Low-rank Constraint Research Articles

Mixed Matrix Completion in Complex Survey Sampling under Heterogeneous Missingness

Modern surveys with large sample sizes and growing mixed-type questionnaires require robust and scalable analysis methods. In this work, we consider recovering a mixed dataframe matrix, obtained by complex survey sampling, with entries following different canonical exponential distributions and subject to heterogeneous missingness. To tackle this challenging task, we propose a two-stage procedure: in the first stage, we model the entry-wise missing mechanism by logistic regression, and in the second stage, we complete the target parameter matrix by maximizing a weighted log-likelihood with a low-rank constraint. We propose a fast and scalable estimation algorithm that achieves sublinear convergence, and the upper bound for the estimation error of the proposed method is rigorously derived. Experimental results support our theoretical claims, and the proposed estimator shows its merits compared to other existing methods. The proposed method is applied to analyze the National Health and Nutrition Examination Survey data. Supplementary materials for this article are available online.

Low-Rank Kernel Tensor Learning for Incomplete Multi-View Clustering

Incomplete Multiple Kernel Clustering algorithms, which aim to learn a common latent representation from pre-constructed incomplete multiple kernels from the original data, followed by k-means for clustering. They have attracted intensive attention due to their high computational efficiency. However, our observation reveals that the imputation of these approaches for each kernel ignores the influence of other incomplete kernels. In light of this, we present a novel method called Low-Rank Kernel Tensor Learning for Incomplete Multiple Views Clustering (LRKT-IMVC) to address the above issue. Specifically, LRKT-IMVC first introduces the concept of kernel tensor to explore the inter-view correlations, and then the low-rank kernel tensor constraint is used to further capture the consistency information to impute missing kernel elements, thereby improving the quality of clustering. Moreover, we carefully design an alternative optimization method with promising convergence to solve the resulting optimization problem. The proposed method is compared with recent advances in experiments with different missing ratios on seven well-known datasets, demonstrating its effectiveness and the advantages of the proposed interpolation method.

A novel multi-task TSK fuzzy system modeling method based on multi-task fuzzy clustering

The traditional multi-task Takagi-Sugeno-Kang (TSK) fuzzy system modeling methods pay more attention to utilizing the inter-task correlation to learn the consequent parameters but ignore the importance of the antecedent parameters of the model. To this end, we propose a novel multi-task TSK fuzzy system modeling method based on multi-task fuzzy clustering. This method first proposes a novel multi-task fuzzy c-means clustering method that learns multiple specific clustering centers for each task and some common clustering centers for all tasks. Secondly, for the consequent parameters of the fuzzy system, the novel low-rank and row-sparse constraints are proposed to better implement multi-task learning. The experimental results demonstrate that the proposed model shows better performance compared with other existing methods.

Compressive sensing ISAR imaging with low-rank constraint and anisotropic spatial total variation processing

In order to suppress random noise and remove stripe interference in ISAR imaging, a Compressive Sensing method is proposed for super-resolution ISAR imaging in this paper, which is named LR-ASTV (Low-rank and Anisotropic Spatial Total Variation) algorithm here. In this algorithm, the original echo HRRP is transformed into echo HRRP of MMV model with radial interpolation processing at first. Subsequently, an optimization objective function based on Compressive Sensing framework is formulated which includes the sparsity constraint and low-rank constraint, and this optimization problem is solved by JLRS algorithm to generate an initial ISAR image from which the random noise has been eliminated. The initial image is then subjected to further refinement using the Anisotropic Spatial Total Variation (ASTV) processing, ultimately yielding the final ISAR image with stripe interference removed. To validate the effectiveness of the LR-ASTV algorithm, ISAR imaging experiments based on simulated and measured data at different SNRs are completed, and the imaging results of the LR-ASTV algorithm are compared with those of other three algorithms including the LSM-ME2 algorithm, the JLRS algorithm and the LRPB algorithm. It can be found that the LR-ASTV algorithm has obvious superiority in suppressing random noise and removing stripe interference, and can provide ISAR images of higher clarity. The quality evaluation for ISAR images also shows that the LR-ASTV algorithm has lower image entropy index and higher image contrast index than the other three ISAR imaging algorithms.

