information through aligning the semantic labels and the selected high-confidence clustering pseudo labels. Extensive experimental results on seven datasets demonstrate the effectiveness of the proposed method. We release the code and appendix of CONVERT at https://github.com/xihongyang1999/CONVERT on GitHub.

Reasoning on temporal knowledge graphs (TKGR), aiming to infer missing events along the timeline, has been widely studied to alleviate incompleteness issues in TKG, which is composed of a series of KG snapshots at different timestamps. Two types of information, i.e., intra-snapshot structural information and inter-snapshot temporal interactions, mainly contribute to the learned representations for reasoning in previous models. However, these models fail to leverage (1) semantic correlations between relationships for the former information and (2) the periodic temporal patterns along the timeline for the latter one. Thus, such insufficient mining manners hinder expressive ability, leading to sub-optimal performances. To address these limitations, we propose a novel reasoning model, termed RPC, which sufficiently mines the information underlying the Relational correlations and Periodic patterns via two novel Correspondence units, i.e., relational correspondence unit (RCU) and periodic correspondence unit (PCU). Concretely, relational graph convolutional network (RGCN) and RCU are used to encode the intra-snapshot graph structural information for entities and relations, respectively. Besides, the gated recurrent units (GRU) and PCU are designed for sequential and periodic inter-snapshot temporal interactions, separately. Moreover, the model-agnostic time vectors are generated by time2vector encoders to guide the time-dependent decoder for fact scoring. Extensive experiments on six benchmark datasets show that RPC outperforms the state-of-the-art TKGR models, and also demonstrate the effectiveness of two novel strategies in our model.

Clustering methods have been widely used in single-cell RNA-seq data for investigating tumor heterogeneity. Since traditional clustering methods fail to capture the high-dimension methods, deep clustering methods have drawn increasing attention these years due to their promising strengths on the task. However, existing methods consider either the attribute information of each cell or the structure information between different cells. In other words, they cannot sufficiently make use of all of this information simultaneously. To this end, we propose a novel single-cell deep fusion clustering model, which contains two modules, i.e. an attributed feature clustering module and a structure-attention feature clustering module. More concretely, two elegantly designed autoencoders are built to handle both features regardless of their data types. Experiments have demonstrated the validity of the proposed approach, showing that it is efficient to fuse attributes, structure, and attention information on single-cell RNA-seq data. This work will be further beneficial for investigating cell subpopulations and tumor microenvironment. The Python implementation of our work is now freely available at https://github.com/DayuHuu/scDFC.

Existing unsupervised outlier detection (OD) solutions face a grave challenge with surging visual data like images. Although deep neural networks (DNNs) prove successful for visual data, deep OD remains difficult due to OD’s unsupervised nature. This paper proposes a novel framework namedE$^{3}$Outlierthat can performeffective andend-to-end deep outlier removal. Its core idea is to introduceself-supervisioninto deep OD. Specifically, our major solution is to adopt a discriminative learning paradigm that creates multiple pseudo classes from given unlabeled data by various data operations, which enables us to apply prevalent discriminative DNNs (e.g. ResNet) to the unsupervised OD problem. Then, with theoretical and empirical demonstration, we argue that inlier priority, a property that encourages DNN to prioritize inliers during self-supervised learning, makes it possible to perform end-to-end OD. Meanwhile, unlike frequently-used outlierness measures (e.g. density, proximity) in previous OD methods, we explore network uncertainty and validate it as a highly effective outlierness measure, while two practical score refinement strategies are also designed to improve OD performance. Finally, in addition to the discriminative learning paradigm above, we also explore the solutions that exploit other learning paradigms (i.e. generative learning and contrastive learning) to introduce self-supervision forE$^{3}$Outlier. Such extendibility not only brings further performance gain on relatively difficult datasets, but also enablesE$^{3}$Outlierto be applied to other OD applications like video abnormal event detection. Extensive experiments demonstrate thatE$^{3}$Outliercan considerably outperform state-of-the-art counterparts by 10%-30% AUROC. Demo codes are available athttps://github.com/demonzyj56/E3Outlier.

