Tensor-based multi-view clustering algorithms have attracted considerable attention due to their superior clustering performance. However, these algorithms typically treat each view independently, failing to utilize the complementary information across all views, thus lacking globality. Additionally, employing low-rank tensor constraints to extract consistent information among views may result in the loss of important information due to weak consistency constraints. These limitations significantly hinder the clustering performance. To address these issues, we propose Simple Multi-view Tensor Clustering (SimMTC), which achieves globality and strong consistency. SimMTC first applies Fast Fourier Transform (FFT) to the anchor graphs to obtain high-frequency and low-frequency information, which encode similarities between samples and anchors from all views, thereby capturing global information. Orthogonal tensor factorization is then conducted in the frequency domain. Moreover, a novel strong consistency constraint based on FFT is introduced, which enhances the extraction of consistent information in the frequency domain. What's more, an efficient alternating optimization algorithm is designed to solve the optimization problem in SimMTC. Finally, extensive experiments on real-world datasets demonstrate that SimMTC achieves state-of-the-art clustering performance. The code has been made publicly available on GitHub at: https://github.com/haonanxin/SimMTC_code.

K-means algorithm divides samples into c classes based on their structural characteristics. However, due to the non convex nature of the clustering problem, algorithms are prone to converge to poor local minima. To address the aforementioned issues, we propose the Local Structure Preserving Clustering with Learnable Anchors (LSPC-LA) method. We assume that with a well-designed anchor selection strategy, samples near the same anchor tend to belong to the same cluster, which reveal high confidence Must-Link local structural information for clustering. Based on this observation, we first construct an anchor-based bipartite graph, transforming the sample clustering problem into anchor clustering problem by local structural information, thus reducing the solution space and minimizing the risk of poor local minima. Then we create an anchor guiding matrix to allow anchors to learn the sample structure, improving clustering performance. Subsequently, an alternating iterative algorithm is proposed to optimize the LSPC-LA model. Finally, extensive experiments demonstrate the accuracy of the local structural information and the effectiveness of LSPC-LA.

The growing volume of remote sensing (RS) data highlights the need for enhanced data integration and processing. While combining hyperspectral and LiDAR data improves analysis by addressing spectral variability, challenges persist due to the high dimensionality, noise, and outliers in hyperspectral images (HSI). Additionally, supervised classification is labor-intensive, further motivating the need for advanced unsupervised clustering methods. Current clustering approaches, however, struggle with underutilization of spatial information, redundant spectral bands, and information divergence across multimodal data. To overcome these issues, we propose a Dimensionality-Reduced Spatial Bipartite Graph Clustering for Hyperspectral and LiDAR Data. This method integrates spatial information through bipartite graphs, reduces dimensionality by eliminating redundant bands, and employs a tensor-based framework to explore consistent structures in the low-rank space. This reduces information divergence and enhances clustering stability and performance. Extensive experiments demonstrate the effectiveness and robustness of the proposed method on real datasets.

Ensemble clustering using co-association matrices integrates multiple base clusterings but often overlooks interactions between crucial samples and base clusterings. This neglect can introduce noise and lead to information loss and instability. To address these issues, we propose the Consensus Graph-Based Spectral Ensemble Clustering via Low-Rank Tensor Learning (SECGTL) model. SECGTL organizes base clusterings into a third-order tensor and applies the Fast Fourier Transform (FFT) to capture inter-relations in the frequency domain. By rotating the tensor and minimizing the Tensor Schatten p-norm, SECGTL extracts shared information in a low-rank space, reducing noise and enhancing the learned common graph. With Laplacian rank constraints, SECGTL directly learns a graph with c-connected components, representing the clustering structure without post-processing. Extensive experiments on real-world datasets demonstrate SECGTL’s superior performance and robustness to noise.