Multi-target feature selection with subspace learning and manifold regularization

Existing supervised Multi-Target Feature Selection (MTFS) methods seldom consider the nearest-neighbor relationship and statistical correlation of samples underlying the output space, which leads the result of feature selection to be easily interfered by the output noise, thus making it difficult to achieve satisfactory performance. This paper proposes a novel MTFS method to preserve both the global and local target correlations. Specifically, the low-rank constraint is introduced to achieve multi-layer regression structure to better decouple the inter-input and inter-target relationships. Moreover, the local nearest-neighbor relationships and variable correlations of the sample points in the output space are also explored through adaptive graph and manifold learning, to better utilize the target correlations to improve the MTFS performance. Following the above principle, the resulting objective function and the corresponding optimization algorithm are proposed. Extensive experiments on several public datasets show that the proposed method is superior to other state-of-the-art methods.

Unpaired robust hashing with noisy labels for zero-shot cross-modal retrieval

With new social media concepts emerging, zero-shot cross-modal retrieval methods have gained significant attention. Most of the existing methods assume that the labels of training data are correct and the different modalities are perfectly matched, which is unrealistic in real-life retrieval scenarios. This paper presents a novel approach, termed unpaired robust hashing with noisy labels (URHNL), for zero-shot cross-modal retrieval. Specifically, we developed a zero-shot cross-modal hash retrieval framework that can learn distinct hash codes for different modalities, which is suitable for unpaired cross-modal retrieval scenarios. In addition, it incorporates the sparse constraint on the noise matrix and the low-rank constraint on the recovered label matrix, respectively. These constraints are applied to mitigate the negative effects of noisy labels. Furthermore, we introduce the concept of drag ɛ into the learning process of label semantic embedding, which aims to generate more discriminative hash codes. To improve the similarity of semantic information within hash codes, we consider both intra-modal and inter-modal similarity. A large number of experiments on cross-modal datasets show the effectiveness of the URHNL approach in real and complex zero-shot cross-modal retrieval scenarios. The source code of this word can be found at https://github.com/szq0816/URHNL.

Learning All-In Collaborative Multiview Binary Representation for Clustering.

Multiview clustering via binary representation has attracted intensive attention due to its effectiveness in handling large-scale multiple view data. However, these kind of clustering approaches usually ignore a very important potential high-order correlation in discrete representation learning. In this article, we propose a novel all-in collaborative multiview binary representation for clustering (AC-MVBC) framework, where multiview collaborative binary representation and clustering structure are learned in a joint manner. Specifically, using a new type of tensor low-rank constraint, the high-order collaborations, i.e., cross-view and inner view collaborations, can be effectively captured in our model. Moreover, by incorporating the Bregman discrepancy, the projective consistency among different views can be guaranteed to achieve a more powerful binary representation. An efficient optimization algorithm is also proposed to solve the objective function with fast convergence empirically. Experimental results on several challenge datasets demonstrate that the proposed method has achieved highly competent performance compared with the state-of-the-art multiview clustering (MVC) methods while maintaining low computational and memory requirements.