Multiple kernel clustering (MKC) optimally utilizes a group of pre-specified base kernels to improve clustering performance. Among existing MKC algorithms, the recently proposed late fusion MKC methods demonstrate promising clustering performance in various applications and enjoy considerable computational acceleration. However, we observe that the kernel partition learning and late fusion processes are separated from each other in the existing mechanism, which may lead to suboptimal solutions and adversely affect the clustering performance. In this article, we propose a novel late fusion multiple kernel clustering with proxy graph refinement (LFMKC-PGR) framework to address these issues. First, we theoretically revisit the connection between late fusion kernel base partition and traditional spectral embedding. Based on this observation, we construct a proxy self-expressive graph from kernel base partitions. The proxy graph in return refines the individual kernel partitions and also captures partition relations in graph structure rather than simple linear transformation. We also provide theoretical connections and considerations between the proposed framework and the multiple kernel subspace clustering. An alternate algorithm with proved convergence is then developed to solve the resultant optimization problem. After that, extensive experiments are conducted on 12 multi-kernel benchmark datasets, and the results demonstrate the effectiveness of our proposed algorithm. The code of the proposed algorithm is publicly available at https://github.com/wangsiwei2010/graphlatefusion_MKC.

Multiple kernel clustering (MKC) has recently achieved remarkable progress in fusing multisource information to boost the clustering performance. However, the$\mathcal {O}({n}^{2})$memory consumption and$\mathcal {O}({n}^{3})$computational complexity prohibit these methods from being applied into median- or large-scale applications, where$n$denotes the number of samples. To address these issues, we carefully redesign the formulation of subspace segmentation-based MKC, which reduces the memory and computational complexity to$\mathcal {O}({n})$and$\mathcal {O}({n}^{2})$, respectively. The proposed algorithm adopts a novel sampling strategy to enhance the performance and accelerate the speed of MKC. Specifically, we first mathematically model the sampling process and then learn it simultaneously during the procedure of information fusion. By this way, the generated anchor point set can better serve data reconstruction across different views, leading to improved discriminative capability of the reconstruction matrix and boosted clustering performance. Although the integrated sampling process makes the proposed algorithm less efficient than the linear complexity algorithms, the elaborate formulation makes our algorithm straightforward for parallelization. Through the acceleration of GPU and multicore techniques, our algorithm achieves superior performance against the compared state-of-the-art methods on six datasets with comparable time cost to the linear complexity algorithms.

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/wx-liang/RG-MVC.

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.

Multiview clustering has received increasing attention due to its effectiveness in fusing complementary information without manual annotations. Most previous methods hold the assumption that each instance appears in all views. However, it is not uncommon to see that some views may contain some missing instances, which gives rise to incomplete multi-view clustering (IMVC) in literature. Although many IMVC methods have been recently proposed, they always encounter high complexity and expensive time expenditure from being applied into large-scale tasks. In this paper, we present a flexible highly-efficient incomplete large-scale multi-view clustering approach based on bipartite graph framework to solve these issues. Specifically, we formalize multi-view anchor learning and incomplete bipartite graph into a unified framework, which coordinates with each other to boost cluster performance. By introducing the flexible bipartite graph framework to handle IMVC for the first practice, our proposed method enjoys linear complexity respecting to instance numbers, which is more applicable for large-scale IMVC tasks. Comprehensive experimental results on various benchmark datasets demonstrate the effectiveness and efficiency of our proposed algorithm against other IMVC competitors. The code is available at11https://github.com/wangsiwei2010/CVPR22-IMVC-CBG.

Attributed graph clustering is a basic yet essential method for graph data exploration. Recent efforts over graph contrastive learning have achieved impressive clustering performance. However, we observe that the commonly adopted InfoMax operation tends to capture redundant information, limiting the downstream clustering performance. To this end, we develop a novel method termed attributed graph clustering with dual redundancy reduction (AGC-DRR) to reduce the information redundancy in both input space and latent feature space. Specifically, for the input space redundancy reduction, we introduce an adversarial learning mechanism to adaptively learn a redundant edge-dropping matrix to ensure the diversity of the compared sample pairs. To reduce the redundancy in the latent space, we force the correlation matrix of the cross-augmentation sample embedding to approximate an identity matrix. Consequently, the learned network is forced to be robust against perturbation while discriminative against different samples. Extensive experiments have demonstrated that AGC-DRR outperforms the state-of-the-art clustering methods on most of our benchmarks. The corresponding code is available at https://github.com/gongleii/AGC-DRR.

