Low-rank Representation Model Research Articles

A Hierarchical Low-Rank Denoising Model for Remote Sensing Images Based on Deep Unfolding.

Recently, the low-rank representation (LRR) model has been widely used in the field of remote sensing image denoising due to its excellent noise suppression capability. However, those low-rank-based methods always discard important edge details as residuals, leading to a common issue of blurred edges in denoised results. To address this problem, we take a new look at low-rank residuals and try to extract edge information from them. Therefore, a hierarchical denoising framework was combined with a low-rank model to extract edge information from low-rank residuals within the edge subspace. A prior knowledge matrix was designed to enable the model to learn necessary structural information rather than noise. Also, such traditional model-driven approaches require multiple iterations, and the solutions may be very complex and computationally intensive. To further enhance the noise suppression performance and computing efficiency, a hierarchical low-rank denoising model based on deep unrolling (HLR-DUR) was proposed, integrating deep neural networks into the hierarchical low-rank denoising framework to expand the information capture and representation capabilities of the proposed shallow model. Sufficient experiments on optical images, hyperspectral images (HSI), and synthetic aperture radar (SAR) images showed that HLR-DUR achieved state-of-the-art (SOTA) denoising results.

Robust Corrupted Data Recovery and Clustering via Generalized Transformed Tensor Low-Rank Representation.

Tensor analysis has received widespread attention in high-dimensional data learning. Unfortunately, the tensor data are often accompanied by arbitrary signal corruptions, including missing entries and sparse noise. How to recover the characteristics of the corrupted tensor data and make it compatible with the downstream clustering task remains a challenging problem. In this article, we study a generalized transformed tensor low-rank representation (TTLRR) model for simultaneously recovering and clustering the corrupted tensor data. The core idea is to find the latent low-rank tensor structure from the corrupted measurements using the transformed tensor singular value decomposition (SVD). Theoretically, we prove that TTLRR can recover the clean tensor data with a high probability guarantee under mild conditions. Furthermore, by using the transform adaptively learning from the data itself, the proposed TTLRR model can approximately represent and exploit the intrinsic subspace and seek out the cluster structure of the tensor data precisely. An effective algorithm is designed to solve the proposed model under the alternating direction method of multipliers (ADMMs) algorithm framework. The effectiveness and superiority of the proposed method against the compared methods are showcased over different tasks, including video/face data recovery and face/object/scene data clustering.

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.

MLRR-ATV: A Robust Manifold Nonnegative LowRank Representation with Adaptive Total-Variation Regularization for scRNA-seq Data Clustering.

Since genomics was proposed, the exploration of genes has been the focus of research. The emergence of single-cell RNA sequencing (scRNA-seq) technology makes it possible to explore gene expression at the single-cell level. Due to the limitations of sequencing technology, the data contains a lot of noise. At the same time, it also has the characteristics of highdimensional and sparse. Clustering is a common method of analyzing scRNA-seq data. This paper proposes a novel singlecell clustering method called Robust Manifold Nonnegative LowRank Representation with Adaptive Total-Variation Regularization (MLRR-ATV). The Adaptive Total-Variation (ATV) regularization is introduced into Low-Rank Representation (LRR) model to reduce the influence of noise through gradient learning. Then, the linear and nonlinear manifold structures in the data are learned through Euclidean distance and cosine similarity, and more valuable information is retained. Because the model is non-convex, we use the Alternating Direction Method of Multipliers (ADMM) to optimize the model. We tested the performance of the MLRRATV model on eight real scRNA-seq datasets and selected nine state-of-the-art methods as comparison methods. The experimental results show that the performance of the MLRRATV model is better than the other nine methods.

Multimanifold Bistructured Low Rank Representation of hyperspectral images

Hyperspectral images (HSIs) are obtained by imaging surface materials using a spectral imager. In practical applications, the hyperspectral remote sensing images are inevitably contaminated by noise, leading to errors in image processing results. Gaussian noise, Poisson noise, and stripe noise are common in HSIs. This article presents an HSI denoising model based on the low rank representation of multi manifold double constructions. Introducing multiple manifolds into the field of hyperspectral image denoising for the first time, comprehensively obtaining complex information on hyperspectral surfaces. We extended the graph-regularized low-rank representation model (GLRR) by using maximum data variance to construct global information. GLRR obtains local information, and the parallel effects of nearest neighbor and maximum variance graphs take into account both global and local consistency in the denoising process. Our model is not only applicable to the case of a single manifold, but also to the case of multiple manifolds, especially in the case of complex ground target images with multiple manifold spectra. Use the LADMAP iterative algorithm to iteratively solve the proposed algorithm. Avoid introducing auxiliary variables to reduce runtime costs and algorithm complexity. Both on simulated and real datasets, the runtime is relatively fast. We experiments on both real and simulated datasets, as well as real datasets, to verify that our method has good denoising performance when Gaussian, Poisson, and stripe noise occur simultaneously.