View-specific anchors coupled tensorial bipartite graph learning for incomplete multi-view clustering

The incomplete multi-view clustering (IMVC) aims to explore the consensus and complementary information embedded in incomplete multi-view data, so as to accurately aggregate all samples into different clusters. Existing IMVC methods still have the following issues that need to be further solved: how to efficiently (1) alleviate the computational complexity; (2) capture the complementary information from views; (3) uncover the high-order correlations underlying incomplete multi-view data. To address these problems, a new method, called view-specific anchors coupled tensorial bipartite graph learning for incomplete multi-view clustering (VA-TBGIMC), is proposed in this paper. Specifically, view-specific anchors are learned from non-missing samples to represent the distribution of all samples including missing ones. With the help of high-quality anchors, the bipartite graph between all samples and anchors is constructed, which can preserve the complementary information. Meanwhile, these bipartite graphs are stacked into a tensor which is imposed with a low-rank constraint to adequately capture the inter-view and inter-sample correlations from incomplete multi-view data. Further, the augmented graph of bipartite graph is constrained by Laplacian rank to learn a consensus cluster indicator. A large number of experiments validate the superiority and efficiency of the proposed method in terms of clustering performance and time consumption.

Motion compensated structured low-rank reconstruction for 3D multi-shot EPI.

The 3D multi-shot EPI imaging offers several benefits including higher SNR and high isotropic resolution compared to 2D single shot EPI. However, it suffers from shot-to-shot inconsistencies arising from physiologically induced phase variations and bulk motion. This work proposed a motion compensated structured low-rank (mcSLR) reconstruction method to address both issues for 3D multi-shot EPI. Structured low-rank reconstruction has been successfully used in previous work to deal with inter-shot phase variations for 3D multi-shot EPI imaging. It circumvents the estimation of phase variations by reconstructing an individual image for each phase state which are then sum-of-squares combined, exploiting their linear interdependency encoded in structured low-rank constraints. However, structured low-rank constraints become less effective in the presence of inter-shot motion, which corrupts image magnitude consistency and invalidates the linear relationship between shots. Thus, this work jointly models inter-shot phase variations and motion corruptions by incorporating rigid motion compensation for structured low-rank reconstruction, where motion estimates are obtained in a fully data-driven way without relying on external hardware or imaging navigators. Simulation and in vivo experiments at 7T have demonstrated that the mcSLR method can effectively reduce image artifacts and improve the robustness of 3D multi-shot EPI, outperforming existing methods which only address inter-shot phase variations or motion, but not both. The proposed mcSLR reconstruction compensates for rigid motion, and thus improves the validity of structured low-rank constraints, resulting in improved robustness of 3D multi-shot EPI to both inter-shot motion and phase variations.

Dynamic functional network connectivity analysis in schizophrenia based on a spatiotemporal CPD framework.

Objective.Dynamic functional network connectivity (dFNC), based on data-driven group independent component (IC) analysis, is an important avenue for investigating underlying patterns of certain brain diseases such as schizophrenia. Canonical polyadic decomposition (CPD) of a higher-way dynamic functional connectivity tensor, can offer an innovative spatiotemporal framework to accurately characterize potential dynamic spatial and temporal fluctuations. Since multi-subject dFNC data from sliding-window analysis are also naturally a higher-order tensor, we propose an innovative sparse and low-rank CPD (SLRCPD) for the three-way dFNC tensor to excavate significant dynamic spatiotemporal aberrant changes in schizophrenia.Approach.The proposed SLRCPD approach imposes two constraints. First, the L1regularization on spatial modules is applied to extract sparse but significant dynamic connectivity and avoid overfitting the model. Second, low-rank constraint is added on time-varying weights to enhance the temporal state clustering quality. Shared dynamic spatial modules, group-specific dynamic spatial modules and time-varying weights can be extracted by SLRCPD. The strength of connections within- and between-IC networks and connection contribution are proposed to inspect the spatial modules. K-means clustering and classification are further conducted to explore temporal group difference.Main results.82 subject resting-state functional magnetic resonance imaging (fMRI) dataset and opening Center for Biomedical Research Excellence (COBRE) schizophrenia dataset both containing schizophrenia patients (SZs) and healthy controls (HCs) were utilized in our work. Three typical dFNC patterns between different brain functional regions were obtained. Compared to the spatial modules of HCs, the aberrant connections among auditory network, somatomotor, visual, cognitive control and cerebellar networks in 82 subject dataset and COBRE dataset were detected. Four temporal states reveal significant differences between SZs and HCs for these two datasets. Additionally, the accuracy values for SZs and HCs classification based on time-varying weights are larger than 0.96.Significance.This study significantly excavates spatio-temporal patterns for schizophrenia disease.