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.

Anchor enhanced multi-view late fusion clustering has attracted numerous researchers' attention for its high clustering accuracy and promising efficiency. However, in the existing methods, the anchor points are usually generated through sampling or linearly combining the samples within the datasets, which could result in enormous time consumption and limited representation capability. To solve the problem, in our method, we learn the view-specific anchor points by learning them directly. Specifically, in our method, we first reconstruct the partition matrix of each view through multiplying a view-specific anchor matrix by a consensus reconstruction matrix. Then, by maximizing the weighted alignment between the base partition matrix and its estimated version in each view, we learn the optimal anchor points for each view. In particular, unlike previous late fusion algorithms, which define anchor points as linear combinations of existing samples, we define anchor points as a series of orthogonal vectors that are directly learned through optimization, which expands the learning space of the anchor points. Moreover, based on the above design, the resultant algorithm has only linear complexity and no hyper-parameter. Experiments on $12$ benchmark kernel datasets and 5 large-scale datasets illustrate that the proposed Efficient Anchor Learning-based Multi-view Clustering (AL-MVC) algorithm achieves the state-of-the-art performance in both clustering performance and efficiency.

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.

Multi-view spectral clustering can effectively reveal the intrinsic cluster structure among data by performing clustering on the learned optimal embedding across views. Though demonstrating promising performance in various applications, most of existing methods usually linearly combine a group of pre-specified first-order Laplacian matrices to construct the optimal Laplacian matrix, which may result in limited representation capability and insufficient information exploitation. Also, storing and implementing complex operations on the{$n\times n}$Laplacian matrices incurs intensive storage and computation complexity. To address these issues, this paper first proposes a multi-view spectral clustering algorithm that learns a high-order optimal neighborhood Laplacian matrix, and then extends it to the late fusion version for accurate and efficient multi-view clustering. Specifically, our proposed algorithm generates the optimal Laplacian matrix by searching the neighborhood of the linear combination of both the first-order and high-order base Laplacian matrices simultaneously. By this way, the representative capacity of the learned optimal Laplacian matrix is enhanced, which is helpful to better utilize the hidden high-order connection information among data, leading to improved clustering performance. We design an efficient algorithm with proved convergence to solve the resultant optimization problem. Extensive experimental results on nine datasets demonstrate the superiority of the proposed algorithm

Multiple kernel clustering (MKC) algorithm aims to group data into different categories by optimally integrating information from a group of pre-specified kernels. Though demonstrating superiorities in various applications, we observe that existing MKC algorithms usuallydo not sufficiently consider the local density around individual data samplesandexcessively limit the representation capacity of the learned optimal kernel, leading to unsatisfying performance. In this paper, we propose an algorithm, called optimal neighborhood MKC with adaptive local kernels (ON-ALK), to address the two issues. In specific, we construct adaptive local kernels to sufficiently consider the local density around individual data samples, where different numbers of neighbors are discriminatingly selected on each sample. Further, the proposed ON-ALK algorithm boosts the representation of the learned optimal kernel via relaxing it into the neighborhood area of weighted combination of the pre-specified kernels. To solve the resultant optimization problem, a three-step iterative algorithm is designed and theoretically proven to be convergent. After that, we also study the generalization bound of the proposed algorithm. Extensive experiments have been conducted to evaluate the clustering performance. As indicated, the algorithm significantly outperforms state-of-the-art methods in recent literatures on six challenging benchmark datasets, verifying its advantages and effectiveness.

