Subspace Clustering Research Articles

Anchor-based multi-view subspace clustering with hierarchical feature descent

Multi-view clustering has attracted growing attention owing to its capabilities of aggregating information from various sources and its promising horizons in public affairs. Up till now, many advanced approaches have been proposed in recent literature. However, there are several ongoing difficulties to be tackled. One common dilemma occurs while attempting to align the features of different views. Moreover, due to the fact that many existing multi-view clustering algorithms stem from spectral clustering, this results to cubic time complexity w.r.t. the number of dataset. However, we propose Anchor-based Multi-view Subspace Clustering with Hierarchical Feature Descent(MVSC-HFD) to tackle the discrepancy among views through hierarchical feature descent and project to a common subspace( STAGE 1), which reveals dependency of different views. We further reduce the computational complexity to linear time cost through a unified sampling strategy in the common subspace( STAGE 2), followed by anchor-based subspace clustering to learn the bipartite graph collectively( STAGE 3). Extensive experimental results on public benchmark datasets demonstrate that our proposed model consistently outperforms the state-of-the-art techniques. Our code is publicly available at https://github.com/QiyuanOu/MVSC-HFD/tree/main.

Tensorial multi-view subspace clustering with side constraints for elevator security warning

Tensorial multi-view subspace clustering with side constraints for elevator security warning

An end-to-end Graph Convolutional Network for Semi-supervised Subspace Clustering via label self-expressiveness

Semi-supervised clustering provides accurate assignments by leveraging a limited amount of supervisory information. There are two main groups of conventional semi-supervised subspace clustering algorithms: Pairwise Constraints (PC)-based methods and Gaussian Fields and Harmonic Function (GFHF)-based methods. Nevertheless, PC-based methods are limited because of their reliance on weak supervisory information. GFHF-based methods, on the other hand, focus on the local relationship between the affinity matrix and the assignment matrix, which restricts their clustering efficacy. Recently, graph convolutional network (GCN) has been employed to effectively transmit the local graph topology of the raw data into the feature domain, which motivates the proposed GCN model for Semi-supervised Subspace Clustering via label self-expressiveness (GSSC). Conventional semi-supervised clustering has been enhanced by incorporating a novel concept known as label self-expressiveness, which serves as a guiding factor for the clustering process. Furthermore, GSSC considers the global geometric structure of the assignment matrix and generates a discriminable assignment matrix using an end-to-end mechanism. Additionally, a well-designed loss function is introduced to train the novel GSSC. The experimental results conducted on four benchmark datasets demonstrate that the proposed GSSC algorithm exhibits superior performance compared to existing semi-supervised clustering algorithms.

Self-Supervised Deep Multi-Level Representation Learning Fusion-Based Maximum Entropy Subspace Clustering for Hyperspectral Band Selection

As one of the most important techniques for hyperspectral image dimensionality reduction, band selection has received considerable attention, whereas self-representation subspace clustering-based band selection algorithms have received quite a lot of attention with good effect. However, many of them lack the self-supervision of representations and ignore the multi-level spectral–spatial information of HSI and the connectivity of subspaces. To this end, this paper proposes a novel self-supervised multi-level representation learning fusion-based maximum entropy subspace clustering (MLRLFMESC) method for hyperspectral band selection. Firstly, to learn multi-level spectral–spatial information, self-representation subspace clustering is embedded between the encoder layers of the deep-stacked convolutional autoencoder and its corresponding decoder layers, respectively, as multiple fully connected layers to achieve multi-level representation learning (MLRL). A new auxiliary task is constructed for multi-level representation learning and multi-level self-supervised training to improve its capability of representation. Then, a fusion model is designed to fuse the multi-level spectral–spatial information to obtain a more distinctive coefficient matrix for self-expression, where the maximum entropy regularization (MER) method is employed to promote connectivity and the uniform dense distribution of band elements in each subspace. Finally, subspace clustering is conducted to obtain the final band subset. Experiments have been conducted on three hyperspectral datasets, and the corresponding results show that the proposed MLRLFMESC algorithm significantly outperforms several other band selection methods in classification performance.