Kernel-Based Sparse Representation Learning With Global and Local Low-Rank Label Constraint

Kernel-Based Sparse Representation Learning With Global and Local Low-Rank Label Constraint

ISAR Super-Resolution Imaging Approach Based on Low-Rank Sparse Joint Constraint Under Low SNR

ISAR Super-Resolution Imaging Approach Based on Low-Rank Sparse Joint Constraint Under Low SNR

Review of Matrix Rank Constraint Model for Impulse Interference Image Inpainting

Camera failure or loss of storage components in imaging equipment may result in the loss of important image information or random pulse noise interference. The low-rank prior is one of the most important priors in image optimization processing. This paper reviews and compares some low-rank constraint models for image matrices. Firstly, an overview of image-inpainting models based on nuclear norm, truncated nuclear norm, weighted nuclear norm, and matrix-factorization-based F norm is presented, and corresponding optimization iterative algorithms are provided. Then, we use different image matrix low-order constraint models to recover satellite images from three types of pulse interference and provide our experimental visual and numerical results. Finally, it can be concluded that the method based on the weighted nuclear norm can achieve the best image restoration effect. The F norm method based on matrix factorization has the shortest computational time and can be used for large-scale low-rank matrix calculations. Compared with nuclear norm-based methods, weighted nuclear norm-based methods and truncated nuclear norm-based methods can significantly improve repair performance.

Structured low-rank representation learning for hyperspectral sparse unmixing

ABSTRACT Sparse unmixing methods have been widely used to estimate the abundance of each material component from hyperspectral images. However, conventional sparse unmixing approaches only consider matrix factorization without limited explorations on the high-dimensional structures of the third-order tensors. To address this issue, we propose SUnSLRR, a novel approach to sparse unmixing of hyperspectral data based on structured low-rank tensor modelling. In contrast to traditional methods, SUnSLRR leverages the low-rank property underlying the abundance tensor to exploit structural details from multiple modes. By incorporating sparsity regularization and a low-rank constraint, SUnSLRR can effectively extract the intrinsic features of hyperspectral data. We apply the alternating direction method of multipliers framework to solve the optimization problem induced by SUnSLRR, and experiments conducted on simulated and real hyperspectral images demonstrate the superior effectiveness of our proposed method compared to traditional methods in terms of both accuracy and efficiency.

Tensorized Multi-View Low-Rank Approximation Based Robust Hand-Print Recognition.

Since hand-print recognition, i.e., palmprint, finger-knuckle-print (FKP), and hand-vein, have significant superiority in user convenience and hygiene, it has attracted greater enthusiasm from researchers. Seeking to handle the long-standing interference factors, i.e., noise, rotation, shadow, in hand-print images, multi-view hand-print representation has been proposed to enhance the feature expression by exploiting multiple characteristics from diverse views. However, the existing methods usually ignore the high-order correlations between different views or fuse very limited types of features. To tackle these issues, in this paper, we present a novel tensorized multi-view low-rank approximation based robust hand-print recognition method (TMLA_RHR), which can dexterously manipulate the multi-view hand-print features to produce a high-compact feature representation. To achieve this goal, we formulate TMLA_RHR by two key components, i.e., aligned structure regression loss and tensorized low-rank approximation, in a joint learning model. Specifically, we treat the low-rank representation matrices of different views as a tensor, which is regularized with a low-rank constraint. It models the across information between different views and reduces the redundancy of the learned sub-space representations. Experimental results on eight real-world hand-print databases prove the superiority of the proposed method in comparison with other state-of-the-art related works.

Learning Consistency and Specificity of Cells From Single-Cell Multi-Omic Data.