Ensemble clustering based on co-association matrices integrates multiple connective matrices from base clusterings to achieve superior results. However, these methods primarily focus on inter-sample relationships, neglecting variations across different base clusterings, potentially introducing noise. Additionally, they overlook interactions between samples and base clusterings, which are crucial for extracting common information and avoiding post-processing steps that may cause information loss and instability in clustering results. To address these issues, we propose the Tensorized Graph Learning for Spectral Ensemble Clustering (TGLSEC) model. TGLSEC stacks all connective matrices into a third-order tensor, employs Fast Fourier Transform (FFT) for encoding, and elucidates inter-relations in the frequency domain. By minimizing the tensor Schatten p-norm, TGLSEC extracts common information in the low-rank space, eliminating noise and improving the quality of the common shared graph. Incorporating Laplacian rank constraints, TGLSEC learns a common shared graph with c-connected components, directly representing the clustering structure and avoiding post-processing steps, leading to more stable clustering results. To enhance computational efficiency for large-scale datasets, TGLSEC has been expanded into a bipartite-graph-based model, TGLSEC-BG, reducing complexity and computational time. Extensive experiments on real-world datasets demonstrate that TGLSEC and TGLSEC-BG exhibit superior clustering performance and robustness to noise.

Clustering based on structured graph learning involves acquiring a proximity matrix with an explicit clustering structure from the original one. However, the original proximity matrix often lacks some must-links compared to the groundtruth, constraining the upper bound of clustering performance. High-order proximity information can mitigate this limitation, yet traditional high-order proximity matrix-based methods are time-intensive. To tackle this, we propose the Tensorized High-order Bipartite Graphs-based structured proximity matrix learning method (THBG). Firstly, we introduce a high-order bipartite graph proximity matrix with a swift computation method, incorporating high-order information and significantly reducing computational overhead. Secondly, we apply tensor nuclear norm minimization to the tensor composed of high-order bipartite graphs, learning a low-rank tensor representation that effectively harnesses the consistency of high-order information. Concurrently, a structured bipartite graph proximity matrix with an explicit clustering structure is adaptively learned based on the low-rank tensor representation and Laplace rank constraint. Experimental results demonstrate the superiority and great potential of this method. Code available:https://anonymous.4open.science/r/THBG-D10D.

The surge in remote sensing (RS) data underscores the need for improved data diversity and processing. While integrating hyperspectral (HS) and light detection and ranging (LiDAR) data enhances analysis and addresses spectral variability, the high dimensionality, noise, and outliers inherent in hyperspectral images present significant challenges. In addition, the precise labeling required for HS makes supervised classification labor-intensive, professional-focused, and time-consuming, further motivating the development of advanced HS clustering algorithms to address these issues. Unsupervised clustering addresses the above issues but still struggles due to the underutilization of auxiliary spatial and structural information, high data dimensionality with redundant hyperspectral bands, and information divergence from heterogeneity among multimodal data. These challenges impede the effective extraction of consistent structures, undermining clustering stability and overall model performance. To address these challenges, we propose a superpixel-based bipartite graph clustering (SBGC) enriched with spatial information for hyperspectral and LiDAR data models. Our proposed method fully utilizes spatial information to construct meaningful bipartite graphs for the efficient processing of multimodal RS data. By adopting a projected clustering paradigm, our approach simultaneously clusters and reduces dimensionality, effectively eliminating redundant bands. In addition, it innovatively stacks multimodal data into tensors, thoroughly exploring the consistent structures in the low-rank space among different modalities. This reduces the heterogeneity-induced information divergence and significantly enhances clustering performance. Extensive experiments on real datasets confirm the method’s effectiveness and advanced capabilities.

