Low-rank Representation Method Research Articles

An adaptive kernel dictionary-based low-rank representation method for subspace clustering

Low-rank representation (LRR) is a classic subspace clustering (SC) algorithm, and many LRR-based methods have been proposed. Generally, LRR-based methods use denoized data as dictionaries for data reconstruction purpose. However, the dictionaries used in LRR-based algorithms are fixed, leading to poor clustering performance. In addition, most of these methods assume that the input data are linearly correlated. However, in practice, data are mostly nonlinearly correlated. To address these problems, we propose a novel adaptive kernel dictionary-based LRR (AKDLRR) method for SC. Specifically, to explore nonlinear information, the given data are mapped to the Hilbert space via the kernel technique. The dictionary in AKDLRR is not fixed; it adaptively learns from the data in the kernel space, making AKDLRR robust to noise and yielding good clustering performance. To solve the AKDLRR model, an efficient procedure including an alternative optimization strategy is proposed. In addition, a theoretical analysis of the convergence performance of AKDLRR is presented, which reveals that AKDLRR can converge in at most three iterations under certain conditions. The experimental results show that AKDLRR can achieve the best clustering performance and has excellent speed in comparison with other algorithms.

Multi-dimensional classification via class space fusion and comprehensive label correlations

Multi-dimensional Classification (MDC) is a new multi-output learning paradigm, where each instance in this framework is annotated with labels from multiple semantic class spaces. The vital challenge in MDC problem is how to address the heterogeneity of output space. Existing methods typically focus on the decomposition of output space, rarely consider the comprehensive fine-grained label correlations and the exploration of the intrinsic structure of the output space. And the local label correlations, which only exist within specific groups of instances, remain largely untapped in existing MDC methods. Therefore, we focus on tackling these above problems in this paper by simultaneously conducting label space fusion and considering the comprehensive label correlations to fully exploit the latent discriminative information hidden in the output space. Heuristically, we utilize low-rank representation method to achieve label space fusion to capture the intrinsic structure and implicit global correlation of label space. Then the predictive MDC model is extrapolated from the reconstructed instances equipped with the fused label space. Moreover, the topological structure information of samples is fully taken advantage of for MDC model establishment. Benefiting from these strategies, the heterogeneous label space can be fully excavated to boost the performance of MDC. Empirically, comparative experiments are conducted over several multi-dimensional benchmark data sets, and corresponding experimental results firmly illustrate that the proposed algorithm can effectively solve the MDC problem and outperform state-of-the-art methods.

Hyperspectral Anomaly Detection via Low-Rank Representation with Dual Graph Regularizations and Adaptive Dictionary

In a hyperspectral image, there is a close correlation between spectra and a certain degree of correlation in the pixel space. However, most existing low-rank representation (LRR) methods struggle to utilize these two characteristics simultaneously to detect anomalies. To address this challenge, a novel low-rank representation with dual graph regularization and an adaptive dictionary (DGRAD-LRR) is proposed for hyperspectral anomaly detection. To be specific, dual graph regularization, which combines spectral and spatial regularization, provides a new paradigm for LRR, and it can effectively preserve the local geometrical structure in the spectral and spatial information. To obtain a robust background dictionary, a novel adaptive dictionary strategy is utilized for the LRR model. In addition, extensive comparative experiments and an ablation study were conducted to demonstrate the superiority and practicality of the proposed DGRAD-LRR method.

Global structure graph mapping for multimodal change detection

ABSTRACT Multimodal change detection (MCD) combines multiple remote sensing data sources to realize surface change monitoring, which is essential for disaster evaluation and environmental monitoring. However, due to the ‘incomparable’ features in multimodal data, traditional change detection methods for unimodal (homogenous) data no longer apply. To address this issue, this paper proposes a novel MCD method with global structure graph mapping (GSGM) which extracts the ‘comparable’ structural features between multimodal datasets and constructs a global structure graph (GSG) to express the structure information for each of the multi-temporal images, which are then cross-mapped to the other data domain. The change intensity (CI) is determined by measuring the change of GSGs after mapping and the differences between GSGs and mapped GSGs. The forward and backward CI maps (CIMs) are then fused with the latent low-rank representation method (LLRR), and the change map (CM) is obtained by threshold segmentation. Experiments on five multimodal and four unimodal datasets demonstrate the effectiveness and robustness of the proposed method (source code is made available at https://github.com/rshante0426/GSGM).

