Zero-shot event extraction (ZSEE) remains a significant challenge for large language models (LLMs) due to the need for complex reasoning and domain-specific understanding. Direct prompting often yields incomplete or structurally invalid outputs—such as misclassified triggers, missing arguments, and schema violations. To address these limitations, we present Agent-Event-Coder (AEC), a novel multi-agent framework that treats event extraction like software engineering: as a structured, iterative code-generation process. AEC decomposes ZSEE into specialized subtasks—retrieval, planning, coding, and verification—each handled by a dedicated LLM agent. Event schemas are represented as executable class definitions, enabling deterministic validation and precise feedback via a verification agent. This programming-inspired approach allows for systematic disambiguation and schema enforcement through iterative refinement. By leveraging collaborative agent workflows, AEC enables LLMs to produce precise, complete, and schema-consistent extractions in zero-shot settings. Experiments across five diverse domains and six LLMs demonstrate that AEC consistently outperforms prior zero-shot baselines, showcasing the power of treating event extraction like code generation.

Marked Temporal Point Processes (MTPPs) provide a principled framework for modeling asynchronous event sequences by conditioning on the history of past events. However, most existing MTPP models rely on channel-mixing strategies that encode information from different event types into a single, fixed-size latent representation. This entanglement can obscure type-specific dynamics, leading to performance degradation and increased risk of overfitting. In this work, we introduce ITPP, a novel channel-independent architecture for MTPP modeling that decouples event type information using an encoder-decoder framework with an ODE-based backbone. Central to ITPP is a type-aware inverted self-attention mechanism, designed to explicitly model inter-channel correlations among heterogeneous event types. This architecture enhances effectiveness and robustness while reducing overfitting. Comprehensive experiments on multiple real-world and synthetic datasets demonstrate that ITPP consistently outperforms state-of-the-art MTPP models in both predictive accuracy and generalization.

Multi-view clustering (MVC) is intended to enhance clustering performance by integrating complementary information from diverse sources. However, prevailing low-rank tensor based MVC methods often exhibit suboptimal performance, as they tend to treat singular values equally and lack structured sparsity constraints. A novel framework termed EUGL-WTSN is proposed to address the drawbacks of existing methods. It enhances unified graph learning and low-rank tensor learning model through the joint application of weighted tensor Schatten$p$-norm and$\ell \_{1,2}$-norm. Specifically, weighted tensor Schatten$p$-norm is employed in our model to more accurately capture inter-view relationships and spatial structures embedded within the multi-view data. This approach yields a tighter relaxation bound for the tensor rank through adaptive truncation of singular values. Furthermore, the$\ell \_{1,2}$-norm regularization is applied to the view-specific affinity matrices to induce row sparsity, which enhances the discriminability and robustness of the learned graph structures. To optimize the proposed model, we propose an efficient iterative optimization algorithm with provable convergence guarantees. Experimental evaluations reveal that our proposed framework achieves better performance than existing methodologies, demonstrating significant improvements in clustering performance and model robustness. Codes and datasets are available:https://github.com/yangming1984/EUGL-WTSN.

Most existing graph clustering methods primarily focus on exploiting topological structure, often neglecting the "missing-half" node feature information, especially how these features can enhance clustering performance. This issue is further compounded by the challenges associated with high-dimensional features. Feature selection in graph clustering is particularly difficult because it requires simultaneously discovering clusters and identifying the relevant features for these clusters. To address this gap, we introduce a novel paradigm called "one node one model", which builds an exclusive model for each node and defines the node label as a combination of predictions for node groups. Specifically, the proposed "Feature Personalized Graph Clustering (FPGC)" method identifies cluster-relevant features for each node using a squeeze-and-excitation block, integrating these features into each model to form the final representations. Additionally, the concept of feature cross is developed as a data augmentation technique to learn low-order feature interactions. Extensive experimental results demonstrate that FPGC outperforms state-of-the-art clustering methods. Moreover, the plug-and-play nature of our method provides a versatile solution to enhance GNN-based models from the feature perspective.

Despite the recent success of two-stage prototypical networks in few-shot named entity recognition (NER), challenges such as over/under-detected false spans in the span detection stage and unaligned entity prototypes in the type classification stage persist. Additionally, LLMs have not proven to be effective few-shot information extractors in general. In this paper, we propose an approach called Boundary-Aware LLMs for Few-Shot Named Entity Recognition to address these issues. We introduce a boundary-aware contrastive learning strategy to enhance the LLM’s ability to perceive entity boundaries for generalized entity spans. Additionally, we utilize LoRAHub to align information from the target domain to the source domain, thereby enhancing adaptive cross-domain classification capabilities. Extensive experiments across various benchmarks demonstrate that our framework outperforms prior methods, validating its effectiveness. In particular, the proposed strategies demonstrate effectiveness across a range of LLM architectures. The code and data are released on https://github.com/UESTC-GQJ/BANER.

Graph Domain Adaptation (GDA) addresses a pressing challenge in cross-network learning, particularly pertinent due to the absence of labeled data in real-world graph datasets. Recent studies attempted to learn domain invariant representations by eliminating structural shifts between graphs. In this work, we show that existing methodologies have overlooked the significance of the graph node attribute, a pivotal factor for graph domain alignment. Specifically, we first reveal the impact of node attributes for GDA by theoretically proving that in addition to the graph structural divergence between the domains, the node attribute discrepancy also plays a critical role in GDA. Moreover, we also empirically show that the attribute shift is more substantial than the topology shift, which further underscore the importance of node attribute alignment in GDA. Inspired by this finding, a novel cross-channel module is developed to fuse and align both views between the source and target graphs for GDA. Experimental results on a variety of benchmark verify the effectiveness of our method.

Fusing heterogeneous information remains a persistent challenge in modern data analysis. While significant progress has been made, existing approaches often fail to account for the inherent heterogeneity of object patterns across different semantic spaces. To address this limitation, we propose the **Cooperation of Experts (CoE)** framework, which encodes multi-typed information into unified heterogeneous multiplex networks. By transcending modality and connection differences, CoE provides a powerful and flexible model for capturing the intricate structures of real-world complex data. In our framework, dedicated encoders act as domain-specific experts, each specializing in learning distinct relational patterns in specific semantic spaces. To enhance robustness and extract complementary knowledge, these experts collaborate through a novel **large margin** mechanism supported by a tailored optimization strategy. Rigorous theoretical analyses guarantee the framework’s feasibility and stability, while extensive experiments across diverse benchmarks demonstrate its superior performance and broad applicability.

Recent advances in CV and NLP have inspired researchers to develop general-purpose graph foundation models through pre-training across diverse domains. However, a fundamental challenge arises from the substantial differences in graph topologies across domains. Additionally, real-world graphs are often sparse and prone to noisy connections and adversarial attacks. To address these issues, we propose the Multi-Domain Graph Foundation Model (MDGFM), a unified framework that aligns and leverages cross-domain topological information to facilitate robust knowledge transfer. MDGFM bridges different domains by adaptively balancing features and topology while refining original graphs to eliminate noise and align topological structures. To further enhance knowledge transfer, we introduce an efficient prompt-tuning approach. By aligning topologies, MDGFM not only improves multi-domain pre-training but also enables robust knowledge transfer to unseen domains. Theoretical analyses provide guarantees of MDGFM's effectiveness and domain generalization capabilities. Extensive experiments on both homophilic and heterophilic graph datasets validate the robustness and efficacy of our method.