Enhanced video clustering using multiple riemannian manifold-valued descriptors and audio-visual information

Videos inherently blend multiple modalities in real-world scenarios, primarily visual and auditory cues. When synergized, these cues foster enhanced data representations. Standard clustering techniques, primarily designed for managing vectorial data in Euclidean spaces, struggle to handle multidimensional data with nonlinear manifold structures, such as video or image sets. While recent subspace clustering methods using Riemannian manifold representation tackle this issue, they often sideline auditory information, overlooking the potential harmony between visual and auditory modalities. This paper presents an innovative approach that crafts multiple Riemannian manifold-valued descriptors to bridge this gap, encapsulating multimodal video information in a unified structure. We architect a single-modality Riemannian subspace clustering for individual modal data and extend it to a multi-modality framework, leveraging the interplay of audio-visual data. Detailed optimization and convergence analysis are also provided. The proposed approach significantly outperforms the existing state-of-the-art methods, improving accuracy by 4%, 1%, and 2% on UCF-101, UCF-sport, and AVE datasets, respectively.

Adaptive fuzzy weighted C-mean image segmentation algorithm combining a new distance metric and prior entropy

The fuzzy C-mean clustering algorithm (FCM) is effective in image segmentation. However, its sensitivity to initialization settings and the limitation of the Euclidean distance metric in measuring similarity lead to unsatisfactory image segmentation. To overcome these shortcomings, we propose an adaptive fuzzy weighted C-mean image segmentation algorithm that combines a new distance metric and prior entropy. This algorithm significantly contributes in three aspects. First, we employ an improved sparse subspace clustering (SSC) algorithm based on the superpixel image for initialization settings. This step aims to obtain the initial number of clusters and the membership matrix, ensuring the algorithm’s convergence to the optimal solution. Second, to better capture differences between image regions, we introduce a novel distance metric that combines Euclidean and non-Euclidean distances. Simultaneously, the fuzzy weight is introduced to mitigate redundant feature interference, making the clustering result more reasonable. Finally, leveraging prior entropy – a maximum entropy under conditional constraints – we refine the algorithm’s adaptability to unknown features, thereby improving clustering accuracy. Comparative experiments with several state-of-the-art algorithms validate the effectiveness and robustness of our proposed algorithm.

GRESS: Grouping Belief-Based Deep Contrastive Subspace Clustering.

The self-expressive coefficient plays a crucial role in the self-expressiveness-based subspace clustering method. To enhance the precision of the self-expressive coefficient, we propose a novel deep subspace clustering method, named grouping belief-based deep contrastive subspace clustering (GRESS), which integrates the clustering information and higher-order relationship into the coefficient matrix. Specifically, we develop a deep contrastive subspace clustering module to enhance the learning of both self-expressive coefficients and cluster representations simultaneously. This approach enables the derivation of relatively noiseless self-expressive similarities and cluster-based similarities. To enable interaction between these two types of similarities, we propose a unique grouping belief-based affinity refinement module. This module leverages grouping belief to uncover the higher-order relationships within the similarity matrix, and integrates the well-designed noisy similarity suppression and similarity increment regularization to eliminate redundant connections while complete absent information. Extensive experimental results on four benchmark datasets validate the superiority of our proposed method GRESS over several state-of-the-art methods.

Data-driven derivation of an adverse outcome pathway linking vascular endothelial growth factor receptor (VEGFR), endocrine disruption, and atherosclerosis.

Dysregulation of vascular endothelial growth factor (VEGF) and its receptor (VEGFR) contributes to atherosclerosis and cardiovascular disease (CVD), making it a potential target for CVD risk assessment. High-throughput screening (HTS) approaches have resulted in large-scale in vitro data, providing mechanistic information that can help assess chemical toxicity and identify molecular ini­tiating events (MIEs) of adverse outcome pathways (AOPs). AOPs represent a logical sequence of biological responses contributing to toxicity and are valuable tools to inform chemical risk assessment. Here, we used HTS data to formulate an AOP relating VEGF signaling perturbation to atheroscle­rosis. ToxCast, Tox21, and PubChem data were evaluated to obtain bioprofiles of 4165 compounds active in assays targeting VEGFR. Cheminformatics analysis identified 109 enriched structural fin­gerprints. Applying a subspace clustering approach based on chemical structure bioactivity yielded 12 primary targets, whose relevance to CVD was confirmed by an AI-assisted literature review. An AOP was hypothesized by coupling mechanistic relationships highlighted by HTS data with literature review findings, linking serotonin receptor (HTR), estrogen receptor alpha (ERα), and vasopressin receptor (AVPR) targets with VEGFR activity, angiogenic signaling, and atherosclerosis. Several endocrine disrupting chemicals (EDCs), e.g., bisphenols, triclosan, dichlorodiphenyltrichloroethane (DDT), and polychlorinated biphenyls (PCBs), were identified as relevant chemical stressors. Sub­space clustering of these chemicals evaluated potential MIEs and highlighted associations with use case classes. By applying computational methods to profile HTS data and hypothesize a mechanistic AOP, this study proposes a data-driven approach to evaluating environmental cardiotoxicity, which could eventually supplement and reduce the need for animal testing in toxicological assessments.