Reweighted robust and discriminative latent subspace projection for face recognition

Subspace projection has been widely studied to implement the feature extraction for face recognition. However, it scarcely facilitates exploring the label information in the subspace projection procedure. The feature extraction and classification are usually divided into two separate procedures. This fails to explore the discriminative information from the training data, and thus degrades the discrimination of the extracted features and lowers the face recognition accuracy. To address this issue, we present a novel reweighted robust and discriminative latent subspace projection (ReRDLSP) method which organically integrates the reweighted latent low-rank representation model and discriminative ridge regression into a union framework. We employ a reweighted nuclear norm minimization to realize the low-rank regularization, which provides adaptive weighted values assignment, regularizes the representation matrix adaptively, and thus boosts the capability and flexibility of the method. Moreover, a discriminative ridge regression method is presented by employing a nonnegative relaxation, which enlarges the margins of the face samples from different classes as much as possible and boosts the freedom of fitting the label information. The computational complexity and convergence analysis are also discussed in detail. Extensive experiments are demonstrated and very promising results are achieved compared with some state-of-the-art face recognition methods.

A Precise and Adaptive Graph Regularized Low Rank Representation Model for Recognizing Oil-bearing

A Precise and Adaptive Graph Regularized Low Rank Representation Model for Recognizing Oil-bearing

Image inpainting exploiting global prior refined weighted low-rank representation

Low-rank and nonlocal self-similarity are important priors for image restoration. Based on nonlocal self-similarity assumption, similar patches are grouped into a matrix that is of low-rank or approximately low-rank. Traditional algorithms model low-rank prior of local group matrices (intra-group) and ignore the global inter-group relationship, which will result in suboptimal performance without considering global consistency. Due to overlapping of patches, groups are dependent, however, conventional methods process each group independently. To make full use of the intrinsic relationship among groups, we consider all groups simultaneously and propose a global prior refined weighted low-rank representation model for image inpainting. The local-groups and the aggregation of all groups are taken into account in the proposed model. By introducing auxiliary variable, we decouple the local–global model and optimize iteratively using the alternating direction method of multipliers. The proposed global refinement model significantly improves the performance of local low-rank model. A new strategy for grouping similar patches is also proposed by dividing the neighborhood of a target patch into multiple subregions and searching for a given number of similar patches within each subregion. The proposed method is applied to various tasks (line inpainting, destriping, and depth map completion) and obtains promising performance.

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.

Image Segmentation Based on Fuzzy Low-Rank Structural Clustering

Fuzzy clustering is an essential algorithm in image segmentation, and most of them are based on fuzzy c-mean (FCM) algorithms. However, it is sensitive to noise, center point selection, cluster number, and distance metric. To address this problem, we propose a new fuzzy clustering method based on low-rank representation (LRR) for image segmentation, which integrates low-rank structure with fuzzy theory. First, we improve the morphological reconstruction super-pixel method based on edge detection by introducing anisotropy to enhance the image edge. Thus, on the one hand, the improved morphological reconstruction super-pixel method can improve its noise-resistance performance; on the other hand, the complexity of the subsequent low-rank computation can be reduced by enhancing the superpixels constructed by the edges. Second, inspired by the fact that rank can represent correlation, we propose the concept of fuzzy low-rank structure, which is not dealing with data directly but with the relationship between data. Specifically, we perform rank minimization on the constructed membership matrix to obtain the optimal matrix. To obtain better clustering results, we added the Frobenius norm of the fuzzy matrix as a fuzzy regularization term in the LRR model to achieve global convergence and obtain a membership matrix with a strong element correlation. Finally, we obtain the final clustering results by clustering the processed membership matrix using a subspace clustering with a lowrank structure constraint. Experiments performed on artificial and real-world images show that the proposed method is more effective and efficient than the current state-of-the-art methods.

A Personalized Low-Rank Subspace Clustering Method Based on Locality and Similarity Constraints for scRNA-seq Data Analysis.