Few-Shot Relation Extraction (FSRE) remains a challenging task due to the scarcity of annotated data and the limited generalization capabilities of existing models. Although large language models (LLMs) have shown potential in FSRE through in-context learning, their general-purpose training objectives often result in suboptimal performance for task-specific relation extraction. To overcome these challenges, we propose TKRE (Two-Stage Knowledge-Guided Pre-training for Relation Extraction), a novel framework that synergistically integrates LLMs with traditional relation extraction models, bridging generative and discriminative learning paradigms. TKRE introduces two key innovations: (1) leveraging LLMs to generate explanation-driven knowledge and schema-constrained synthetic data, addressing the issue of data scarcity; and (2) a two-stage pre-training strategy combining Masked Span Language Modeling (MSLM) and Span-Level Contrastive Learning (SCL) to enhance relational reasoning and generalization. Together, these components enable TKRE to effectively handle FSRE tasks. Comprehensive experiments on benchmark datasets demonstrate the efficacy of TKRE, achieving new state-of-the-art performance in FSRE and underscoring its potential for broader application in low-resource scenarios. The code and data are released on https://github.com/UESTC-GQJ/TKRE.

Multimodal graphs, which integrate unstructured heterogeneous data with structured interconnections, offer substantial real-world utility but remain insufficiently explored in unsupervised learning. In this work, we initiate the study of multimodal graph clustering, aiming to bridge this critical gap. Through empirical analysis, we observe that real-world multimodal graphs often exhibit hybrid neighborhood patterns, combining both homophilic and heterophilic relationships. To address this challenge, we propose a novel framework---Disentangled Multimodal Graph Clustering (DMGC) ---which decomposes the original hybrid graph into two complementary views: (1) a homophily-enhanced graph that captures cross-modal class consistency, and (2) heterophily-aware graphs that preserve modality-specific inter-class distinctions. We introduce a Multimodal Dual-frequency Fusion mechanism that jointly filters these disentangled graphs through a dual-pass strategy, enabling effective multimodal integration while mitigating category confusion. Our self-supervised alignment objectives further guide the learning process without requiring labels. Extensive experiments on both multimodal and multi-relational graph datasets demonstrate that DMGC achieves state-of-the-art performance, highlighting its effectiveness and generalizability across diverse settings. Our code is available at https://github.com/Uncnbb/DMGC.

In multimodal representation learning, synergistic interactions between modalities not only provide complementary information but also create unique outcomes through specific interaction patterns that no single modality could achieve alone. Existing methods may struggle to effectively capture the full spectrum of synergistic information, leading to suboptimal performance in tasks where such interactions are critical. This is particularly problematic because synergistic information constitutes the fundamental value proposition of multimodal representation. To address this challenge, we introduce InfMasking, a contrastive synergistic information extraction method designed to enhance synergistic information through an Infinite Masking strategy. InfMasking stochastically occludes most features from each modality during fusion, preserving only partial information to create representations with varied synergistic patterns. Unmasked fused representations are then aligned with masked ones through mutual information maximization to encode comprehensive synergistic information. This infinite masking strategy enables capturing richer interactions by exposing the model to diverse partial modality combinations during training. As computing mutual information estimates with infinite masking is computationally prohibitive, we derive an InfMasking loss to approximate this calculation. Through controlled experiments, we demonstrate that InfMasking effectively enhances synergistic information between modalities. In evaluations on large-scale real-world datasets, InfMasking achieves state-of-the-art performance across seven benchmarks. Code is released at https://github.com/brightest66/InfMasking.

Event prediction tasks often handle spatio-temporal data distributed in a large spatial area. Different regions in the area exhibit different characteristics while having latent correlations. This spatial heterogeneity and correlations greatly affect the spatio-temporal distributions of event occurrences, which has not been addressed by state-of-the-art models. Learning spatial dependencies of events in a continuous space is challenging due to its fine granularity and a lack of prior knowledge. In this work, we propose a novel Graph Spatio-Temporal Point Process (GSTPP) model for fine-grained event prediction. It adopts an encoder-decoder architecture that jointly models the state dynamics of spatially localized regions using neural Ordinary Differential Equations (ODEs). The state evolution is built on the foundation of a novel Self-Adaptive Anchor Graph (SAAG) that captures spatial dependencies. By adaptively localizing the anchor nodes in the space and jointly constructing the correlation edges between them, the SAAG enhances the model’s ability of learning complex spatial event patterns. The proposed GSTPP model greatly improves the accuracy of fine-grained event prediction. Extensive experimental results show that our method greatly improves the prediction accuracy over existing spatio-temporal event prediction approaches.

In today's digital era driven by data, the amount and complexity of the collected data, such as multiview, non-Euclidean, and multirelational, are growing exponentially or even faster. Clustering, which unsupervisedly extracts valid knowledge from data, is extremely useful in practice. However, existing methods are independently developed to handle one particular challenge at the expense of the others. In this work, we propose a simple but effective framework for complex data clustering (CDC) that can efficiently process different types of data with linear complexity. We first use graph filtering (GF) to fuse geometric structure and attribute information. We then reduce complexity with high-quality anchors that are adaptively learned via a novel similarity-preserving (SP) regularizer. We illustrate the cluster-ability of our proposed method theoretically and experimentally. In particular, we deploy CDC to graph data of size 111 M.

Unsupervised heterogeneous graph representation learning (UHGRL) has gained increasing attention due to its significance in handling practical graphs without labels. However, heterophily has been largely ignored, despite its ubiquitous presence in real-world heterogeneous graphs. In this article, we define semantic heterophily and propose an innovative framework called latent graphs guided unsupervised representation learning (LatGRL) to handle this problem. First, we develop a similarity mining method that couples global structures and attributes, enabling the construction of fine-grained homophilic and heterophilic latent graphs (LGs) to guide the representation learning. Moreover, we propose an adaptive dual-frequency semantic fusion mechanism to address the problem of node-level semantic heterophily. To cope with the massive scale of real-world data, we further design a scalable implementation. Extensive experiments on benchmark datasets validate the effectiveness and efficiency of our proposed framework. The source code and datasets have been made available at https://github.com/zxlearningdeep/LatGRL.

Recently, many carefully designed graph representation learning methods have achieved impressive performance on either strong heterophilic or homophilic graphs, but not both. Therefore, they are incapable of generalizing well across real-world graphs with different levels of homophily. This is attributed to their neglect of homophily in heterophilic graphs, and vice versa. In this paper, we propose a two-fold filtering mechanism to mine homophily in heterophilic graphs, and vice versa. In particular, we extend the graph heat equation to perform heterophilic aggregation of global information from a long distance. The resultant filter can be exactly approximated by the Possion-Charlier (PC) polynomials. To further exploit information at multiple orders, we introduce a powerful graph convolution PC-Conv and its instantiation PCNet for the node classification task. Compared to the state-of-the-art GNNs, PCNet shows competitive performance on well-known homophilic and heterophilic graphs. Our implementation is available at https://github.com/uestclbh/PC-Conv.

Multi-relational clustering is a challenging task due to the fact that diverse semantic information conveyed in multi-layer graphs is difficult to extract and fuse. Recent methods integrate topology structure and node attribute information through graph filtering. However, they often use a low-pass filter without fully considering the correlation among multiple graphs. To overcome this drawback, we propose to learn a graph filter motivated by the theoretical analysis of Barlow Twins. We find that input with a negative semi-definite inner product provides a lower bound for Barlow Twins loss, which prevents it from reaching a better solution. We thus learn a filter that yields an upper bound for Barlow Twins. Afterward, we design a simple clustering architecture and demonstrate its state-of-the-art performance on four benchmark datasets. The source code is available at https://github.com/XweiQ/BTGF.