Unified Framework for Faster Clustering via Joint Schatten p-Norm Factorization With Optimal Mean.

To enhance the effectiveness and efficiency of subspace clustering in visual tasks, this work introduces a novel approach that automatically eliminates the optimal mean, which is embedded in the subspace clustering framework of low-rank representation (LRR) methods, along with the computationally factored formulation of Schatten p -norm. By addressing the issues related to meaningful computations involved in some LRR methods and overcoming biased estimation of the low-rank solver, we propose faster nonconvex subspace clustering methods through joint Schatten p -norm factorization with optimal mean (JS p NFOM), forming a unified framework for enhancing performance while reducing time consumption. The proposed approach employs tractable and scalable factor techniques, which effectively address the disadvantages of higher computational complexity, particularly when dealing with large-scale coefficient matrices. The resulting nonconvex minimization problems are reformulated and further iteratively optimized by multivariate weighting algorithms, eliminating the need for singular value decomposition (SVD) computations in the developed iteration procedures. Moreover, each subproblem can be guaranteed to obtain the closed-form solver, respectively. The theoretical analyses of convergence properties and computational complexity further support the applicability of the proposed methods in real-world scenarios. Finally, comprehensive experimental results demonstrate the effectiveness and efficiency of the proposed nonconvex clustering approaches compared to existing state-of-the-art methods on several publicly available databases. The demonstrated improvements highlight the practical significance of our work in subspace clustering tasks for visual data analysis. The source code for the proposed algorithms is publicly accessible at https://github.com/ZhangHengMin/TRANSUFFC.

Nighttime Thermal Infrared Image Translation Integrating Visible Images

Nighttime Thermal InfraRed (NTIR) image colorization, also known as the translation of NTIR images into Daytime Color Visible (DCV) images, can facilitate human and intelligent system perception of nighttime scenes under weak lighting conditions. End-to-end neural networks have been used to learn the mapping relationship between temperature and color domains, and translate NTIR images with one channel into DCV images with three channels. However, this mapping relationship is an ill-posed problem with multiple solutions without constraints, resulting in blurred edges, color disorder, and semantic errors. To solve this problem, an NTIR2DCV method that includes two steps is proposed: firstly, fuse Nighttime Color Visible (NCV) images with NTIR images based on an Illumination-Aware, Multilevel Decomposition Latent Low-Rank Representation (IA-MDLatLRR) method, which considers the differences in illumination conditions during image fusion and adjusts the fusion strategy of MDLatLRR accordingly to suppress the adverse effects of nighttime lights; secondly, translate the Nighttime Fused (NF) image to DCV image based on HyperDimensional Computing Generative Adversarial Network (HDC-GAN), which ensures feature-level semantic consistency between the source image (NF image) and the translated image (DCV image) without creating semantic label maps. Extensive comparative experiments and the evaluation metrics values show that the proposed algorithms perform better than other State-Of-The-Art (SOTA) image fusion and translation methods, such as FID and KID, which decreased by 14.1 and 18.9, respectively.

Estimating Functional Brain Networks by Low-Rank Representation With Local Constraint.

The functional architecture undergoes alterations during the preclinical phase of Alzheimer's disease. Consequently, the primary research focus has shifted towards identifying Alzheimer's disease and its early stages by constructing a functional connectivity network based on resting-state fMRI data. Recent investigations show that as Alzheimer's Disease (AD) progresses, modular tissue and connections in the core brain areas of AD patients diminish. Sparse learning methods are powerful tools for understanding Functional Brain Networks (FBNs) with Regions of Interest (ROIs) and a connectivity matrix measuring functional coherence between them. However, these tools often focus exclusively on functional connectivity measures, neglecting the brain network's modularity. Modularity orchestrates dynamic activities within the FBN to execute intricate cognitive tasks. To provide a comprehensive delineation of the FBN, we propose a local similarity-constrained low-rank sparse representation (LSLRSR) method that encodes modularity information under a manifold-regularized network learning framework and further formulate it as a low-rank sparse graph learning problem, which can be solved by an efficient optimization algorithm. Specifically, for each modularity structure, the Schatten p-norm regularizer reduces the reconstruction error and provides a better approximation of the low-rank constraint. Furthermore, we adopt a manifold-regularized local similarity prior to infer the intricate relationship between subnetwork similarity and modularity, guiding the modeling of FBN. Additionally, the proximal average method approximates the joint solution's proximal map, and the resulting nonconvex optimization problems are solved using the alternating direction multiplier method (ADMM). Compared to state-of-the-art methods for constructing FBNs, our algorithm generates a more modular FBN. This lays the groundwork for further research into alterations in brain network modularity resulting from diseases.