Multi-view clustering has attracted increasing attention in multimedia, machine learning and data mining communities. As one kind of the essential multi-view clustering algorithm, multi-view subspace clustering (MVSC) becomes more and more popular due to its strong ability to reveal the intrinsic low dimensional clustering structure hidden across views. Despite superior clustering performance in various applications, we observe that existing MVSC methodsdirectly fuse multi-view information in the similarity level by merging noisy affinity matrices; andisolate the processes of affinity learning, multi-view information fusion and clustering. Both factors may cause insufficient utilization of multi-view information, leading to unsatisfying clustering performance. This paper proposes a novel consensus one-step multi-view subspace clustering (COMVSC) method to address these issues. Instead of directly fusing multiple affinity matrices, COMVSC optimally integrates discriminative partition-level information, which is helpful to eliminate noise among data. Moreover, the affinity matrices, consensus representation and final clustering labels matrix are learned simultaneously in a unified framework. By doing so, the three steps can negotiate with each other to best serve the clustering task, leading to improved performance. Accordingly, we propose an iterative algorithm to solve the resulting optimization problem. Extensive experiment results on benchmark datasets demonstrate the superiority of our method against other state-of-the-art approaches.

Detecting Out-of-Distribution (OoD) data is one of the greatest challenges in safe and robust deployment of machine learning algorithms in medicine. When the algorithms encounter cases that deviate from the distribution of the training data, they often produce incorrect and over-confident predictions. OoD detection algorithms aim to catch erroneous predictions in advance by analysing the data distribution and detecting potential instances of failure. Moreover, flagging OoD cases may support human readers in identifying incidental findings. Due to the increased interest in OoD algorithms, benchmarks for different domains have recently been established. In the medical imaging domain, for which reliable predictions are often essential, an open benchmark has been missing. We introduce the Medical-Out-Of-Distribution-Analysis-Challenge (MOOD) as an open, fair, and unbiased benchmark for OoD methods in the medical imaging domain. The analysis of the submitted algorithms shows that performance has a strong positive correlation with the perceived difficulty, and that all algorithms show a high variance for different anomalies, making it yet hard to recommend them for clinical practice. We also see a strong correlation between challenge ranking and performance on a simple toy test set, indicating that this might be a valuable addition as a proxy dataset during anomaly detection algorithm development.

Multiple kernel subspace clustering (MKSC), as an important extension for handling multi-view non-linear subspace data, has shown notable success in a wide variety of machine learning tasks. The key objective of MKSC is to build a flexible and appropriate graph for clustering from the kernel space. However, existing MKSC methods apply a mechanism utilizing the kernel trick to the traditional self-expressive principle, where the similarity graphs are built on the respective high-dimensional (or even infinite) reproducing kernel Hilbert space (RKHS). Regarding this strategy, we argue that the original high-dimensional spaces usually include noise and unreliable similarity measures and, therefore, output a low-quality graph matrix, which degrades clustering performance. In this paper, inspired by projective clustering, we propose the utilization of a complementary similarity graph by fusing the multiple kernel graphs constructed in the low-dimensional partition space, termed projective multiple kernel subspace clustering (PMKSC). By incorporating intrinsic structures with multi-view data, PMKSC alleviates the noise and redundancy in the original kernel space and obtains high-quality similarity to uncover the underlying clustering structures. Furthermore, we design a three-step alternate algorithm with proven convergence to solve the proposed optimization problem. The experimental results on ten multiple kernel benchmark datasets validate the effectiveness of our proposed PMKSC, compared to the state-of-the-art multiple kernel and kernel subspace clustering methods, by a large margin. Our code is available athttps://github.com/MengjingSun/PMKSC-code.

Current multiple kernel clustering algorithms compute a partition with the consensus kernel or graph learned from the pre-specified ones, while the emerging late fusion methods firstly construct multiple partitions from each kernel separately, and then obtain a consensus one with them. However, both of them directly distill the clustering information from kernels or graphs to partition matrices, where the sudden dimension drop would result in loss of advantageous details for clustering. In this paper, we provide a brief insight of the aforementioned issue and propose a hierarchical approach to perform clustering while preserving advantageous details maximumly. Specifically, we gradually group samples into fewer clusters, together with generating a sequence of intermediary matrices of descending sizes. The consensus partition with is simultaneously learned and conversely guides the construction of intermediary matrices. Nevertheless, this cyclic process is modeled into an unified objective and an alternative algorithm is designed to solve it. In addition, the proposed method is validated and compared with other representative multiple kernel clustering algorithms on benchmark datasets, demonstrating state-of-the-art performance by a large margin.