Multiview Deep Subspace Clustering Networks.

Multiview subspace clustering aims to discover the inherent structure of data by fusing multiple views of complementary information. Most existing methods first extract multiple types of handcrafted features and then learn a joint affinity matrix for clustering. The disadvantage of this approach lies in two aspects: 1) multiview relations are not embedded into feature learning and 2) the end-to-end learning manner of deep learning is not suitable for multiview clustering. Even when deep features have been extracted, it is a nontrivial problem to choose a proper backbone for clustering on different datasets. To address these issues, we propose the multiview deep subspace clustering networks (MvDSCNs), which learns a multiview self-representation matrix in an end-to-end manner. The MvDSCN consists of two subnetworks, i.e., a diversity network (Dnet) and a universality network (Unet). A latent space is built using deep convolutional autoencoders, and a self-representation matrix is learned in the latent space using a fully connected layer. Dnet learns view-specific self-representation matrices, whereas Unet learns a common self-representation matrix for all views. To exploit the complementarity of multiview representations, the Hilbert-Schmidt independence criterion (HSIC) is introduced as a diversity regularizer that captures the nonlinear, high-order interview relations. Because different views share the same label space, the self-representation matrices of each view are aligned to the common one by universality regularization. The MvDSCN also unifies multiple backbones to boost clustering performance and avoid the need for model selection. Experiments demonstrate the superiority of the MvDSCN.

Segmentation and Completion of Human Motion Sequence via Temporal Learning of Subspace Variety Model.

Subspace-based models have been extensively employed in unsupervised segmentation and completion of human motion sequence (HMS). However, existing approaches often neglect the incorporation of temporal priors embedded in HMS, resulting in suboptimal results. This paper presents a subspace variety model for HMS, along with an innovative Temporal Learning of Subspace Variety Model (TL-SVM) method for enhanced segmentation and completion in HMS. The key idea is to segment incomplete HMS into motion clusters and extracting the subspace features of each motion through the temporal learning of the subspace variety model. Subsequently, the HMS is completed based on the extracted subspace features. Thus, the main challenge is to learn the subspace variety model with temporal priors when confronted with missing entries. To tackle this, the paper develops a spatio-temporal assignment consistency (STAC) constraint for the subspace variety model, leveraging temporal priors embedded in HMS. In addition, a subspace clustering approach under the STAC constraint is proposed to learn the subspace variety model by extracting subspace features from HMS and segmenting HMS into motion clusters alternatively. The proposed subspace clustering model can also handle missing entries with theoretical guarantees. Furthermore, the missing entries of HMS are completed by minimizing the distance between each human motion frame and its corresponding subspace. Extensive experimental results, along with comparisons to state-of-the-art methods on four benchmark datasets, underscore the advantages of the proposed method.

Learning Unified Anchor Graph for Joint Clustering of Hyperspectral and LiDAR Data.

The joint clustering of multimodal remote sensing (RS) data poses a critical and challenging task in Earth observation. Although recent advances in multiview subspace clustering have shown remarkable success, existing methods become computationally prohibitive when dealing with large-scale RS datasets. Moreover, they neglect intrinsic nonlinear and spatial interdependencies among heterogeneous RS data and lack generalization ability for out-of-sample data, thereby restricting their applicability. This article introduces a novel unified framework called anchor-based multiview kernel subspace clustering with spatial regularization (AMKSC). It learns a scalable anchor graph in the kernel space, leveraging contributions from each modality instead of seeking a consensus full graph in the feature space. To ensure spatial consistency, we incorporate a spatial smoothing operation into the formulation. The method is efficiently solved using an alternating optimization strategy, and we provide theoretical evidence of its scalability with linear computational complexity. Furthermore, an out-of-sample extension of AMKSC based on multiview collaborative representation-based classification is introduced, enabling the handling of larger datasets and unseen instances. Extensive experiments on three real heterogeneous RS datasets confirm the superiority of our proposed approach over state-of-the-art methods in terms of clustering performance and time efficiency. The source code is available at https://github.com/AngryCai/AMKSC.

Grouping Subspace Segmentation

This work studies the subspace segmentation problem. Given a set of data points which are drawn from a union of multiple subspaces. The goal of subspace segmentation is to cluster the data into the underlying subspaces from which the data are drawn from. The most recent works use spectral clustering based on the affinity matrix obtained by Sparse Subspace Clustering (SSC), Low-Rank Representation (LRR) and Least Squares Regression (LSR). They write each data point as a linear combination of all the data points, and use the representation coefficients to form the affinity matrix. LSR shows that it is more effective due to the grouping effect for data with high correlation. In this work, we propose the Grouping Subspace Segmentation (GSS) method by enhancing the grouping effect of correlated data points. The affinity graph is constructed to encode the local structure of data. Experiments on the real data sets show that the proposed method GSS is more effective than the state-of-the-art methods.