Document-level Relation Extraction (DocRE) aims to identify relation labels between entities within a single document. It requires handling several sentences and reasoning over them. State-of-the-art DocRE methods use a graph structure to connect entities across the document to capture dependency syntax information. However, this is insufficient to fully exploit the rich syntax information in the document. In this work, we propose to fuse constituency and dependency syntax into DocRE. It uses constituency syntax to aggregate the whole sentence information and select the instructive sentences for the pairs of targets. It exploits dependency syntax in a graph structure with constituency syntax enhancement and chooses the path between entity pairs based on the dependency graph. The experimental results on datasets from various domains demonstrate the effectiveness of the proposed method.

In this paper, we propose a novel concept factorization method that seeks factor matrices using a cross-order positive semi-definite neighbor graph, which provides comprehensive and complementary neighbor information of the data. The factor matrices are learned with bipartite graph partitioning, which exploits explicit cluster structure of the data and is more geared towards clustering application. We develop an effective and efficient optimization algorithm for our method, and provide elegant theoretical results about the convergence. Extensive experimental results confirm the effectiveness of the proposed method.

Knowledge graph (KG) has been used to provide additional relational knowledge about stance targets, thereby enhancing stance detection performance. However, the utilization efficiency of KG remains unconcerned and we find that the knowledge adoption amount is low in practice. In this work, we propose an efficient framework to improve the exploitation of KG, in which we integrate three different matching mechanisms to improve knowledge usage. A knowledge injection module is also introduced to explore enriched knowledge by constructing a supplementary set. These supplements contribute to stance detection through a text-pair classification mechanism. The experimental results on different datasets demonstrate that our approach outperforms existing works on knowledge graph exploitation and stance detection. Our code is available at https://github.com/kxy-cheng/EMKG.

Few-shot document-level relation extraction suffers from poor performance due to the challenging cross-domain transferability of NOTA (none-of-the-above) relation representation. In this paper, we introduce a Transferable Proto-Learning Network (TPN) to address the challenging issue. It comprises three core components: Hybrid Encoder hierarchically encodes semantic content of input text combined with attention information to enhance the relation representations. As a plug-and-play module for Out-of-Domain (OOD) Detection, Transferable Proto-Learner computes NOTA prototype through an adaptive learnable block, effectively mitigating NOTA bias across various domains. Dynamic Weighting Calibrator detects relation-specific classification confidence, serving as dynamic weights to calibrate the NOTA-dominant loss function. Finally, to bolster the model’s cross-domain performance, we complement it with virtual adversarial training (VAT). We conduct extensive experimental analyses on FREDo and ReFREDo, demonstrating the superiority of TPN. Compared to state-of-the-art methods, our approach achieves competitive performance with approximately half the parameter size. Data and code are available at https://github.com/EchoDreamer/TPN.

Multi-relational graph clustering has demonstrated remarkable success in uncovering underlying patterns in complex networks. Representative methods manage to align different views motivated by advances in contrastive learning. Our empirical study finds the pervasive presence of imbalance in real-world graphs, which is in principle contradictory to the motivation of alignment. In this paper, we first propose a novel metric, the Aggregation Class Distance, to empirically quantify structural disparities among different graphs. To address the challenge of view imbalance, we propose Balanced Multi-Relational Graph Clustering (BMGC), comprising unsupervised dominant view mining and dual signals guided representation learning. It dynamically mines the dominant view throughout the training process, synergistically improving clustering performance with representation learning. Theoretical analysis ensures the effectiveness of dominant view mining. Extensive experiments and in-depth analysis on real-world and synthetic datasets showcase that BMGC achieves state-of-the-art performance, underscoring its superiority in addressing the view imbalance inherent in multi-relational graphs. The source code and datasets are available at https://github.com/zxlearningdeep/BMGC.

Unsupervised Multiplex Graph Learning (UMGL) aims to learn node representations on various edge types without manual labeling. However, existing research overlooks a key factor: the reliability of the graph structure. Real-world data often exhibit a complex nature and contain abundant task-irrelevant noise, severely compromising UMGL's performance. Moreover, existing methods primarily rely on contrastive learning to maximize mutual information across different graphs, limiting them to multiplex graph redundant scenarios and failing to capture view-unique task-relevant information. In this paper, we focus on a more realistic and challenging task: to unsupervisedly learn a fused graph from multiple graphs that preserve sufficient task-relevant information while removing task-irrelevant noise. Specifically, our proposed Information-aware Unsupervised Multiplex Graph Fusion framework (InfoMGF) uses graph structure refinement to eliminate irrelevant noise and simultaneously maximizes view-shared and view-unique task-relevant information, thereby tackling the frontier of non-redundant multiplex graph. Theoretical analyses further guarantee the effectiveness of InfoMGF. Comprehensive experiments against various baselines on different downstream tasks demonstrate its superior performance and robustness. Surprisingly, our unsupervised method even beats the sophisticated supervised approaches. The source code and datasets are available at https://github.com/zxlearningdeep/InfoMGF.

Community detection is a crucial task in complex network analysis, and existing game-theoretic-based community detection methods struggle to achieve a balance between local and global competition and cooperation. This paper introduce a Dual-scale Game theoretical Framework (Dual-GTF) for community detection. First, a new modularity function is proposed, enabling each node to incorporate additional expansion information at the community scale by collaborating closely with the individual scale modularity function. Subsequently, leveraging cooperative and competitive strategies informed by realistic empiricism, this paper integrate community-scale information to facilitate effective role division within communities. Evaluations of real-world datasets demonstrate that this approach, Dual-GTF, achieves superior convergence and performance results in most cases.

Abstract Image anomaly detection and localization perform not only image-level anomaly classification but also locate pixel-level anomaly regions. Recently, it has received much research attention due to its wide application in various fields. This paper proposes ProtoAD, a prototype-based neural network for image anomaly detection and localization. First, the patch features of normal images are extracted by a deep network pre-trained on nature images. Then, the prototypes of the normal patch features are learned by non-parametric clustering. Finally, we construct an image anomaly localization network (ProtoAD) by appending the feature extraction network with L 2 feature normalization, a $$1\times 1$$ 1 × 1 convolutional layer, a channel max-pooling, and a subtraction operation. We use the prototypes as the kernels of the $$1\times 1$$ 1 × 1 convolutional layer; therefore, our neural network does not need a training phase and can conduct anomaly detection and localization in an end-to-end manner. Extensive experiments on two challenging industrial anomaly detection datasets, MVTec AD and BTAD, demonstrate that ProtoAD achieves competitive performance compared to the state-of-the-art methods with a higher inference speed. The code and pre-trained models are publicly available at https://github.com/98chao/ProtoAD .

Multi-view subspace clustering (MVSC) has drawn significant attention in recent study. In this paper, we propose a novel approach to MVSC. First, the new method is capable of preserving high-order neighbor information of the data, which provides essential and complicated underlying relationships of the data that is not straightforwardly preserved by the first-order neighbors. Second, we design log-based nonconvex approximations to both tensor rank and tensor sparsity, which are effective and more accurate than the convex approximations. For the associated shrinkage problems, we provide elegant theoretical results for the closed-form solutions, for which the convergence is guaranteed by theoretical analysis. Moreover, the new approximations have some interesting properties of shrinkage effects, which are guaranteed by elegant theoretical results. Extensive experimental results confirm the effectiveness of the proposed method.