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.

As a representative of multiple kernel clustering (MKC), simple multiple kernel k-means (SimpleMKKM) is recently put forward to boosting the clustering performance by optimally fusing a group of pre-specified kernel matrices. Despite achieving significant improvement in a variety of applications, we find out that SimpleMKKM could indiscriminately force all sample pairs to be equally aligned with the same ideal similarity. As a result, it does not sufficiently take the variation of samples into consideration, leading to unsatisfying clustering performance. 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. After that, we theoretically show that the objective of SimpleMKKM is a special case of this local kernel alignment criterion with normalizing each base kernel matrix. Based on this observation, the proposed localized SimpleMKKM can be readily implemented by existing SimpleMKKM package. Moreover, we conduct extensive experiments on several widely used benchmark datasets to evaluate the clustering performance of localized SimpleMKKM. The experimental results have demonstrated that our algorithm consistently outperforms the state-of-the-art ones, verifying the effectiveness of the proposed local kernel alignment criterion. The code of Localized SimpleMKKM is publicly available at: https://github.com/xinwangliu/LocalizedSMKKM.

Incomplete multi-view clustering is an important research topic in multimedia where partial data entries of one or more views are missing. Current subspace clustering approaches mostly employ matrix factorization on the observed feature matrices to address this issue. Meanwhile, self-representation technique is left unexplored, since it explicitly relies on full data entries to construct the coefficient matrix, which is contradictory to the incomplete data setting. However, it is widely observed that self-representation subspace method enjoys a better clustering performance over the factorization based one. Therefore, we adapt it to incomplete data by jointly performing data imputation and self-representation learning. To the best of our knowledge, this is the first attempt in incomplete multi-view clustering literature. Besides, the proposed method is carefully compared with current advances in experiment with respect to different missing ratios, verifying its effectiveness.

Multi-view subspace clustering has received widespread attention to effectively fuse multi-view information among multimedia applications. Considering that most existing approaches' cubic time complexity makes it challenging to apply to realistic large-scale scenarios, some researchers have addressed this challenge by sampling anchor points to capture distributions in different views. However, the separation of the heuristic sampling and clustering process leads to weak discriminate anchor points. Moreover, the complementary multi-view information has not been well utilized since the graphs are constructed independently by the anchors from the corresponding views. To address these issues, we propose a Scalable Multi-view Subspace Clustering with Unified Anchors (SMVSC). To be specific, we combine anchor learning and graph construction into a unified optimization framework. Therefore, the learned anchors can represent the actual latent data distribution more accurately, leading to a more discriminative clustering structure. Most importantly, the linear time complexity of our proposed algorithm allows the multi-view subspace clustering approach to be applied to large-scale data. Then, we design a four-step alternative optimization algorithm with proven convergence. Compared with state-of-the-art multi-view subspace clustering methods and large-scale oriented methods, the experimental results on several datasets demonstrate that our SMVSC method achieves comparable or better clustering performance much more efficiently. The code of SMVSC is available at https://github.com/Jeaninezpp/SMVSC.

Multi-view clustering (MVC) has been extensively studied to collect multiple source information in recent years. One typical type of MVC methods is based on matrix factorization to effectively perform dimension reduction and clustering. However, the existing approaches can be further improved with following considerations: i) The current one-layer matrix factorization framework cannot fully exploit the useful data representations. ii) Most algorithms only focus on the shared information while ignore the view-specific structure leading to suboptimal solutions. iii) The partition level information has not been utilized in existing work. To solve the above issues, we propose a novel multi-view clustering algorithm via deep matrix decomposition and partition alignment. To be specific, the partition representations of each view are obtained through deep matrix decomposition, and then are jointly utilized with the optimal partition representation for fusing multi-view information. Finally, an alternating optimization algorithm is developed to solve the optimization problem with proven convergence. The comprehensive experimental results conducted on six benchmark multi-view datasets clearly demonstrates the effectiveness of the proposed algorithm against the SOTA methods. The code address for this algorithm is https://github.com/ZCtalk/MVC-DMF-PA.