Learning Disentangled Priors for Hyperspectral Anomaly Detection: A Coupling Model-Driven and Data-Driven Paradigm.

Accurately distinguishing between background and anomalous objects within hyperspectral images poses a significant challenge. The primary obstacle lies in the inadequate modeling of prior knowledge, leading to a performance bottleneck in hyperspectral anomaly detection (HAD). In response to this challenge, we put forth a groundbreaking coupling paradigm that combines model-driven low-rank representation (LRR) methods with data-driven deep learning techniques by learning disentangled priors (LDP). LDP seeks to capture complete priors for effectively modeling the background, thereby extracting anomalies from hyperspectral images more accurately. LDP follows a model-driven deep unfolding architecture, where the prior knowledge is separated into the explicit low-rank prior formulated by expert knowledge and implicit learnable priors by means of deep networks. The internal relationships between explicit and implicit priors within LDP are elegantly modeled through a skip residual connection. Furthermore, we provide a mathematical proof of the convergence of our proposed model. Our experiments, conducted on multiple widely recognized datasets, demonstrate that LDP surpasses most of the current advanced HAD techniques, exceling in both detection performance and generalization capability.

PDRLRR: A novel low-rank representation with projection distance regularization via manifold optimization for clustering

The low-rank representation (LRR) method has attracted widespread attention due to its excellent performance in pattern recognition and machine learning. LRR-based variants have been proposed to solve the three existing problems in LRR: (1) the projection matrix is permanently fixed when dimensionality reduction techniques are adopted; (2) LRR fails to capture the local geometric structure; and (3) the solution deviates from the real low-rank solution. To address these problems, this paper proposes a low-rank representation with projection distance regularization (PDRLRR) via manifold optimization for clustering. In detail, we first introduce a low-dimensional projection matrix and a projection distance regularization term to fit the projected data automatically and capture the local structure of the data, respectively. Consequently, the projection matrix and representation matrix are obtained jointly. Then, we obtain a more accurate low-rank solution by minimizing the Schatten-p norm instead of the nuclear norm. Next, the projection matrix is optimized through a generalized Stiefel manifold. Extensive experiments demonstrate that our proposed method outperforms the state-of-the-art methods.

EEG classification based on Grassmann manifold and matrix recovery

Extracting features from EEG signals through time, frequency and spatial-domain gives rise to the problem of neglecting the property of nonlinear manifold structure of the data, and traditional feature extractions based on Euclidean space are unfavorable for the full utilization of the manifold feature. In this paper, a new EEG classification method is proposed by representing EEG signals on the Grassmann manifold. Firstly, a low rank representation method based on matrix recovery is introduced into the Grassmann manifold to explore the subspace information and re-express the EEG signals. Then a deep neural network is proposed to reduce the dimension of the recovered EEG data, and the low rank representation makes the EEG data separable by using T-SNE visualization; Finally, the dimension reduced features are input to the traditional classifier for classification. The proposed method is performed on four datasets for seizure detection, disease recognition and mental arithmetic recognition respectively. The corresponding accuracy reaches 99.99%, 99.61%, 100%, and 99.72% which shows that the proposed method outperforms other state of art methods on EEG classification.

ARGLRR: A Sparse Low-Rank Representation Single-Cell RNA-Sequencing Data Clustering Method Combined with a New Graph Regularization.