Graph convolutional network (GCN) outputs powerful representation by considering the structure information of the data to conduct representation learning, but its robustness is sensitive to the quality of both the feature matrix and the initial graph. In this article, we propose a novel multigraph fusion method to produce a high-quality graph and a low-dimensional space of original high-dimensional data for the GCN model. Specifically, the proposed method first extracts the common information and the complementary information among multiple local graphs to obtain a unified local graph, which is then fused with the global graph of the data to obtain the initial graph for the GCN model. As a result, the proposed method conducts the graph fusion process twice to simultaneously learn the low-dimensional space and the intrinsic graph structure of the data in a unified framework. Experimental results on real datasets demonstrated that our method outperformed the comparison methods in terms of classification tasks.

Graph neural networks (GNNs) based methods have achieved impressive performance on node clustering task. However, they are designed on the homophilic assumption of graph and clustering on heterophilic graph is overlooked. Due to the lack of labels, it is impossible to first identify a graph as homophilic or heterophilic before a suitable GNN model can be found. Hence, clustering on real-world graph with various levels of homophily poses a new challenge to the graph research community. To fill this gap, we propose a novel graph clustering method, which contains three key components: graph reconstruction, a mixed filter, and dual graph clustering network. To be graph-agnostic, we empirically construct two graphs which are high homophily and heterophily from each data. The mixed filter based on the new graphs extracts both low-frequency and high-frequency information. To reduce the adverse coupling between node attribute and topological structure, we separately map them into two subspaces in dual graph clustering network. Extensive experiments on 11 benchmark graphs demonstrate our promising performance. In particular, our method dominates others on heterophilic graphs.

Fake news detection aims to detect fake news widely spreading on social media platforms, which can negatively influence the public and the government. Many approaches have been developed to exploit relevant information from news images, text, or videos. However, these methods may suffer from the following limitations: (1) ignore the inherent emotional information of the news, which could be beneficial since it contains the subjective intentions of the authors; (2) pay little attention to the relation (similarity) between the title and textual information in news articles, which often use irrelevant title to attract reader' attention. To this end, we propose a novel Title-Text similarity and emotion-aware Fake news detection (TieFake) method by jointly modeling the multi-modal context information and the author sentiment in a unified framework. Specifically, we respectively employ BERT and ResNeSt to learn the representations for text and images, and utilize publisher emotion extractor to capture the author's subjective emotion in the news content. We also propose a scale-dot product attention mechanism to capture the similarity between title features and textual features. Experiments are conducted on two publicly available multi-modal datasets, and the results demonstrate that our proposed method can significantly improve the performance of fake news detection. Our code is available at https://github.com/UESTC-GQJ/TieFake.

Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as ℓ 1 -norm and ℓ 2 , p -norm, can deal with noise or outliers to some extent. However, real-world data may display structures that can not be fully captured by these simple functions. In addition, existing methods treat complex and simple samples equally. By contrast, a learning pattern typically adopted by human beings is to learn from simple to complex and less to more. Based on this principle, we propose a novel method called Self-paced PCA (SPCA) to further reduce the effect of noise and outliers. Notably, the complexity of each sample is calculated at the beginning of each iteration in order to integrate samples from simple to more complex into training. Based on an alternating optimization, SPCA finds an optimal projection matrix and filters out outliers iteratively. Theoretical analysis is presented to show the rationality of SPCA. Extensive experiments on popular data sets demonstrate that the proposed method can improve the state-of-the-art results considerably.

Multi-view graph clustering has been intensively investigated during the past years. However, existing methods are still limited in two main aspects. On the one hand, most of them can not deal with data that have both attributes and graphs. Nowadays, multi-view attributed graph data are ubiquitous and the need for effective clustering methods is growing. On the other hand, many state-of-the-art algorithms are either shallow or deep models. Shallow methods may seriously restrict their capacity for modeling complex data, while deep approaches often involve large number of parameters and are expensive to train in terms of running time and space needed. In this paper, we propose a novel multi-view attributed graph clustering (MAGC) framework, which exploits both node attributes and graphs. Our novelty lies in three aspects. First, instead of deep neural networks, we apply a graph filtering technique to achieve a smooth node representation. Second, the original graph could be noisy or incomplete and is not directly applicable, thus we learn a consensus graph from data by considering the heterogeneous views. Third, high-order relations are explored in a flexible way by designing a new regularizer. Extensive experiments demonstrate the superiority of our method in terms of effectiveness and efficiency.

Hypergraph streams provide an efficient model to express and preserve complex connections in various applications. Triangles in a hypergraph can be formed by vertices and hyperedges. The specific counts of triangles are important to analyze various applications. Due to the huge costs of counting triangles based on the whole datasets, a sampling-and-estimating framework has low overhead while obtaining a relatively accurate result. However, existing sampling algorithms focus on pairwise graph streams, they estimate the counts of triangles formed by vertices with large estimation errors and can not be applied to count triangles formed by hyperedges. Therefore, this paper first proposes a sampling-and-estimating framework that produces hyperedge samples using a reservoir with static capacity to estimate the total counts of triangles by inferring the probabilities of forming the triangles respectively. Furthermore, to improve the estimation accuracy, this paper proposes another sampling-and-estimating framework to produce samples in the form of hyperedge pairs which can be used to compute the probabilities of the formations of triangles more accurately and then estimate the total triangle counts with smaller estimation variances. The extensive experiments based on real-world datasets confirm the efficiency and accuracy of our proposed frameworks for counting triangles in different types of hypergraphs at a small sampling ratio.

Though graph representation learning (GRL) has made significant progress, it is still a challenge to extract and embed the rich topological structure and feature information in an adequate way. Most existing methods focus on local structure and fail to fully incorporate the global topological structure. To this end, we propose a novel Structure-Preserving Graph Representation Learning (SPGRL) method, to fully capture the structure information of graphs. Specifically, to reduce the uncertainty and misinformation of the original graph, we construct a feature graph as a complementary view via k-Nearest Neighbor method. The feature graph can be used to contrast at node-level to capture the local relation. Besides, we retain the global topological structure information by maximizing the mutual information (MI) of the whole graph and feature embeddings, which is theoretically reduced to exchanging the feature embeddings of the feature and the original graphs to reconstruct themselves. Extensive experiments show that our method has quite superior performance on semi-supervised node classification task and excellent robustness under noise perturbation on graph structure or node features. The source code is available at https://github.com/uestc-lese/SPGRL.

Graph clustering is a prevalent issue associated with social networks, data mining, and machine learning; its objective is to detect communities or groups in networks. Inspired by the recent success of deep learning (DL), new DL-based graph clustering methods have achieved promising results. However, a deep neural network involves a large number of training parameters. Moreover, existing methods typically select the similarity metric by an ad hoc approach, which considerably affects the resulting output. In this study, we propose a principled graph learning perspective, fine-grained attributed graph clustering. Based on a shallow approach, the proposed method sufficiently exploits both node features and structure information by benefiting from graph convolution. Consequently, a fine-grained graph encoded higher-order relations is automatically learned. Comprehensive experiments on benchmark datasets demonstrate the superiority of the proposed method over state-of-the-art algorithms, including several DL methods.

