Low-rank Constraint Research Articles

Unsupervised dimensionality reduction of medical hyperspectral imagery in tensor space

Background and objectivesCompared with traditional RGB images, medical hyperspectral imagery (HSI) has numerous continuous narrow spectral bands, which can provide rich information for cancer diagnosis. However, the abundant spectral bands also contain a large amount of redundancy information and increase computational complexity. Thus, dimensionality reduction (DR) is essential in HSI analysis. All vector-based DR methods ignore the cubic nature of HSI resulting from vectorization. To overcome the disadvantage of vector-based DR methods, tensor-based techniques have been developed by employing multi-linear algebra. MethodsTo fully exploit the structure features of medical HSI and enhance computational efficiency, a novel method called unsupervised dimensionality reduction via tensor-based low-rank collaborative graph embedding (TLCGE) is proposed. TLCGE introduces entropy rate superpixel (ERS) segmentation algorithm to generate superpixels. Then, a low-rank collaborative graph weight matrix is constructed on each superpixel, greatly improving the efficiency and robustness of the proposed method. After that, TLCGE reduces dimensions in tensor space to well preserve intrinsic structure of HSI. ResultsThe proposed TLCGE is tested on cholangiocarcinoma microscopic hyperspectral data sets. To further demonstrate the effectiveness of the proposed algorithm, other machine learning DR methods are used for comparison. Experimental results on cholangiocarcinoma microscopic hyperspectral data sets validate the effectiveness of the proposed TLCGE. ConclusionsThe proposed TLCGE is a tensor-based DR method, which can maintain the intrinsic 3-D data structure of medical HSI. By imposing the low-rank and sparse constraints on the objective function, the proposed TLCGE can fully explore the local and global structures within each superpixel. The computational efficiency of the proposed TLCGE is better than other tensor-based DR methods, which can be used as a preprocessing step in real medical HSI classification or segmentation.

Dynamic cell tracking using time-lapse MRI with variable temporal resolution Cartesian sampling.

Temporal resolution of time-lapse MRI to track individual iron-labeled cells is limited by the required data-acquisition time to fill k-space and to reach sufficient SNR. Although motion of slowly patrolling monocytes can be resolved, detection of fast-moving immune cells requires improved acquisition and reconstruction strategies. For accelerated MRI cell tracking, a Cartesian sampling scheme was designed, in which the fully sampled and undersampled k-space data for different acceleration factors were acquired simultaneously, and multiple undersampling ratios could be chosen retrospectively. Compressed-sensing reconstruction was applied using dictionary learning and low-rank constraints. Detection of iron-labeled monocytes was evaluated with simulations, rotating phantom experiments and in vivo mouse brain measurements at 9.4 T. Fully sampled and 2.4-times and 4.8-times accelerated images were reconstructed and had sufficient contrast-to-noise ratio (CNR) for single cells to be resolved and followed dynamically. The phantom experiments showed an improvement in CNR of 6.1% per μm/s in the 4.8-times undersampled images. Geometric distortion of cells caused by motion was visibly reduced in the accelerated images, which enabled detection of moving cells with velocities of up to 7.0 μm/s. In vivo, additional cells were resolved in the accelerated images due to the improved temporal resolution. The easy-to-implement flexible Cartesian sampling scheme with compressed-sensing reconstruction permits simultaneous acquisition of both fully sampled and high temporal resolution images. The CNR of moving cells is effectively improved, enabling the recovery of high velocity cells with sufficient contrast at virtually no cost.

Deep and Low-Rank Quaternion Priors for Color Image Processing

Due to the physical nature of color images, color image processing such as denoising and inpainting has shown extensive and versatile possibilities over grayscale image processing. The monochromatic and the concatenation model have been widely used to process color images by processing each color channel independently or concatenating three color channels as one unified one and then used existing grayscale image processing methods directly without specific operations. These above schemes, however, have some limitations: (1) they would destroy the inherent correlation among three color channels since they cannot represent color images holistically; (2) they usually focus on one specific handcrafted prior such as smoothness, low-rankness, or even deep prior and thus failing to fuse deep and handcrafted priors of color images flexibly. To conquer these limitations, we propose one unified model to integrate deep prior and low-rank quaternion prior (DLRQP) for color image processing under the plug-and-play (PnP) framework. Specifically, the quaternion representation with low-rank constraint is introduced to denote the color image in a holistic way and one advanced denoiser is adopted to explore the deep prior in an iterative process. To tightly approximate the quaternion rank, one nonconvex penalty function is further utilized. We derive an alternate iterative approach to tackle the proposed model. We empirically demonstrate that our model can achieve superior performance over existing methods on both color image denoising and inpainting tasks.