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.

Self-supervised learning is a thriving research direction since it can relieve the burden of human labeling for machine learning by seeking for supervision from data instead of human annotation. Although demonstrating promising performance in various applications, we observe that the existing methods usually model the auxiliary learning tasks as classification tasks with finite discrete labels, leading to insufficient supervisory signals, which in turn restricts the representation quality. In this paper, to solve the above problem and make full use of the supervision from data, we design a regression model to predict the continuous parameters of a group of transformations, i.e., image rotation, translation, and scaling. Surprisingly, this naive modification stimulates tremendous potential from data and the resulting supervisory signal has largely improved the performance of image representation learning. Extensive experiments on four image datasets, including CIFAR10, CIFAR100, STL10, and SVHN, indicate that our proposed algorithm outperforms the state-of-the-art unsupervised learning methods by a large margin in terms of classification accuracy. Crucially, we find that with our proposed training mechanism as an initialization, the performance of the existing state-of-the-art classification deep architectures can be preferably improved.

Automatic image segmentation is an essential step for many medical image analysis applications, include computer-aided radiation therapy, disease diagnosis, and treatment effect evaluation. One of the major challenges for this task is the blurry nature of medical images (e.g., CT, MR and, microscopic images), which can often result in low-contrast and vanishing boundaries. With the recent advances in convolutional neural networks, vast improvements have been made for image segmentation, mainly based on the skip-connection-linked encoder-decoder deep architectures. However, in many applications (with adjacent targets in blurry images), these models often fail to accurately locate complex boundaries and properly segment tiny isolated parts. In this paper, we aim to provide a method for blurry medical image segmentation and argue that skip connections are not enough to help accurately locate indistinct boundaries. Accordingly, we propose a novel high-resolution multi-scale encoder-decoder network (HMEDN), in which multi-scale dense connections are introduced for the encoder-decoder structure to finely exploit comprehensive semantic information. Besides skip connections, extra deeply-supervised high-resolution pathways (comprised of densely connected dilated convolutions) are integrated to collect high-resolution semantic information for accurate boundary localization. These pathways are paired with a difficulty-guided cross-entropy loss function and a contour regression task to enhance the quality of boundary detection. Extensive experiments on a pelvic CT image dataset, a multi-modal brain tumor dataset, and a cell segmentation dataset show the effectiveness of our method for 2D/3D semantic segmentation and 2D instance segmentation, respectively. Our experimental results also show that besides increasing the network complexity, raising the resolution of semantic feature maps can largely affect the overall model performance. For different tasks, finding a balance between these two factors can further improve the performance of the corresponding network.

Generalized nucleus segmentation techniques can contribute greatly to reducing the time to develop and validate visual biomarkers for new digital pathology datasets. We summarize the results of MoNuSeg 2018 Challenge whose objective was to develop generalizable nuclei segmentation techniques in digital pathology. The challenge was an official satellite event of the MICCAI 2018 conference in which 32 teams with more than 80 participants from geographically diverse institutes participated. Contestants were given a training set with 30 images from seven organs with annotations of 21,623 individual nuclei. A test dataset with 14 images taken from seven organs, including two organs that did not appear in the training set was released without annotations. Entries were evaluated based on average aggregated Jaccard index (AJI) on the test set to prioritize accurate instance segmentation as opposed to mere semantic segmentation. More than half the teams that completed the challenge outperformed a previous baseline. Among the trends observed that contributed to increased accuracy were the use of color normalization as well as heavy data augmentation. Additionally, fully convolutional networks inspired by variants of U-Net, FCN, and Mask-RCNN were popularly used, typically based on ResNet or VGG base architectures. Watershed segmentation on predicted semantic segmentation maps was a popular post-processing strategy. Several of the top techniques compared favorably to an individual human annotator and can be used with confidence for nuclear morphometrics.