Graph-based subspace clustering methods have exhibited promising performance. However, they still suffer some of these drawbacks: they encounter the expensive time overhead, they fail to explore the explicit clusters, and cannot generalize to unseen data points. In this work, we propose a scalable graph learning framework, seeking to address the above three challenges simultaneously. Specifically, it is based on the ideas of anchor points and bipartite graph. Rather than building an n×n graph, where n is the number of samples, we construct a bipartite graph to depict the relationship between samples and anchor points. Meanwhile, a connectivity constraint is employed to ensure that the connected components indicate clusters directly. We further establish the connection between our method and the K -means clustering. Moreover, a model to process multiview data is also proposed, which is linearly scaled with respect to n . Extensive experiments demonstrate the efficiency and effectiveness of our approach with respect to many state-of-the-art clustering methods.

In this paper, we propose a novel nonconvex approach to robust principal component analysis for HSI denoising, which focuses on simultaneously developing more accurate approximations to both rank and column-wise sparsity for the low-rank and sparse components, respectively. In particular, the new method adopts the log-determinant rank approximation and a novell2,lognorm, to restrict the local low-rank or column-wisely sparse properties for the component matrices, respectively. For thel2,log-regularized shrinkage problem, we develop an efficient, closed-form solution, which is namedl2,log-shrinkage operator. The new regularization and the corresponding operator can be generally used in other problems that require column-wise sparsity. Moreover, we impose the spatial-spectral total variation regularization in the log-based nonconvex RPCA model, which enhances the global piece-wise smoothness and spectral consistency from the spatial and spectral views in the recovered HSI. Extensive experiments on both simulated and real HSIs demonstrate the effectiveness of the proposed method in denoising HSIs.

Two-dimensional PCA (2DPCA) is an effective approach to reduce dimension and extract features in the image domain. Most recently developed techniques use different error measures to improve their robustness to outliers. When certain data points are overly contaminated, the existing methods are frequently incapable of filtering out and eliminating the excessively polluted ones. Moreover, natural systems have smooth dynamics, an opportunity is lost if an unsupervised objective function remains static. Unlike previous studies, we explicitly differentiate the samples to alleviate the impact of outliers and propose a novel method called Self-Paced 2DPCA (SP2DPCA)algorithm, which progresses from `easy’ to `complex’ samples. By using an alternative optimization strategy, SP2DPCA looks for optimal projection matrix and filters out outliers iteratively. Theoretical analysis demonstrates the robustness nature of our method. Extensive experiments on image reconstruction and clustering verify the superiority of our approach.

Graph clustering has become an important research topic due to the proliferation of graph data. However, existing methods suffer from two major drawbacks. On the one hand, most methods can not simultaneously exploit attribute and graph structure information. On the other hand, most methods are incapable of handling multi-view data which contain sets of different features and graphs. In this paper, we propose a novel Multi-view Attributed Graph Clustering (MvAGC) method, which is simple yet effective. Firstly, a graph filter is applied to features to obtain a smooth representation without the need of learning the parameters of neural networks. Secondly, a novel strategy is designed to select a few anchor points, so as to reduce the computation complexity. Thirdly, a new regularizer is developed to explore high-order neighborhood information. Our extensive experiments indicate that our method works surprisingly well with respect to state-of-the-art deep neural network methods. The source code is available at https://github.com/sckangz/MvAGC.

Attempting to fully exploit the rich information of topological structure and node features for attributed graph, we introduce self-supervised learning mechanism to graph representation learning and propose a novel Self-supervised Consensus Representation Learning (SCRL) framework. In contrast to most existing works that only explore one graph, our proposed SCRL method treats graph from two perspectives: topology graph and feature graph. We argue that their embeddings should share some common information, which could serve as a supervisory signal. Specifically, we construct the feature graph of node features via k-nearest neighbour algorithm. Then graph convolutional network (GCN) encoders extract features from two graphs respectively. Self-supervised loss is designed to maximize the agreement of the embeddings of the same node in the topology graph and the feature graph. Extensive experiments on real citation networks and social networks demonstrate the superiority of our proposed SCRL over the state-of-the-art methods on semi-supervised node classification task. Meanwhile, compared with its main competitors, SCRL is rather efficient.

With the explosive growth of information technology, multi-view graph data have become increasingly prevalent and valuable. Most existing multi-view clustering techniques either focus on the scenario of multiple graphs or multi-view attributes. In this paper, we propose a generic framework to cluster multi-view attributed graph data. Specifically, inspired by the success of contrastive learning, we propose multi-view contrastive graph clustering (MCGC) method to learn a consensus graph since the original graph could be noisy or incomplete and is not directly applicable. Our method composes of two key steps: we first filter out the undesirable high-frequency noise while preserving the graph geometric features via graph filtering and obtain a smooth representation of nodes; we then learn a consensus graph regularized by graph contrastive loss. Results on several benchmark datasets show the superiority of our method with respect to state-of-the-art approaches. In particular, our simple approach outperforms existing deep learning-based methods.

Common spatial pattern (CSP) is one of the most successful feature extraction algorithms for brain-computer interfaces (BCIs). It aims to find spatial filters that maximize the projected variance ratio between the covariance matrices of the multichannel electroencephalography (EEG) signals corresponding to two mental tasks, which can be formulated as a generalized eigenvalue problem (GEP). However, it is challenging in principle to impose additional regularization onto the CSP to obtain structural solutions (e.g., sparse CSP) due to the intrinsic nonconvexity and invariance property of GEPs. This article reformulates the CSP as a constrained minimization problem and establishes the equivalence of the reformulated and the original CSPs. An efficient algorithm is proposed to solve this optimization problem by alternately performing singular value decomposition (SVD) and least squares. Under this new formulation, various regularization techniques for linear regression can then be easily implemented to regularize the CSPs for different learning paradigms, such as the sparse CSP, the transfer CSP, and the multisubject CSP. Evaluations on three BCI competition datasets show that the regularized CSP algorithms outperform other baselines, especially for the high-dimensional small training set. The extensive results validate the efficiency and effectiveness of the proposed CSP formulation in different learning contexts.

Single-image dehazing has been an important topic given the commonly occurred image degradation caused by adverse atmosphere aerosols. The key to haze removal relies on an accurate estimation of global air-light and the transmission map. Most existing methods estimate these two parameters using separate pipelines which reduces the efficiency and accumulates errors, thus leading to a suboptimal approximation, hurting the model interpretability, and degrading the performance. To address these issues, this article introduces a novel generative adversarial network (GAN) for single-image dehazing. The network consists of a novel compositional generator and a novel deeply supervised discriminator. The compositional generator is a densely connected network, which combines fine-scale and coarse-scale information. Benefiting from the new generator, our method can directly learn the physical parameters from data and recover clean images from hazy ones in an end-to-end manner. The proposed discriminator is deeply supervised, which enforces that the output of the generator to look similar to the clean images from low-level details to high-level structures. To the best of our knowledge, this is the first end-to-end generative adversarial model for image dehazing, which simultaneously outputs clean images, transmission maps, and air-lights. Extensive experiments show that our method remarkably outperforms the state-of-the-art methods. Furthermore, to facilitate future research, we create the HazeCOCO dataset which is currently the largest dataset for single-image dehazing.

Auto-Encoder (AE)-based deep subspace clustering (DSC) methods have achieved impressive performance due to the powerful representation extracted using deep neural networks while prioritizing categorical separability. However, self-reconstruction loss of an AE ignores rich useful relation information and might lead to indiscriminative representation, which inevitably degrades the clustering performance. It is also challenging to learn high-level similarity without feeding semantic labels. Another unsolved problem facing DSC is the huge memory cost due to n×n similarity matrix, which is incurred by the self-expression layer between an encoder and decoder. To tackle these problems, we use pairwise similarity to weigh the reconstruction loss to capture local structure information, while a similarity is learned by the self-expression layer. Pseudo-graphs and pseudo-labels, which allow benefiting from uncertain knowledge acquired during network training, are further employed to supervise similarity learning. Joint learning and iterative training facilitate to obtain an overall optimal solution. Extensive experiments on benchmark datasets demonstrate the superiority of our approach. By combining with the k -nearest neighbors algorithm, we further show that our method can address the large-scale and out-of-sample problems. The source code of our method is available: https://github.com/sckangz/SelfsupervisedSC.