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.

Semi-Supervised Subspace Clustering via Tensor Low-Rank Representation

In this letter, we propose a novel semi-supervised subspace clustering method, which is able to simultaneously augment the initial supervisory information and construct a discriminative affinity matrix. By representing the limited amount of supervisory information as a pairwise constraint matrix, we observe that the ideal affinity matrix for clustering shares the same low-rank structure as the ideal pairwise constraint matrix. Thus, we stack the two matrices into a 3-D tensor, where a global low-rank constraint is imposed to promote the affinity matrix construction and augment the initial pairwise constraints synchronously. Besides, we use the local geometry structure of input samples to complement the global low-rank prior to achieve better affinity matrix learning. The proposed model is formulated as a Laplacian graph regularized convex low-rank tensor representation problem, which is further solved with an alternative iterative algorithm. In addition, we propose to refine the affinity matrix with the augmented pairwise constraints. Comprehensive experimental results on eight commonly-used benchmark datasets demonstrate the superiority of our method over state-of-the-art methods. The code is publicly available at https://github.com/GuanxingLu/Subspace-Clustering.

Tensorized Incomplete Multi-View Clustering with Intrinsic Graph Completion

Most of the existing incomplete multi-view clustering (IMVC) methods focus on attaining a consensus representation from different views but ignore the important information hidden in the missing views and the latent intrinsic structures in each view. To tackle these issues, in this paper, a unified and novel framework, named tensorized incomplete multi-view clustering with intrinsic graph completion (TIMVC_IGC) is proposed. Firstly, owing to the effectiveness of the low-rank representation in revealing the inherent structure of the data, we exploit it to infer the missing instances and construct the complete graph for each view. Afterwards, inspired by the structural consistency, a between-view consistency constraint is imposed to guarantee the similarity of the graphs from different views. More importantly, the TIMVC_IGC simultaneously learns the low-rank structures of the different views and explores the correlations of the different graphs in a latent manifold sub-space using a low-rank tensor constraint, such that the intrinsic graphs of the different views can be obtained. Finally, a consensus representation for each sample is gained with a co-regularization term for final clustering. Experimental results on several real-world databases illustrates that the proposed method can outperform the other state-of-the-art related methods for incomplete multi-view clustering.

Low-rank constraint-based multiple projections learning for cross-domain classification

Transfer learning aims to apply previously learned knowledge to new unknown domains by mining the potential relationships between data from different domains. Because of its ability to process data from different domains, the projection transfer learning methods have attracted much attention. However, most of the methods only focus on the reconstruction between different domains and do not fully use the data. Here, we put forward a novel transfer learning method called low-rank constraint-based multiple projections learning (LRMPL) for cross-domain classification. LRMPL works on both the overall reconstruction of two domains and aligns the data sharing the same label but from different domains by imposing low-rank constraints on the reconstruction coefficient matrix. In this way, the obtained feature representation is transferrable and discriminative. Moreover, LRMPL considers the information preserving during the feature representation learning by integrating a modified PCA-like item into the objective function. To learn a suitable classifier parameter and feature representation, LRMPL also unifies the classifier and feature learning into a single optimization objective. Extensive experiments on several benchmark datasets show LRMPL outperforms the existing traditional transfer learning methods in cross-domain classification. The demo code is available in https://github.com/892384750/LRMPL.

Semi-Supervised Multi-View Fusion for Identifying CAP and COVID-19 With Unlabeled CT Images

Recently, under the condition of reducing nucleic acid testing for COVID-19 in large population, the computer-aided diagnosis with the chest computed tomography (CT) image has become increasingly important in differential diagnosis of community-acquired pneumonia (CAP) and COVID-19. In practice, there usually exist a mass of unlabeled CT images, especially in regions without adequate medical resources, and the existing diagnosis methods cannot take advantage of the useful information among them. Therefore, it is practical and urgent need to develop a computer-aided diagnosis model that can effectively exploit both labeled and unlabeled samples. To this end, in this paper, we propose a semi-supervised multi-view fusion method for the diagnosis of COVID-19. It explores both the discriminative features from labeled samples and the structure information from unlabeled samples and fuses multi-view features extracted from CT images, including image feature, statistical feature, and lesions specific feature, for improving the diagnostic performance. Specifically, in the proposed model, we utilize semi-supervised learning technique with pairwise constraint regularization to learn the model with both labeled samples and unlabeled samples. Simultaneously, we employ low-rank multi-view constraint to capture latent complementary information among different features from CT images. Experimental results show that the proposed method outperforms the state-of-the-art methods in differential diagnosis of CAP vs. COVID-19.