Graph-based multiview clustering methods have gained significant attention in recent years. In particular, incorporating graph filtering into these methods allows for the exploration and utilization of both feature and topological information, resulting in a commendable improvement in clustering accuracy. However, these methods still exhibit several limitations: 1) the graph filters are predetermined, which disconnects the link with subsequent clustering tasks and 2) the separability of the filtered features is poor, which may not be suitable for the clustering. To mitigate these aforementioned issues, we propose Multiview Clustering via Block Diagonal Graph Filtering (MvC-BDGF), which can learn cluster-friendly graph filters. Specifically, the block diagonal graph filter with localized characteristics, which could make the filtered features very discriminating, is innovatively designed. The MvC-BDGF model seamlessly integrates the learning of graph filters with the acquisition of consensus graphs, forming a unified framework. This integration allows the model to obtain optimal filters and simultaneously acquire corresponding clustering labels. To solve the optimization problem in the MvC-BDGF model, an iterative solver based on the coordinate descent method is devised. Finally, a large number of experiments on benchmark datasets fully demonstrate the effectiveness and superiority of the proposed model. The code is available at https://github.com/haonanxin/MvC-BDGF_code.

Graph Neural Networks (GNNs) have emerged as the predominant approach for analyzing graph data on the web and beyond. Contrastive learning (CL), a self-supervised paradigm, not only mitigates reliance on annotations but also has potential in performance. The hard negative sampling strategy that benefits CL in other domains proves ineffective in the context of Graph Contrastive Learning (GCL) due to the message passing mechanism. Embracing the subspace hypothesis in clustering, we propose a method towards expansive and adaptive hard negative mining, referred to as G raph contR astive leA rning via subsP ace prE serving (GRAPE ). Beyond homophily, we argue that false negatives are prevalent over an expansive range and exploring them confers benefits upon GCL. Diverging from existing neighbor-based methods, our method seeks to mine long-range hard negatives throughout subspace, where message passing is conceived as interactions between subspaces. %Empirical investigations back up this strategy. Additionally, our method adaptively scales the hard negatives set through subspace preservation during training. In practice, we develop two schemes to enhance GCL that are pluggable into existing GCL frameworks. The underlying mechanisms are analyzed and the connections to related methods are investigated. Comprehensive experiments demonstrate that our method outperforms across diverse graph datasets and remains competitive across varied application scenarios\footnoteOur code is available at https://github.com/zz-haooo/WWW24-GRAPE. .

Clustering is used widely in various kinds of signal processing tasks, in which$k$-means is warmly welcomed by the researchers due to its efficiency and simplicity. Nevertheless, it fails to process non-spherical clusters which are common data distribution. As a variant of$k$-means, kernel$k$-means uses a kernel trick to map the raw data into a feature space to better describe the data with improved clustering performance. But the algorithms still have a lot of shortcomings in the application of signal processing: 1) Not all features contain a wealth of useful information, so all dimensions of features cannot be treated equally; 2) The use of high dimensional features for clustering exceedingly increases computational complexity with negligible improvement of clustering performance. To solve the problems, we propose a self-weighted Euler$k$-means (SWEKM) model, which can adaptively identify the importance of different features, perfectly integrating clustering and feature selection into a joint framework. Moreover, Euler kernel is adopted in SWEKM, which is capable of suppressing the interference of noise points and outliers with comparable computational complexity. Extensive experiments on datasets from the UCI database show that the SWEKM outperforms the state-of-the-art kernel$k$-means for clustering-based signal processing tasks.

With its simplicity and effectiveness, k-means is immensely popular, but it cannot perform well on complex nonlinear datasets. Multiple kernel k-means (MKKM) demonstrates the ability to describe highly complex nonlinear separable data structures. However, its speed requirement cannot scale as well as the data size grows beyond tens of thousands. Nowadays, digital data explosion mandates more scalable clustering methods to assist the machine learning tasks in easy-to-access form. To address the issue, we propose to employ the Nystrom scheme for MKKM clustering, termed scalable multiple kernel k-means clustering. It significantly reduces the computational complexity by replacing the original kernel matrix with a low-rank approximation. Analytically and empirically, we demonstrate that our method performs as well as existing state-of-the-art methods, but at a significantly lower compute cost, allowing us to scale the method more effectively for clustering tasks.