A plethora of multi-view subspace clustering (MVSC) methods have been proposed over the past few years. Researchers manage to boost clustering accuracy from different points of view. However, many state-of-the-art MVSC algorithms, typically have a quadratic or even cubic complexity, are inefficient and inherently difficult to apply at large scales. In the era of big data, the computational issue becomes critical. To fill this gap, we propose a large-scale MVSC (LMVSC) algorithm with linear order complexity. Inspired by the idea of anchor graph, we first learn a smaller graph for each view. Then, a novel approach is designed to integrate those graphs so that we can implement spectral clustering on a smaller graph. Interestingly, it turns out that our model also applies to single-view scenario. Extensive experiments on various large-scale benchmark data sets validate the effectiveness and efficiency of our approach with respect to state-of-the-art clustering methods.

Unsupervised active learning has attracted increasing attention in recent years, where its goal is to select representative samples in an unsupervised setting for human annotating. Most existing works are based on shallow linear models by assuming that each sample can be well approximated by the span (i.e., the set of all linear combinations) of certain selected samples, and then take these selected samples as representative ones to label. However, in practice, the data do not necessarily conform to linear models, and how to model nonlinearity of data often becomes the key point to success. In this paper, we present a novel Deep neural network framework for Unsupervised Active Learning, called DUAL. DUAL can explicitly learn a nonlinear embedding to map each input into a latent space through an encoder-decoder architecture, and introduce a selection block to select representative samples in the the learnt latent space. In the selection block, DUAL considers to simultaneously preserve the whole input patterns as well as the cluster structure of data. Extensive experiments are performed on six publicly available datasets, and experimental results clearly demonstrate the efficacy of our method, compared with state-of-the-arts.

Finding a suitable data representation for a specific task has been shown to be crucial in many applications. The success of subspace clustering depends on the assumption that the data can be separated into different subspaces. However, this simple assumption does not always hold since the raw data might not be separable into subspaces. To recover the "clustering-friendly" representation and facilitate the subsequent clustering, we propose a graph filtering approach by which a smooth representation is achieved. Specifically, it injects graph similarity into data features by applying a low-pass filter to extract useful data representations for clustering. Extensive experiments on image and document clustering datasets demonstrate that our method improves upon state-of-the-art subspace clustering techniques. Especially, its comparable performance with deep learning methods emphasizes the effectiveness of the simple graph filtering scheme for many real-world applications. An ablation study shows that graph filtering can remove noise, preserve structure in the image, and increase the separability of classes.

Learning graphs from data automatically have shown encouraging performance on clustering and semisupervised learning tasks. However, real data are often corrupted, which may cause the learned graph to be inexact or unreliable. In this paper, we propose a novel robust graph learning scheme to learn reliable graphs from the real-world noisy data by adaptively removing noise and errors in the raw data. We show that our proposed model can also be viewed as a robust version of manifold regularized robust principle component analysis (RPCA), where the quality of the graph plays a critical role. The proposed model is able to boost the performance of data clustering, semisupervised classification, and data recovery significantly, primarily due to two key factors: 1) enhanced low-rank recovery by exploiting the graph smoothness assumption and 2) improved graph construction by exploiting clean data recovered by RPCA. Thus, it boosts the clustering, semisupervised classification, and data recovery performance overall. Extensive experiments on image/document clustering, object recognition, image shadow removal, and video background subtraction reveal that our model outperforms the previous state-of-the-art methods.

Data similarity is a key concept in many data-driven applications. Many algorithms are sensitive to similarity measures. To tackle this fundamental problem, automatically learning of similarity information from data via self-expression has been developed and successfully applied in various models, such as low-rank representation, sparse subspace learning, semisupervised learning. However, it just tries to reconstruct the original data and some valuable information, e.g., the manifold structure, is largely ignored. In this paper, we argue that it is beneficial to preserve the overall relations when we extract similarity information. Specifically, we propose a novel similarity learning framework by minimizing the reconstruction error of kernel matrices, rather than the reconstruction error of original data adopted by existing work. Taking the clustering task as an example to evaluate our method, we observe considerable improvements compared to other state-ofthe-art methods. More importantly, our proposed framework is very general and provides a novel and fundamental building block for many other similarity-based tasks. Besides, our proposed kernel preserving opens up a large number of possibilities to embed high-dimensional data into low-dimensional space.

To explore underlying complementary information from multiple views, in this paper, we propose a novel Latent Multi-view Semi-Supervised Classification (LMSSC) method. Unlike most existing multi-view semi-supervised classification methods that learn the graph using original features, our method seeks an underlying latent representation and performs graph learning and label propagation based on the learned latent representation. With the complementarity of multiple views, the latent representation could depict the data more comprehensively than every single view individually, accordingly making the graph more accurate and robust as well. Finally, LMSSC integrates latent representation learning, graph construction, and label propagation into a unified framework, which makes each subtask optimized. Experimental results on real-world benchmark datasets validate the effectiveness of our proposed method.

Robust principal component analysis (RPCA) has drawn significant attentions due to its powerful capability in recovering low-rank matrices as well as successful appplications in various real world problems. The current state-of-the-art algorithms usually need to solve singular value decomposition of large matrices, which generally has at least a quadratic or even cubic complexity. This drawback has limited the application of RPCA in solving real world problems. To combat this drawback, in this paper we propose a new type of RPCA method, RES-PCA, which is linearly efficient and scalable in both data size and dimension. For comparison purpose, AltProj, an existing scalable approach to RPCA requires the precise knowlwdge of the true rank; otherwise, it may fail to recover low-rank matrices. By contrast, our method works with or without knowing the true rank; even when both methods work, our method is faster. Extensive experiments have been performed and testified to the effectiveness of proposed method quantitatively and in visual quality, which suggests that our method is suitable to be employed as a light-weight, scalable component for RPCA in any application pipelines.

Multi-view clustering is an important yet challenging task due to the difficulty of integrating the information from multiple representations. Most existing multi-view clustering methods explore the heterogeneous information in the space where the data points lie. Such common practice may cause significant information loss because of unavoidable noise or inconsistency among views. Since different views admit the same cluster structure, the natural space should be all partitions. Orthogonal to existing techniques, in this paper, we propose to leverage the multi-view information by fusing partitions. Specifically, we align each partition to form a consensus cluster indicator matrix through a distinct rotation matrix. Moreover, a weight is assigned for each view to account for the clustering capacity differences of views. Finally, the basic partitions, weights, and consensus clustering are jointly learned in a unified framework. We demonstrate the effectiveness of our approach on several real datasets, where significant improvement is found over other state-of-the-art multi-view clustering methods.