Multiple kernel clustering (MKC) has been intensively studied during the last few decades. Even though they demonstrate promising clustering performance in various applications, existing MKC algorithms do not sufficiently consider the intrinsic neighborhood structure among base kernels, which could adversely affect the clustering performance. In this paper, we propose a simple yet effective neighbor-kernel-based MKC algorithm to address this issue. Specifically, we first define a neighbor kernel, which can be utilized to preserve the block diagonal structure and strengthen the robustness against noise and outliers among base kernels. After that, we linearly combine these base neighbor kernels to extract a consensus affinity matrix through an exact-rank-constrained subspace segmentation. The naturally possessed block diagonal structure of neighbor kernels better serves the subsequent subspace segmentation, and in turn, the extracted shared structure is further refined through subspace segmentation based on the combined neighbor kernels. In this manner, the above two learning processes can be seamlessly coupled and negotiate with each other to achieve better clustering. Furthermore, we carefully design an efficient iterative optimization algorithm with proven convergence to address the resultant optimization problem. As a by-product, we reveal an interesting insight into the exact-rank constraint in ridge regression by careful theoretical analysis: it back-projects the solution of the unconstrained counterpart to its principal components. Comprehensive experiments have been conducted on several benchmark data sets, and the results demonstrate the effectiveness of the proposed algorithm.

Medical image segmentation is a key step for various applications, such as image-guided radiation therapy and diagnosis. Recently, deep neural networks provided promising solutions for automatic image segmentation; however, they often perform good on regular samples (i.e., easy-to-segment samples), since the datasets are dominated by easy and regular samples. For medical images, due to huge inter-subject variations or disease-specific effects on subjects, there exist several difficult-to-segment cases that are often overlooked by the previous works. To address this challenge, we propose a difficulty-aware deep segmentation network with confidence learning for end-to-end segmentation. The proposed framework has two main contributions: 1) Besides the segmentation network, we also propose a fully convolutional adversarial network for confidence learning to provide voxel-wise and region-wise confidence information for the segmentation network. We relax the adversarial learning to confidence learning by decreasing the priority of adversarial learning, so that we can avoid the training imbalance between generator and discriminator. 2) We propose a difficulty-aware attention mechanism to properly handle hard samples or hard regions considering structural information, which may go beyond the shortcomings of focal loss. We further propose a fusion module to selectively fuse the concatenated feature maps in encoder-decoder architectures. Experimental results on clinical and challenge datasets show that our proposed network can achieve state-of-the-art segmentation accuracy. Further analysis also indicates that each individual component of our proposed network contributes to the overall performance improvement.

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 pre-specified 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.

In this paper, we propose an unsupervised feature selection framework which simultaneously preserves the local geometric structure and global discriminative structure of data. Also, the spectral clustering algorithm is incorporated into this framework to exploit the discriminative structure. To demonstrate the generality of our framework, we instantiate our framework into two specific algorithms by characterizing the local geometric structure of data with two well-known models, i.e., locally linear embedding and linear preserve projection. After that, we provide an efficient algorithm with proved convergence to solve the resultant optimization problem. Comprehensive experiments have been conducted on eleven benchmark data sets and the results demonstrate the superior performance of our framework.

In this paper, we propose a binary feature selection framework in kernel spaces, where each feature is projected into kernel spaces and a binary classification task is constructed in this space. Subsequently, the features are selected according to the normal vector of the learned classifier, which reflects the importance of each feature. To achieve the effect of feature selection, an £i-norm regularization is imposed on the normal vector to enforce its sparsity. Also, our framework can be naturally extended to the semi-supervised feature selection scenario via the well-known manifold regularization technique. Furthermore, the issue of eliminating the potential redundancy among the selected features is well discussed. Finally, we provide some theoretical results which guarantee the feasibility of the proposed framework. Comprehensive experiments have been conducted on six benchmark data sets and the results demonstrate the performance of our framework.