The development of single-cell transcriptome sequencing technologies has opened new ways to study biological phenomena at the cellular level. A key application of such technologies involves the employment of single-cell RNA sequencing (scRNA-seq) data to identify distinct cell types through clustering, which in turn provides evidence for revealing heterogeneity. Despite the promise of this approach, the inherent characteristics of scRNA-seq data, such as higher noise levels and lower coverage, pose major challenges to existing clustering methods and compromise their accuracy. In this study, we propose a method called Adjusted Random walk Graph regularization Sparse Low-Rank Representation (ARGLRR), a practical sparse subspace clustering method, to identify cell types. The fundamental low-rank representation (LRR) model is concerned with the global structure of data. To address the limited ability of the LRR method to capture local structure, we introduced adjusted random walk graph regularization in its framework. ARGLRR allows for the capture of both local and global structures in scRNA-seq data. Additionally, the imposition of similarity constraints into the LRR framework further improves the ability of the proposed model to estimate cell-to-cell similarity and capture global structural relationships between cells. ARGLRR surpasses other advanced comparison approaches on nine known scRNA-seq data sets judging by the results. In the normalized mutual information and Adjusted Rand Index metrics on the scRNA-seq data sets clustering experiments, ARGLRR outperforms the best-performing comparative method by 6.99% and 5.85%, respectively. In addition, we visualize the result using Uniform Manifold Approximation and Projection. Visualization results show that the usage of ARGLRR enhances the separation of different cell types within the similarity matrix.

Robust Low Rank and Sparse Representation for Multiple Kernel Dimensionality Reduction

In the fields of pattern recognition and data mining, two problems need to be addressed. First, the curse of dimensionality degrades the performance of many practical data processing techniques. Second, due to the existence of noise and outliers, feature extraction on corrupted data cannot be effectively achieved. Recently, some representation based methods have produced promising results. However, these methods cannot handle the case in which nonlinear similarity exists and have failed to provide the quantized interpretability for the importance of features. In this paper, we propose a novel low rank and sparse representation method to realize dimensionality reduction and robustly extract latent low dimensional discriminative features. Specifically, we first adopt multiple kernel learning to map the original data into an embedded reproducing kernel Hilbert space (RKHS) and then kernel based similarity discriminative projection is learned to explore the within-class and between-class variability. Notably, this low dimensional feature learning strategy is definitely integrated into the low rank matrix recovery of the kernel matrix. Next, we introduce the regularization of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{2,1}$ </tex-math></inline-formula> norm on error matrix to eliminate noise and on projection matrix to lead the selected features to be more compact and interpretable. The non-convex optimization problem is effectively solved by the alternating direction method of multipliers (ADMM) methods. Extensive experiments on seven benchmark datasets are conducted to demonstrate the effectiveness of our method.

Learning Tensor Low-Rank Representation for Hyperspectral Anomaly Detection.

Recently, low-rank representation (LRR) methods have been widely applied for hyperspectral anomaly detection, due to their potentials in separating the backgrounds and anomalies. However, existing LRR models generally convert 3-D hyperspectral images (HSIs) into 2-D matrices, inevitably leading to the destruction of intrinsic 3-D structure properties in HSIs. To this end, we propose a novel tensor low-rank and sparse representation (TLRSR) method for hyperspectral anomaly detection. A 3-D TLR model is expanded to separate the LR background part represented by a tensorial background dictionary and corresponding coefficients. This representation characterizes the multiple subspace property of the complex LR background. Based on the weighted tensor nuclear norm and the LF,1 sparse norm, a dictionary is designed to make its atoms more relevant to the background. Moreover, a principal component analysis (PCA) method can be assigned as one preprocessing step to exact a subset of HSI bands, retaining enough the HSI object information and reducing computational time of the postprocessing tensorial operations. The proposed model is efficiently solved by the well-designed alternating direction method of multipliers (ADMMs). A comparison with the existing algorithms via experiments establishes the competitiveness of the proposed method with the state-of-the-art competitors in the hyperspectral anomaly detection task.

Face Recognition Method under Adaptive Image Matching and Dictionary Learning Algorithm.