Consensus latent incomplete multi-view clustering with low-rank tensor constraint

Consensus latent incomplete multi-view clustering with low-rank tensor constraint

High-fidelity mesoscale in-vivo diffusion MRI through gSlider-BUDA and circular EPI with S-LORAKS reconstruction

PurposeTo develop a high-fidelity diffusion MRI acquisition and reconstruction framework with reduced echo-train-length for less T2* image blurring compared to typical highly accelerated echo-planar imaging (EPI) acquisitions at sub-millimeter isotropic resolution. MethodsWe first proposed a circular-EPI trajectory with partial Fourier sampling on both the readout and phase-encoding directions to minimize the echo-train-length and echo time. We then utilized this trajectory in an interleaved two-shot EPI acquisition with reversed phase-encoding polarity, to aid in the correction of off-resonance-induced image distortions and provide complementary k-space coverage in the missing partial Fourier regions. Using model-based reconstruction with structured low-rank constraint and smooth phase prior, we corrected the shot-to-shot phase variations across the two shots and recover the missing k-space data. Finally, we combined the proposed acquisition/reconstruction framework with an SNR-efficient RF-encoded simultaneous multi-slab technique, termed gSlider, to achieve high-fidelity 720 µm and 500 µm isotropic resolution in-vivo diffusion MRI. ResultsBoth simulation and in-vivo results demonstrate the effectiveness of the proposed acquisition and reconstruction framework to provide distortion-corrected diffusion imaging at the mesoscale with markedly reduced T2*-blurring. The in-vivo results of 720 µm and 500 µm datasets show high-fidelity diffusion images with reduced image blurring and echo time using the proposed approaches. ConclusionsThe proposed method provides high-quality distortion-corrected diffusion-weighted images with ∼40% reduction in the echo-train-length and T2* blurring at 500µm-isotropic-resolution compared to standard multi-shot EPI.

Non-uniformly sampled 2D NMR Spectroscopy reconstruction based on Low Rank Hankel Matrix Fast Tri-Factorization and Non-convex Factorization

Nuclear magnetic resonance (NMR) spectroscopy is widely used in chemistry and medicine to research the composition of matter and the spatial structure of proteins. However, NMR signals with larger sizes and higher dimensions are slower to acquire. Therefore, Non-Uniform Sampling (NUS) methods are used to speed up the acquisition of NMR signals, and some mathematical algorithms are used to recover the original NMR signals from the NUS data. In recent years, low-rank Hankel matrix completion is proved to recover NMR data with less error. However, it requires singular value decomposition (SVD) with high computational complexity in each iteration, which is not suitable for reconstructing signals with large sizes. In this paper, we propose a Fast Tri-Factorization (FTF) method to decompose the low-rank Hankel matrix into three small-scale matrices, and it convert the original problem into a matrix nuclear norm minimization problem on the small-scale matrix to mitigate high computation cost of multiple SVDs. Furthermore, the factor matrix size remains constant for different size of the Hankel matrices. We further replace the low-rank constraint with Non-convex Factorization (NF) to avoid the time-consuming SVD in each iteration. Numerical experiments show that the proposed method can significantly speed up the NMR reconstruction compared with several existing algorithms while ensuring the reconstruction accuracy.

Scalable incomplete multi-view clustering via tensor Schatten p-norm and tensorized bipartite graph

Graph-based incomplete multi-view clustering (IMVC) methods have drawn considerable attention due to their good performance in exploring the nonlinear structure of data. However, they still have the following shortcomings. First, graph construction and eigen decomposition of the Laplacian matrix included in the IMVC methods generally have high computational complexity. Second, most methods do not consider the impact of missing views and neglect the potential relationships between different views. Third, few algorithms consider both intra-view and inter-view information for clustering. Therefore, we innovatively propose a scalable incomplete multi-view clustering via the tensor Schatten p-norm and tensorized bipartite graph (SIMVC/TSTBG) method, which combines tensorized bipartite graph, graph completion, and tensor low-rank constraint into a joint framework. Concretely, we first construct bipartite graphs based on the selected m anchor points and the n data points, reducing the size of the graph from n×n to n×m(m<<n), which considerably reduces the computational complexity. Second, we adaptively complete the missing bipartite graph, which reduces the effect of missing view information on the clustering results. Third, to explore connections between missing views and mine high-order information between views, we splice the bipartite graphs into a tensor and impose a tensor low-rank constraint, i.e., the tensor Schatten p-norm, on it. At the same time, we also design an efficient algorithm to solve SIMVC/TSTBG. To our knowledge, we are the first successful practice to integrate the tensor technique with the scalable IMVC method. Compared with other IMVC methods, the results on seven datasets fully show the high efficiency and effectiveness of SIMVC/TSTBG.