Spectral clustering has found extensive use in many areas. Most traditional spectral clustering algorithms work in three separate steps: similarity graph construction; continuous labels learning; discretizing the learned labels by k-means clustering. Such common practice has two potential flaws, which may lead to severe information loss and performance degradation. First, predefined similarity graph might not be optimal for subsequent clustering. It is well-accepted that similarity graph highly affects the clustering results. To this end, we propose to automatically learn similarity information from data and simultaneously consider the constraint that the similarity matrix has exact c connected components if there are c clusters. Second, the discrete solution may deviate from the spectral solution since k-means method is well-known as sensitive to the initialization of cluster centers. In this work, we transform the candidate solution into a new one that better approximates the discrete one. Finally, those three subtasks are integrated into a unified framework, with each subtask iteratively boosted by using the results of the others towards an overall optimal solution. It is known that the performance of a kernel method is largely determined by the choice of kernels. To tackle this practical problem of how to select the most suitable kernel for a particular data set, we further extend our model to incorporate multiple kernel learning ability. Extensive experiments demonstrate the superiority of our proposed method as compared to existing clustering approaches.

Multiple kernel learning (MKL) method is generally believed to perform better than single kernel method. However, some empirical studies show that this is not always true: the combination of multiple kernels may even yield an even worse performance than using a single kernel. There are two possible reasons for the failure: (i) most existing MKL methods assume that the optimal kernel is a linear combination of base kernels, which may not hold true; and (ii) some kernel weights are inappropriately assigned due to noises and carelessly designed algorithms. In this paper, we propose a novel MKL framework by following two intuitive assumptions: (i) each kernel is a perturbation of the consensus kernel; and (ii) the kernel that is close to the consensus kernel should be assigned a large weight. Impressively, the proposed method can automatically assign an appropriate weight to each kernel without introducing additional parameters, as existing methods do. The proposed framework is integrated into a unified framework for graph-based clustering and semi-supervised classification. We have conducted experiments on multiple benchmark datasets and our empirical results verify the superiority of the proposed framework.

In this article, we introduce a novel, general methodology, called integrate and conquer, for simultaneously accomplishing the tasks of feature extraction, manifold construction, and clustering, which is taken to be superior to building a clustering method as a single task. When the proposed novel methodology is used on two-dimensional (2D) data, it naturally induces a new clustering method highly effective on 2D data. Existing clustering algorithms usually need to convert 2D data to vectors in a preprocessing step, which, unfortunately, severely damages 2D spatial information and omits inherent structures and correlations in the original data. The induced new clustering method can overcome the matrix-vectorization-related issues to enhance the clustering performance on 2D matrices. More specifically, the proposed methodology mutually enhances three tasks of finding subspaces, learning manifolds, and constructing data representation in a seamlessly integrated fashion. When used on 2D data, we seek two projection matrices with optimal numbers of directions to project the data into low-rank, noise-mitigated, and the most expressive subspaces, in which manifolds are adaptively updated according to the projections, and new data representation is built with respect to the projected data by accounting for nonlinearity via adaptive manifolds. Consequently, the learned subspaces and manifolds are clean and intrinsic, and the new data representation is discriminative and robust. Extensive experiments have been conducted and the results confirm the effectiveness of the proposed methodology and algorithm.

Many similarity-based clustering methods work in two separate steps including similarity matrix computation and subsequent spectral clustering. However similarity measurement is challenging because it is usually impacted by many factors, e.g., the choice of similarity metric, neighborhood size, scale of data, noise and outliers. Thus the learned similarity matrix is often not suitable, let alone optimal, for the subsequent clustering. In addition, nonlinear similarity often exists in many real world data which, however, has not been effectively considered by most existing methods. To tackle these two challenges, we propose a model to simultaneously learn cluster indicator matrix and similarity information in kernel spaces in a principled way. We show theoretical relationships to kernel k-means, k-means, and spectral clustering methods. Then, to address the practical issue of how to select the most suitable kernel for a particular clustering task, we further extend our model with a multiple kernel learning ability. With this joint model, we can automatically accomplish three subtasks of finding the best cluster indicator matrix, the most accurate similarity relations and the optimal combination of multiple kernels. By leveraging the interactions between these three subtasks in a joint framework, each subtask can be iteratively boosted by using the results of the others towards an overall optimal solution. Extensive experiments are performed to demonstrate the effectiveness of our method.

Spectral clustering based subspace clustering methods have emerged recently. When the inputs are 2-dimensional (2D) data, most existing clustering methods convert such data to vectors as preprocessing, which severely damages spatial information of the data. In this paper, we propose a novel subspace clustering method for 2D data with enhanced capability of retaining spatial information for clustering. It seeks two projection matrices and simultaneously constructs a linear representation of the projected data, such that the sought projections help construct the most expressive representation with the most variational information. We regularize our method based on covariance matrices directly obtained from 2D data, which have much smaller size and are more computationally amiable. Moreover, to exploit nonlinear structures of the data, a nonlinear version is proposed, which constructs an adaptive manifold according to updated projections. The learning processes of projections, representation, and manifold thus mutually enhance each other, leading to a powerful data representation. Efficient optimization procedures are proposed, which generate non-increasing objective value sequence with theoretical convergence guarantee. Extensive experimental results confirm the effectiveness of proposed method.

Construction of a reliable similarity matrix is fundamental for graph-based clustering methods. However, most of the current work is built upon some simple manifold structure, whereas limited work has been conducted on nonlinear data sets where data reside in a union of manifolds rather than a union of subspaces. Therefore, we construct a similarity graph to capture both global and local manifold structures of the input data set. The global structure is exploited based on the self-expressive property of data in an implicit feature space using kernel methods. Since the similarity graph computation is independent of the subsequent clustering, the final results may be far from optimal. To overcome this limitation, we simultaneously learn similarity graph and clustering structure in a principled way. Experimental studies demonstrate that our proposed algorithms deliver consistently superior results to other state-of-the-art algorithms.

Subspace clustering methods have been widely studied recently. When the inputs are two-dimensional (2-D) data, existing subspace clustering methods usually convert them into vectors, which severely damages inherent structures and relationships from original data. In this letter, we propose a novel subspace clustering method for 2-D data. It directly uses 2-D data as inputs such that the learning of representations benefits from inherent structures and relationships of the data. It simultaneously seeks image projection and representation coefficients such that they mutually enhance each other and lead to powerful data representations. An efficient algorithm is developed to solve the proposed objective function with provable decreasing and convergence property. Extensive experimental results verify the effectiveness of the new method.

Matrix factorization is a useful technique for data representation in many data mining and machine learning tasks. Particularly, for data sets with all nonnegative entries, matrix factorization often requires that factor matrices be nonnegative, leading to nonnegative matrix factorization (NMF). One important application of NMF is for clustering with reduced dimensions of the data represented in the new feature space. In this paper, we propose a new graph regularized NMF method capable of feature learning and apply it to clustering. Unlike existing NMF methods that treat all features in the original feature space equally, our method distinguishes features by incorporating a feature-wise sparse approximation error matrix in the formulation. It enables important features to be more closely approximated by the factor matrices. Meanwhile, the graph of the data is constructed using cleaner features in the feature learning process, which integrates feature learning and manifold learning procedures into a unified NMF model. This distinctly differs from applying the existing graph-based NMF models after feature selection in that, when these two procedures are independently used, they often fail to align themselves toward obtaining a compact and most expressive data representation. Comprehensive experimental results demonstrate the effectiveness of the proposed method, which outperforms state-of-the-art algorithms when applied to clustering.