Advancements in single-cell technologies concomitantly develop the epigenomic and transcriptomic profiles at the cell levels, providing opportunities to explore the potential biological mechanisms. Even though significant efforts have been dedicated to them, it remains challenging for the integration analysis of multi-omic data of single-cell because of the heterogeneity, complicated coupling and interpretability of data. To handle these issues, we propose a novel self-representation Learning-based Multi-omics data Integrative Clustering algorithm (sLMIC) for the integration of single-cell epigenomic profiles (DNA methylation or scATAC-seq) and transcriptomic (scRNA-seq), which the consistent and specific features of cells are explicitly extracted facilitating the cell clustering. Specifically, sLMIC constructs a graph for each type of single-cell data, thereby transforming omics data into multi-layer networks, which effectively removes heterogeneity of omic data. Then, sLMIC employs the low-rank and exclusivity constraints to separate the self-representation of cells into two parts, i.e., the shared and specific features, which explicitly characterize the consistency and diversity of omic data, providing an effective strategy to model the structure of cell types. Feature extraction and cell clustering are jointly formulated as an overall objective function, where latent features of data are obtained under the guidance of cell clustering. The extensive experimental results on 13 multi-omics datasets of single-cell from diverse organisms and tissues indicate that sLMIC observably exceeds the advanced algorithms regarding various measurements.

CMR 3-97 - Simultaneous Multislice Cardiac Multimapping Based on Locally Low-rank and Sparsity Constraints

CMR 3-97 - Simultaneous Multislice Cardiac Multimapping Based on Locally Low-rank and Sparsity Constraints

Smooth Tensor Qatar Riyal Decomposition for Dynamic MRI Reconstruction.

Dynamic magnetic resonance imaging (dMRI) speed and imaging quality have always been a crucial issue in medical imaging research. Most existing methods characterize the tensor rank-based minimization to reconstruct dMRI from sampling k- t space data. However, (1) these approaches that unfold the tensor along each dimension destroy the inherent structure of dMR images. (2) they focus on preserving global information only, while ignoring the local details reconstruction such as the spatial piece-wise smoothness and sharp boundaries. To overcome these obstacles, we suggest a novel low-rank tensor decomposition approach by integrating tensor Qatar Riyal (QR) decomposition, low-rank tensor nuclear norm, and asymmetric total variation to reconstruct dMRI, named TQRTV. Specifically, while preserving the tensor inherent structure by utilizing tensor nuclear norm minimization to approximate tensor rank, QR decomposition reduces the dimensions in the low-rank constraint term, thereby improving the reconstruction performance. TQRTV further exploits the asymmetric total variation regularizer to capture local details. Numerical experiments demonstrate that the proposed reconstruction approach is superior to the existing ones.

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.

Multi-Dimensional Low-Rank with Weighted Schatten p-Norm Minimization for Hyperspectral Anomaly Detection

Hyperspectral anomaly detection is an important unsupervised binary classification problem that aims to effectively distinguish between background and anomalies in hyperspectral images (HSIs). In recent years, methods based on low-rank tensor representations have been proposed to decompose HSIs into low-rank background and sparse anomaly tensors. However, current methods neglect the low-rank information in the spatial dimension and rely heavily on the background information contained in the dictionary. Furthermore, these algorithms show limited robustness when the dictionary information is missing or corrupted by high level noise. To address these problems, we propose a novel method called multi-dimensional low-rank (MDLR) for HSI anomaly detection. It first reconstructs three background tensors separately from three directional slices of the background tensor. Then, weighted schatten p-norm minimization is employed to enforce the low-rank constraint on the background tensor, and LF,1-norm regularization is used to describe the sparsity in the anomaly tensor. Finally, a well-designed alternating direction method of multipliers (ADMM) is employed to effectively solve the optimization problem. Extensive experiments on four real-world datasets show that our approach outperforms existing anomaly detection methods in terms of accuracy.