Motion-compensated low-rank reconstruction for simultaneous structural and functional UTE lung MRI.

Three-dimensional UTE MRI has shown the ability to provide simultaneous structural and functional lung imaging, but it is limited by respiratory motion and relatively low lung parenchyma SNR. The purpose of this paper is to improve this imaging by using a respiratory phase-resolved reconstruction approach, named motion-compensated low-rank reconstruction (MoCoLoR), which directly incorporates motion compensation into a low-rank constrained reconstruction model for highly efficient use of the acquired data. The MoCoLoR reconstruction is formulated as an optimization problem that includes a low-rank constraint using estimated motion fields to reduce the rank, optimizing over both the motion fields and reconstructed images. The proposed reconstruction along with XD and motion state-weighted motion-compensation (MostMoCo) methods were applied to 18 lung MRI scans of pediatric and young adult patients. The data sets were acquired under free-breathing and without sedation with 3D radial UTE sequences in approximately 5 min. After reconstruction, they went through ventilation analyses. Performance across reconstruction regularization and motion-state parameters were also investigated. The in vivo experiments results showed that MoCoLoR made efficient use of the data, provided higher apparent SNR compared with state-of-the-art XD reconstruction and MostMoCo reconstructions, and yielded high-quality respiratory phase-resolved images for ventilation mapping. The method was effective across the range of patients scanned. The motion-compensated low-rank regularized reconstruction approach makes efficient use of acquired data and can improve simultaneous structural and functional lung imaging with 3D-UTE MRI. It enables the scanning of pediatric patients under free-breathing and without sedation.

Multi-View Clustering for Integration of Gene Expression and Methylation Data With Tensor Decomposition and Self-Representation Learning.

The accumulated DNA methylation and gene expression provide a great opportunity to exploit the epigenetic patterns of genes, which is the foundation for revealing the underlying mechanisms of biological systems. Current integrative algorithms are criticized for undesirable performance because they fail to address the heterogeneity of expression and methylation data, and the intrinsic relations among them. To solve this issue, a novel multi-view clustering with self-representation learning and low-rank tensor constraint (MCSL-LTC) is proposed for the integration of gene expression and DNA methylation data, which are treated as complementary views. Specifically, MCSL-LTC first learns the low-dimensional features for each view with the linear projection, and then these features are fused in a unified tensor space with low-rank constraints. In this case, the complementary information of various views is precisely captured, where the heterogeneity of omic data is avoided, thereby enhancing the consistency of different views. Finally, MCSL-LTC obtains a consensus cluster of genes reflecting the structure and features of various views. Experimental results demonstrate that the proposed approach outperforms state-of-the-art baselines in terms of accuracy on both the social and cancer data, which provides an effective and efficient method for the integration of heterogeneous genomic data.

Multi-View Kernel Learning for Identification of Disease Genes.

Gene expression data sets and protein-protein interaction (PPI) networks are two heterogeneous data sources that have been extensively studied, due to their ability to capture the co-expression patterns among genes and their topological connections. Although they depict different traits of the data, both of them tend to group co-functional genes together. This phenomenon agrees with the basic assumption of multi-view kernel learning, according to which different views of the data contain a similar inherent cluster structure. Based on this inference, a new multi-view kernel learning based disease gene identification algorithm, termed as DiGId, is put forward. A novel multi-view kernel learning approach is proposed that aims to learn a consensus kernel, which efficiently captures the heterogeneous information of individual views as well as depicts the underlying inherent cluster structure. Some low-rank constraints are imposed on the learned multi-view kernel, so that it can effectively be partitioned into k or fewer clusters. The learned joint cluster structure is used to curate a set of potential disease genes. Moreover, a novel approach is put forward to quantify the importance of each view. In order to demonstrate the effectiveness of the proposed approach in capturing the relevant information depicted by individual views, an extensive analysis is performed on four different cancer-related gene expression data sets and PPI network, considering different similarity measures.

Spatial temporal Fourier single-pixel imaging.