In this research, a robust face recognition method based on adaptive image matching and a dictionary learning algorithm was proposed. A Fisher discriminant constraint was introduced into the dictionary learning algorithm program so that the dictionary had certain category discrimination ability. The purpose was to use this technology to reduce the influence of pollution, absence, and other factors on face recognition and improve the recognition rate. The optimization method was used to solve the loop iteration to obtain the expected specific dictionary, and the selected specific dictionary was used as the representation dictionary in adaptive sparse representation. In addition, if a specific dictionary was placed in a seed space of the original training data, the mapping matrix can be used to represent the mapping relationship between the specific dictionary and the original training sample, and the test sample could be corrected according to the mapping matrix to remove the contamination in the test sample. Moreover, the feature face method and dimension reduction method were used to process the specific dictionary and the corrected test sample, and the dimensions were reduced to 25, 50, 75, 100, 125, and 150, respectively. In this research, the recognition rate of the algorithm in 50 dimensions was lower than that of the discriminatory low-rank representation method (DLRR), and the recognition rate in other dimensions was the highest. The adaptive image matching classifier was used for classification and recognition. The experimental results showed that the proposed algorithm had a good recognition rate and good robustness against noise, pollution, and occlusion. Health condition prediction based on face recognition technology has the advantages of being noninvasive and convenient operation.

Exploiting the sparse characteristics in probabilistic feature space for hyperspectral anomaly detection

Nowadays, the low-rank representation (LRR) and deep learning-based methods have received much attention in anomaly detection for hyperspectral images (HSIs). However, most of these methods mainly focus on the powerful reconstruction capability of the neural networks while ignoring the potential probability distribution of both anomalies and background pixels. To solve the problem, we propose a sparse component extraction-based probability distribution representation detector (SC-PDRD) framework, which integrates the characteristic of the sparse component obtained by the LRR model with the powerful probability representation ability of the variational autoencoder (VAE) network. The LRR model effectively separates the anomaly component from the background, which also serves as the prior anomaly distribution for each pixel. Moreover, the VAE architecture tries to recover the potential anomaly distribution using the sparse detection map in the feature space. In addition, we employ the Chebyshev neighborhood to leverage spatial information. The modified Wasserstein distance measures the distance between the test pixel and its neighborhood. The final detection map is attained by combining the prior anomalous degree of the anomalies with the output of the VAE network. Experimental results on three real HSIs demonstrate the effectiveness and superiority of SC-PDRD.

Non-negative low-rank representation based on dictionary learning for single-cell RNA-sequencing data analysis

In the analysis of single-cell RNA-sequencing (scRNA-seq) data, how to effectively and accurately identify cell clusters from a large number of cell mixtures is still a challenge. Low-rank representation (LRR) method has achieved excellent results in subspace clustering. But in previous studies, most LRR-based methods usually choose the original data matrix as the dictionary. In addition, the methods based on LRR usually use spectral clustering algorithm to complete cell clustering. Therefore, there is a matching problem between the spectral clustering method and the affinity matrix, which is difficult to ensure the optimal effect of clustering. Considering the above two points, we propose the DLNLRR method to better identify the cell type. First, DLNLRR can update the dictionary during the optimization process instead of using the predefined fixed dictionary, so it can realize dictionary learning and LRR learning at the same time. Second, DLNLRR can realize subspace clustering without relying on spectral clustering algorithm, that is, we can perform clustering directly based on the low-rank matrix. Finally, we carry out a large number of experiments on real single-cell datasets and experimental results show that DLNLRR is superior to other scRNA-seq data analysis algorithms in cell type identification.

Multiview Subspace Clustering Using Low-Rank Representation.

Multiview subspace clustering is one of the most widely used methods for exploiting the internal structures of multiview data. Most previous studies have performed the task of learning multiview representations by individually constructing an affinity matrix for each view without simultaneously exploiting the intrinsic characteristics of multiview data. In this article, we propose a multiview low-rank representation (MLRR) method to comprehensively discover the correlation of multiview data for multiview subspace clustering. MLRR considers symmetric low-rank representations (LRRs) to be an approximately linear spatial transformation under the new base, that is, the multiview data themselves, to fully exploit the angular information of the principal directions of LRRs, which is adopted to construct an affinity matrix for multiview subspace clustering, under a symmetric condition. MLRR takes full advantage of LRR techniques and a diversity regularization term to exploit the diversity and consistency of multiple views, respectively, and this method simultaneously imposes a symmetry constraint on LRRs. Hence, the angular information of the principal directions of rows is consistent with that of columns in symmetric LRRs. The MLRR model can be efficiently calculated by solving a convex optimization problem. Moreover, we present an intuitive fusion strategy for symmetric LRRs from the perspective of spectral clustering to obtain a compact representation, which can be shared by multiple views and comprehensively represents the intrinsic features of multiview data. Finally, the experimental results based on benchmark datasets demonstrate the effectiveness and robustness of MLRR compared with several state-of-the-art multiview subspace clustering algorithms.