Contrastive Consistency and Attentive Complementarity for Deep Multi-View Subspace Clustering

Contrastive Consistency and Attentive Complementarity for Deep Multi-View Subspace Clustering

Interactive Subspace Cluster Analysis Guided by Semantic Attribute Associations.

Multivariate datasets with many variables are increasingly common in many application areas. Most methods approach multivariate data from a singular perspective. Subspace analysis techniques, on the other hand. provide the user a set of subspaces which can be used to view the data from multiple perspectives. However, many subspace analysis methods produce a huge amount of subspaces, a number of which are usually redundant. The enormity of the number of subspaces can be overwhelming to analysts, making it difficult for them to find informative patterns in the data. In this article, we propose a new paradigm that constructs semantically consistent subspaces. These subspaces can then be expanded into more general subspaces by ways of conventional techniques. Our framework uses the labels/meta-data of a dataset to learn the semantic meanings and associations of the attributes. We employ a neural network to learn a semantic word embedding of the attributes and then divide this attribute space into semantically consistent subspaces. The user is provided with a visual analytics interface that guides the analysis process. We show via various examples that these semantic subspaces can help organize the data and guide the user in finding interesting patterns in the dataset.

Exploring the Path of Informatization Construction of Civic Education in Colleges and Universities in the Era of Melting Media

Abstract The development of informatization has increasingly become the transformation direction of the Civic Education in colleges and universities in the new media era. This paper outlines the path of civic and political information technology, in conjunction with campus networks in general, and presents a series of support mechanisms for information technology. Taking S university as a research case, firstly, Fractal Brownian motion is used to scientifically characterize the traffic of campus network users. The network group characteristics are estimated through the determination of the Hurst coefficient. Secondly, the Apriori algorithm is used to extract the association rules of online behaviors hidden in these traffic features to explore the relationship between online behaviors in time series. Finally, by combining the above features and association rules, we developed subspace clustering techniques for college students’ campus Internet usage behavior. We proposed a path for ideological education based on the clustering results. The results show that the online behavior of different students on campus shows significant differences. Class A students like to stay up late on weekends, and the number of such students online fluctuates slightly from 14:30 to 23:30. Class B students generally prefer to go online during the daytime. Class C students also have some students who stay up late, but the average duration is not long, with a maximum of 766 seconds. Class D students all stay up all night, and the peak of the mean value of the online duration occurs at 4:30. Class D students all stay up all night, and the peak of the mean value of the online duration occurs at 4:30. Category D students need to be given more attention in the management of political education.

Double Discrete Cosine Transform-Oriented Multi-View Subspace Clustering.

Low-rank tensor representation with the tensor nuclear norm has been rising in popularity in multi-view subspace clustering (MVSC), in which the tensor nuclear norm is commonly implemented using discrete Fourier transform (DFT). Unfortunately, existing DFT-oriented MVSC methods may provide unsatisfactory results since (1) DFT exploits complex arithmetic in the Fourier domain, usually resulting in high tubal tensor rank, and (2) local structural information is rarely considered. To solve these problems, in this paper, we propose a novel double discrete cosine transform (DCT)-oriented multi-view subspace clustering (D2CTMSC) method, in which the first DCT aims to derive the tensor nuclear norm without complex arithmetic while the second DCT aims to explore the local structure of the self-representation tensor, such that the essential low-rankness and sparsity embedding in multi-view features can be thoroughly exploited. Moreover, we design an effective alternating iteration strategy to solve the proposed model. Experimental results on four types of multi-view datasets (News stories, Face images, Scene images, and Generic objects) demonstrate the superiority of the D2CTMSC method compared with DFT-based methods and other state-of-the-art clustering methods.

Fine-Grained Essential Tensor Learning for Robust Multi-View Spectral Clustering.

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.

Spatial and Cluster Structural Prior-Guided Subspace Clustering for Hyperspectral Image

Spatial and Cluster Structural Prior-Guided Subspace Clustering for Hyperspectral Image

Tensor-Derived Large-Scale Multi-View Subspace Clustering With Faithful Semantics

Tensor-Derived Large-Scale Multi-View Subspace Clustering With Faithful Semantics

Multifeature deep subspace clustering for hyperspectral band selection

Multifeature deep subspace clustering for hyperspectral band selection