Generally, the imaging quality of Fourier single-pixel imaging (FSI) will severely degrade while achieving high-speed imaging at a low sampling rate (SR). To tackle this problem, a new, to the best of our knowledge, imaging technique is proposed: firstly, the Hessian-based norm constraint is introduced to deal with the staircase effect caused by the low SR and total variation regularization; secondly, based on the local similarity prior of consecutive frames in the time dimension, we designed the temporal local image low-rank constraint for the FSI, and combined the spatiotemporal random sampling method, the redundancy image information of consecutive frames can be utilized sufficiently; finally, by introducing additional variables to decompose the optimization problem into multiple sub-problems and analytically solving each one, a closed-form algorithm is derived for efficient image reconstruction. Experimental results show that the proposed method improves imaging quality significantly compared with state-of-the-art methods.

DRRNets: Dynamic Recurrent Routing via Low-Rank Regularization in Recurrent Neural Networks.

Recurrent neural networks (RNNs) continue to show outstanding performance in sequence learning tasks such as language modeling, but it remains difficult to train RNNs for long sequences. The main challenges lie in the complex dependencies, gradient vanishing or exploding, and low resource requirement in model deployment. In order to address these challenges, we propose dynamic recurrent routing neural networks (DRRNets), which can: 1) shorten the recurrent lengths by allocating recurrent routes dynamically for different dependencies and 2) reduce the number of parameters significantly by imposing low-rank constraints on the fully connected layers. A novel optimization algorithm via low-rank constraint and sparsity projection is developed to train the network. We verify the effectiveness of the proposed method by comparing it with multiple competitive approaches in several popular sequential learning tasks, such as language modeling and speaker recognition. The results in terms of different criteria demonstrate the superiority of our proposed method.

Self-Attention Graph Convolution Residual Network for Traffic Data Completion

Complete and accurate traffic data is critical in urban traffic management, planning and operation. In fact, real-world traffic data contains missing values due to multiple factors, such as device outages and communication errors. For traffic data completion task, most of the existing methods are matrix/tensor completion methods, which usually enforce low rank constraint on traffic data matrix/tensor. But they neglect the graph structure of traffic data, resulting in low completion performance. Recently, graph convolutional networks have achieved remarkable results in traffic data forecasting due to their abilities of feature extraction and nonlinear fitting on arbitrarily graph-structured data. However, there are few studies based on graph neural networks for traffic data completion task. In this paper, we propose a traffic data completion model based on graph convolutional network model to impute missing values from the perspective of deep learning. This model utilizes graph convolution to model the local spatial dependency. As for global spatial dependency and temporal dependency, this model incorporates self-attention mechanism, which is applied in the spatial and temporal dimensions respectively. The experimental results on the two real-time datasets demonstrate that the proposed model outperforms the baseline methods significantly under arbitrarily missing scenarios.

Incomplete multi-view clustering based on low-rank representation with adaptive graph regularization

Incomplete multi-view clustering has attracted attention due to its ability to deal with clustering problems with incomplete information. However, most existing methods either ignore the local structure of the data or fail to consider the importance of different views. In addition, some methods based on mean filling may easily introduce useless information when the data has a large missing rate. To address these issues, this paper proposes an incomplete multi-view clustering algorithm based on graph regularized low-rank representations without using filling method. Specifically, we combine a distance regularization term and low-rank representation-based non-negativity constraints to directly learn graphs with global and local data structures from raw data. Furthermore, we introduce a novel weighted fusion mechanism in the model to learn a consistent representation of all views, which effectively avoids bad views from affecting the quality of the final fused consensus graph. Experimental results on six incomplete multi-view datasets demonstrate that our proposed method achieves the best performance compared with the existing state-of-the-art methods.

Elaborate multi-task subspace learning with discrete group constraint

In multi-task learning (MTL), multiple related tasks can be learned simultaneously under the shared information to improve the generalization performance. However, most of MTL methods assume that all the learning tasks are related indeed and appropriate for joint learning. In some real situations, this assumption may not hold and further lead to the problem of negative transfer. Therefore, in this paper, we not only focus on researching the problem of robustly learning the common feature structure shared by tasks, but also discriminate with which tasks one task should share. By combining with the idea of subspace learning, we propose an elaborate multi-task subspace learning model (EMTSL) with discrete group structure constraint, which can cluster the learned tasks into a set of groups. By introducing the Schatten p-norm instead of trace norm, our model EMTSL can better approximate the low-rank constraint and also avoid the trivial solution. Furthermore, we design an efficient algorithm based on the re-weighted method to solve the proposed model. In addition, the convergence analysis of our algorithm is given in this paper. Experimental results on both synthetic and real-world datasets demonstrate the superiority of our method.