Addressing label ambiguity imbalance in candidate labels: Measures and disambiguation algorithm

Partial Label Learning (PLL) is a weakly supervised learning framework where each training instance is associated with more than one candidate label. However, label ambiguity in the case of label imbalance has not been well solved. In this paper, a novel label imbalance-aware algorithm named PL-LIMAP is proposed to effectively solve this problem. Firstly, a partial manifold constrained low-rank representation method is proposed to learn the instance affinity matrix, which can identify instances with the same label by fully mining the manifold structure of the data. Moreover, for making full use of the information hidden in candidate labels, the Jaccard distance is introduced to measure the similarity between candidate labels to obtain the label affinity matrix. The combination of these two affinity matrices can achieve the purpose of disambiguation through complementary information. Meanwhile, aiming to determine the imbalance of ambiguous labels, specialized measures are proposed to evaluate the imbalance level in PLL. According to the imbalance level of different labels, an alternative weighting scheme is proposed to mitigate the imbalance of ambiguous labels. As a consequence, the ground-truth label of an instance can be found out even though its label information is not available in advance. Experiments reveal the overwhelming performances of PL-LIMAP.

CBLRR: a cauchy-based bounded constraint low-rank representation method to cluster single-cell RNA-seq data.

The rapid development of single-cel+l RNA sequencing (scRNA-seq) technology provides unprecedented opportunities for exploring biological phenomena at the single-cell level. The discovery of cell types is one of the major applications for researchers to explore the heterogeneity of cells. Some computational methods have been proposed to solve the problem of scRNA-seq data clustering. However, the unavoidable technical noise and notorious dropouts also reduce the accuracy of clustering methods. Here, we propose the cauchy-based bounded constraint low-rank representation (CBLRR), which is a low-rank representation-based method by introducing cauchy loss function (CLF) and bounded nuclear norm regulation, aiming to alleviate the above issue. Specifically, as an effective loss function, the CLF is proven to enhance the robustness of the identification of cell types. Then, we adopt the bounded constraint to ensure the entry values of single-cell data within the restricted interval. Finally, the performance of CBLRR is evaluated on 15 scRNA-seq datasets, and compared with other state-of-the-art methods. The experimental results demonstrate that CBLRR performs accurately and robustly on clustering scRNA-seq data. Furthermore, CBLRR is an effective tool to cluster cells, and provides great potential for downstream analysis of single-cell data. The source code of CBLRR is available online at https://github.com/Ginnay/CBLRR.

Tensor subspace clustering using consensus tensor low-rank representation

Recently, subspace clustering (SC) has received an increasing amount of attention. Generally, SC methods are implemented on sample data in matrix form. Even for multiway or tensor data, which is prevalent in reality, traditional SC methods should convert each sample to a vector and then form a data matrix. However, the vectorization process will damage the underlying inherent spatial structure of the data. To address this problem, in this paper, we propose a novel consensus tensor low-rank representation (CTLRR) method, which is directly implemented on tensor data. First, the tensor nuclear norm (TNN) and t-product, which is defined as the multiplication of two tensors, are employed to model the data and obtain the low-rank representation tensor. Second, spectral clustering is unified into CTLRR to explore the consensus information among the low-rank representation tensor, which helps obtain the final fusion similarity matrix with the k connected components, where k is the number of clusters. Third, the cluster structure is characterized, and the clustering performance is substantially improved. Last, an optimization procedure for CTLRR is presented. Experimental results on certain challenging datasets show that the proposed CTLRR method outperforms the state-of-the-art methods.