Single-cell RNA sequencing (scRNA-seq) technology can provide expression profile of single cells, which propels biological research into a new chapter. Clustering individual cells based on their transcriptome is a critical objective of scRNA-seq data analysis. However, the high-dimensional, sparse and noisy nature of scRNA-seq data pose a challenge to single-cell clustering. Therefore, it is urgent to develop a clustering method targeting scRNA-seq data characteristics. Due to its powerful subspace learning capability and robustness to noise, the subspace segmentation method based on low-rank representation (LRR) is broadly used in clustering researches and achieves satisfactory results. In view of this, we propose a personalized low-rank subspace clustering method, namely PLRLS, to learn more accurate subspace structures from both global and local perspectives. Specifically, we first introduce the local structure constraint to capture the local structure information of the data, while helping our method to obtain better inter-cluster separability and intra-cluster compactness. Then, in order to retain the important similarity information that is ignored by the LRR model, we utilize the fractional function to extract similarity information between cells, and introduce this information as the similarity constraint into the LRR framework. The fractional function is an efficient similarity measure designed for scRNA-seq data, which has theoretical and practical implications. In the end, based on the LRR matrix learned from PLRLS, we perform downstream analyses on real scRNA-seq datasets, including spectral clustering, visualization and marker gene identification. Comparative experiments show that the proposed method achieves superior clustering accuracy and robustness.

KGLRR: A low-rank representation K-means with graph regularization constraint method for Single-cell type identification

Single-cell RNA sequencing technology provides a tremendous opportunity for studying disease mechanisms at the single-cell level. Cell type identification is a key step in the research of disease mechanisms. Many clustering algorithms have been proposed to identify cell types. Most clustering algorithms perform similarity calculation before cell clustering. Because clustering and similarity calculation are independent, a low-rank matrix obtained only by similarity calculation may be unable to fully reveal the patterns in single-cell data. In this study, to capture accurate single-cell clustering information, we propose a novel method based on a low-rank representation model, called KGLRR, that combines the low-rank representation approach with K-means clustering. The cluster centroid is updated as the cell dimension decreases to better from new clusters and improve the quality of clustering information. In addition, the low-rank representation model ignores local geometric information, so the graph regularization constraint is introduced. KGLRR is tested on both simulated and real single-cell datasets to validate the effectiveness of the new method. The experimental results show that KGLRR is more robust and accurate in cell type identification than other advanced algorithms.

Smooth low-rank representation with a Grassmann manifold for tensor completion

Utilizing low-rank representation, recent methods have efficiently estimated the low-rank tensor for tensor completion (TC). However, owing to the identifiability issue, these methods inevitably preserve some outliers of the sparse tensor as elements of the low-rank tensor, which leads to an imprecise estimation of the low-rank tensor. In this paper, we propose a smooth low-rank representation with a Grassmann manifold (SLRR-GM) model to tackle the identifiability issue. Specifically, we first smooth the low-frequency and high-frequency discontinuities of the low-rank tensor to sufficiently remove the preserved outliers of the sparse tensor. Accordingly, a smooth low-rank representation model is built to precisely estimate the low-rank tensor. Second, we smooth the discontinuities through a small number of the feature vectors that characterize the original vectors of the low-rank tensor. This uses the Grassmann manifold to effectively reduce the computational complexity of smoothing the discontinuities. Third, we integrate the smooth low-rank representation model with the Grassmann manifold to propose SLRR-GM. Based on the alternating direction method of multipliers (ADMM), an algorithm is proposed to solve the SLRR-GM model. We also investigate the complexity and convergence to validate the algorithmic effectiveness. Experiments in different scenarios demonstrate that the proposed method outperforms several state-of-the-art methods in terms of the quantitative and visual aspects with the acceptable processing time.

LRR-Net: An Interpretable Deep Unfolding Network for Hyperspectral Anomaly Detection

Considerable endeavors have been expended towards enhancing the representation performance for Hyperspectral Anomaly Detection (HAD) through physical model-based methods and recent deep learning-based approaches. Of these methods, the Low-Rank Representation (LRR) model is widely adopted for its formidable separation capabilities for background and target features, however, its practical applications are limited due to the reliance on manual parameter selection and subpar generalization performance. To this end, this paper presents a new HAD baseline network, referred to as LRR-Net, which synergizes the LRR model with deep learning techniques. LRR-Net leverages the alternating direction method of multipliers (ADMM) optimizer to solve the LRR model efficiently and incorporates the solution as prior knowledge into the deep network to guide the optimization of parameters. Moreover, LRR-Net transforms the regularized parameters into trainable parameters of the deep neural network, thus alleviating the need for manual parameter tuning. Additionally, this paper proposes a sparse neural network embedding to demonstrate the scalability of the LRR-Net framework. Empirical evaluations on eight distinct datasets illustrate the efficacy and superiority of the proposed approach compared to state-of-the-art methods.

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.

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.