Matrix factorization is often used for data representation in many data mining and machine-learning problems. In particular, for a dataset without any negative entries, nonnegative matrix factorization (NMF) is often used to find a low-rank approximation by the product of two nonnegative matrices. With reduced dimensions, these matrices can be effectively used for many applications such as clustering. The existing methods of NMF are often afflicted with their sensitivity to outliers and noise in the data. To mitigate this drawback, in this paper, we consider integrating NMF into a robust principal component model, and design a robust formulation that effectively captures noise and outliers in the approximation while incorporating essential nonlinear structures. A set of comprehensive empirical evaluations in clustering applications demonstrates that the proposed method has strong robustness to gross errors and superior performance to current state-of-the-art methods.

Top-N recommender systems have been investigated widely both in industry and academia. However, the recommendation quality is far from satisfactory. In this paper, we propose a simple yet promising algorithm. We fill the user-item matrix based on a low-rank assumption and simultaneously keep the original information. To do that, a nonconvex rank relaxation rather than the nuclear norm is adopted to provide a better rank approximation and an efficient optimization strategy is designed. A comprehensive set of experiments on real datasets demonstrates that our method pushes the accuracy of Top-N recommendation to a new level.

Recommender systems play an increasingly important role in online applications to help users find what they need or prefer. Collaborative filtering algorithms that generate predictions by analyzing the user-item rating matrix perform poorly when the matrix is sparse. To alleviate this problem, this paper proposes a simple recommendation algorithm that fully exploits the similarity information among users and items and intrinsic structural information of the user-item matrix. The proposed method constructs a new representation which preserves affinity and structure information in the user-item rating matrix and then performs recommendation task. To capture proximity information about users and items, two graphs are constructed. Manifold learning idea is used to constrain the new representation to be smooth on these graphs, so as to enforce users and item proximities. Our model is formulated as a convex optimization problem, for which we need to solve the well known Sylvester equation only. We carry out extensive empirical evaluations on six benchmark datasets to show the effectiveness of this approach.

Recovering low-rank matrices is a problem common in many applications of data mining and machine learning, such as matrix completion and image denoising. Robust Principal Component Analysis (RPCA) has emerged for handling such kinds of problems; however, the existing RPCA approaches are usually computationally expensive, due to the fact that they need to obtain the singular value decomposition (SVD) of large matrices. In this paper, we propose a novel RPCA approach that eliminates the need for SVD of large matrices. Scalable algorithms are designed for several variants of our approach, which are crucial for real world applications on large scale data. Extensive experimental results confirm the effectiveness of our approach both quantitatively and visually.

Robust principal component analysis (RPCA) has been widely used for recovering low-rank matrices in many data mining and machine learning problems. It separates a data matrix into a low-rank part and a sparse part. The convex approach has been well studied in the literature. However, state-of-the-art algorithms for the convex approach usually have relatively high complexity due to the need of solving (partial) singular value decompositions of large matrices. A non-convex approach, AltProj, has also been proposed with lighter complexity and better scalability. Given the true rank r of the underlying low rank matrix, AltProj has a complexity of O(r2dn), where d × n is the size of data matrix. In this paper, we propose a novel factorization-based model of RPCA, which has a complexity of O(kdn), where k is an upper bound of the true rank. Our method does not need the precise value of the true rank. From extensive experiments, we observe that AltProj can work only when r is precisely known in advance, however, when the needed rank parameter r is specified to a value different from the true rank, AltProj cannot fully separate the two parts while our method succeeds. Even when both work, our method is about 4 times faster than AltProj. Our method can be used as a light-weight, scalable tool for RPCA in the absence of the precise value of the true rank.

The importance of accurate recommender systems has been widely recognized by academia and industry. However, the recommendation quality is still rather low. Recently, a linear sparse and low-rank representation of the user-item matrix has been applied to produce Top-N recommendations. This approach uses the nuclear norm as a convex relaxation for the rank function and has achieved better recommendation accuracy than the state-of-the-art methods. In the past several years, solving rank minimization problems by leveraging nonconvex relaxations has received increasing attention. Some empirical results demonstrate that it can provide a better approximation to original problems than convex relaxation. In this paper, we propose a novel rank approximation to enhance the performance of Top-N recommendation systems, where the approximation error is controllable. Experimental results on real data show that the proposed rank approximation improves the Top-N recommendation accuracy substantially.

We propose a new subspace clustering method that integrates feature selection into subspace clustering. Rather than using all features to construct a low-rank representation of the data, we find such a representation using only relevant features, which helps in revealing more accurate data relationships. Two variants are proposed by using both convex and nonconvex rank approximations. Extensive experimental results confirm the effectiveness of the proposed method and models.

Matrix rank minimization problem is in general NP-hard. The nuclear norm is used to substitute the rank function in many recent studies. Nevertheless, the nuclear norm approximation adds all singular values together and the approximation error may depend heavily on the magnitudes of singular values. This might restrict its capability in dealing with many practical problems. In this paper, an arctangent function is used as a tighter approximation to the rank function. We use it on the challenging subspace clustering problem. For this nonconvex minimization problem, we develop an effective optimization procedure based on a type of augmented Lagrange multipliers (ALM) method. Extensive experiments on face clustering and motion segmentation show that the proposed method is effective for rank approximation.

Numerous applications in data mining and machine learning require recovering a matrix of minimal rank. Robust principal component analysis (RPCA) is a general framework for handling this kind of problems. Nuclear norm based convex surrogate of the rank function in RPCA is widely investigated. Under certain assumptions, it can recover the underlying true low rank matrix with high probability. However, those assumptions may not hold in real-world applications. Since the nuclear norm approximates the rank by adding all singular values together, which is essentially a l1-norm of the singular values, the resulting approximation erroris not trivial and thus the resulting matrix estimator can be significantly biased. To seek a closer approximation and to alleviate the above-mentioned limitations of the nuclear norm, we propose a nonconvex rank approximation. This approximation to the matrix rank is tighter than the nuclear norm. To solve the associated nonconvex minimization problem, we develop an efficient augmented Lagrange multiplier based optimization algorithm. Experimental results demonstrate that our method outperforms current state-of-the-art algorithms in both accuracy and efficiency.

A number of machine learning and computer vision problems, such as matrix completion and subspace clustering, require a matrix to be of low-rank. To meet this requirement, most existing methods use the nuclear norm as a convex proxy of the rank function and minimize it. However, the nuclear norm simply adds all nonzero singular values together instead of treating them equally as the rank function does, which may not be a good rank approximation when some singular values are very large. To reduce this undesirable weighting effect, we use a log-determinant function as a non-convex rank approximation which reduces the contributions of large singular values while keeping those of small singular values close to zero. We apply the method of augmented Lagrangian multipliers to optimize this non-convex rank approximation-based objective function and obtain closed-form solutions for all subproblems of minimizing different variables alternatively. The log-determinant low-rank optimization method is used to solve subspace clustering problem, for which we construct an affinity matrix based on the angular information of the low-rank representation to enhance its separability property. Extensive experimental results on face clustering and motion segmentation data demonstrate the effectiveness of the proposed method.

Matrix rank minimizing subject to affine constraints arises in many application areas, ranging from signal processing to machine learning. Nuclear norm is a convex relaxation for this problem which can recover the rank exactly under some restricted and theoretically interesting conditions. However, for many real-world applications, nuclear norm approximation to the rank function can only produce a result far from the optimum. To seek a solution of higher accuracy than the nuclear norm, in this letter, we propose a rank approximation based on Logarithm-Determinant. We consider using this rank approximation for subspace clustering application. Our framework can model different kinds of errors and noise. Effective optimization strategy is developed with theoretical guarantee to converge to a stationary point. The proposed method gives promising results on face clustering and motion segmentation tasks compared to the state-of-the-art subspace clustering algorithms.