SpBLRSR: Schatten p-norm Constrained Bounded Low-rank Subspace Recovery for Predicting N7-methylguanosine (m7G)-disease Associations

Background: As an essential positively charged RNA modification, N7-methylguanosine (m7G) has been reported to be associated with multiple diseases including cancers. While transcriptome-wide m7G sites have been identified by high-throughput sequencing approaches, the disease-associated m7G sites are still largely unknown. Therefore, computational methods are urgently needed to predict potential m7G-disease associations, which is crucial for understanding the biosynthetic pathways of tumorigenesis at the epi-transcriptome layer. Objective: We hope to develop an effective computational method that can accurately predict the associations between m7G sites and diseases, and then to prioritizing candidate m7G sites for novel diseases. Method: In this article, we proposed a Schatten p-norm constrained bounded low-rank subspace recovery (SpBLRSR) method for m7G-disease association prediction. An m7G-disease block matrix was built to alleviate the sparseness during the association pattern discovery process. By incorporating the low-rank representation (LRR) model and sparse subspace clustering (SSC) model, SpBLRSR was designed to capture both the global and local structures of the association pattern. Results: Compared with the benchmark methods, SpBLRSR achieved the best performance in predicting associations between m7G sites and disease, and in prioritizing m7G sites for novel diseases. Then the robustness of Schatten p-norm in our method was further validated via a noise contamination experiment. Finally, case study of breast cancer was performed to elucidate the biological meaning of our method. Conclusion: SpBLRSR exploits the disease pathogenesis at the epitranscriptome layer by predicting potential m7A sites for disease.

SLRRSC: Single-Cell Type Recognition Method Based on Similarity and Graph Regularization Constraints.

Single-cell clustering is a crucial task of scRNA-seq analysis, which reveals the natural grouping of cells. However, due to the high noise and high dimension in scRNA-seq data, how to effectively and accurately identify cell types from a great quantity of cell mixtures is still a challenge. Considering this, in this paper, we propose a novel subspace clustering algorithm termed SLRRSC. This method is developed based on the low-rank representation model, and it aims to capture the global and local properties inherent in data. In order to make the LRR matrix describe the spatial relationship of samples more accurately, we introduce the manifold-based graph regularization and similarity constraint into the LRR-based method SLRRSC. The graph regularization can preserve the local geometric structure of the data in low-rank decomposition, so that the low-rank representation matrix contains more local structure information. By imposing similarity constraint on the low-rank matrix, the similarity information between sample pairs is further introduced into the SLRRSC model to improve the learning ability of low-rank method for global structure. At the same time, the similarity constraint makes the low-rank representation matrix symmetric, which makes it better interpretable in clustering application. We compare the effectiveness of the SLRRSC algorithm with other single-cell clustering methods on simulated data and real single-cell datasets. The results show that this method can obtain more accurate sample similarity matrix and effectively solve the problem of cell type recognition.

FOC winding defect detection based on improved texture features and low-rank representation model.

The defect detection of fiber-optic coils (FOCs) plays an important role in the quality control of the FOC production. In order to overcome the problems of poor performance and low reliability of existing methods, this paper provides a solution for winding defect detection of FOCs based on low-rank representation (LRR) technology. First, we design a feature matrix, which represents the image. Then the LRR model is employed to formulate the defect detection task as a problem of low rank and sparse matrix decomposition. Meanwhile, Laplacian regularization is introduced as a smoothness constraint to expand the distance between defect regions and low-rank background. Experiments are performed on a real dataset to verify the algorithm. The results show that the proposed winding defect detection method of FOCs achieves the highest detection accuracy and lowest false alarm rate compared to other methods, verifying the effectiveness of the proposed method.

Auto-weighted low-rank representation for clustering

Low-rank representation (LRR) is an effective method to learn the subspace structure embedded in the data. However, most LRR methods make use of different features equally, causing the useless features may degrade the performance of the model. In order to solve this problem, a novel unsupervised low-rank representation model, i.e., Auto-weighted Low-Rank Representation (ALRR), is proposed to construct a more favorable similarity graph (SG) for clustering. In particular, ALRR enhances the discriminability of SG by capturing the multi-subspace structure and extracting the salient features simultaneously. Specifically, an auto-weighted distance penalty is introduced to learn a similarity graph by highlighting the effective features, and meanwhile, overshadowing the disturbed features. Consequently, ALRR obtains a similarity graph that can preserve the intrinsic geometrical structures within the data by enforcing a smaller similarity on two dissimilar samples. Moreover, a block-diagonal regularizer is employed to guarantee that the learned graph contains c diagonal blocks. This can facilitate a more discriminative representation learning for clustering tasks. Extensive experimental results on synthetic and real databases demonstrate the superiority of ALRR over other state-of-the-art methods.