Low-rank Representation Method Research Articles

High-Order Laplacian Regularized Low-Rank Representation for Multimodal Dementia Diagnosis.

Multimodal heterogeneous data, such as structural magnetic resonance imaging (MRI), positron emission tomography (PET), and cerebrospinal fluid (CSF), are effective in improving the performance of automated dementia diagnosis by providing complementary information on degenerated brain disorders, such as Alzheimer's prodromal stage, i.e., mild cognitive impairment. Effectively integrating multimodal data has remained a challenging problem, especially when these heterogeneous data are incomplete due to poor data quality and patient dropout. Besides, multimodal data usually contain noise information caused by different scanners or imaging protocols. The existing methods usually fail to well handle these heterogeneous and noisy multimodal data for automated brain dementia diagnosis. To this end, we propose a high-order Laplacian regularized low-rank representation method for dementia diagnosis using block-wise missing multimodal data. The proposed method was evaluated on 805 subjects (with incomplete MRI, PET, and CSF data) from the real Alzheimer's Disease Neuroimaging Initiative (ADNI) cohort. Experimental results suggest the effectiveness of our method in three tasks of brain disease classification, compared with the state-of-the-art methods.

Tripartite Graph Regularized Latent Low-Rank Representation for Fashion Compatibility Prediction

In recent years, an increasing online shopping demand has greatly promoted the innovation and development of the fashion industry. Visual fashion analysis has become a prospective research topic in computer vision and multimedia fields. Among these studies, fashion compatibility analysis is required in many real applications, such as fashion recommendation, matching, and retrieval. However, learning fashion compatibility is nontrivial, not only due to the uncertain and sparse dependencies among fashion items but also the latent and mutual associations among multiple factors such as color, texture, style, and functionality. To better predict fashion compatibility, in this paper, we proposed a tripartite graph regularized latent low-rank representation method, named TGRLLR, for fashion compatibility prediction. In TGRLLR, to learn more low-dimensional and effective representations, we considered the latent low-rank representation by decomposing the original feature matrix in both the column and row directions to tackle the problem of insufficient observations. On this basis, we simultaneously exploited different regularization strategies to encode the structured correlations among features, the high-order relationships among items, and the geometrical structures of outfits for more informative representations. Extensive experiments conducted on a real-world dataset demonstrate the effectiveness of our proposed method compared with state-of-the-art methods.

Tensor low-rank sparse representation for tensor subspace learning

Many subspace learning methods are implemented on a matrix of sample data. For multi-dimensional data, these methods have to convert data samples into vectors in advance, which often destroys the inherent spatial structure of the sample data. In this paper, we propose a robust tensor low-rank sparse representation (TLRSR) method that can directly perform subspace learning on three-dimensional tensors. Firstly, the dual constraints of low-rankness and sparseness make the representation tensor effectively capture the global structure and local structure of sample data, respectively. Secondly, in order to deal with outliers and noise, we adopt the tensor ℓ2,1-norm to characterize the noise of tensor composed of multiple samples. Thirdly, the denoised tensor instead of the original tensor is used as the dictionary to find the low-rank sparse representation tensor. Finally, an iterative update algorithm is proposed for the optimization of TLRSR, compared with the state-of-the-art methods, clustering on face images and denoising on real images verify the good performance of our proposed TLRSR in tensor subspace learning.

An infrared and visible image fusion method based on multi-scale transformation and norm optimization

In this paper, we propose a new infrared and visible image fusion method based on multi-scale transformation and norm optimization. In this method, a new loss function is designed with contrast fidelity (L2 norm) and sparse constraint (L1 norm), and the split Bregman method is used to optimize the loss function to obtain pre-fusion images. The final fused base layer is obtained by using a multi-level decomposition latent low-rank representation (MDLatLRR) method to decompose the pre-fusion images. Then, using the pre-fusion image as the reference, image structure similarity (SSIM) is introduced to evaluate the validity of detail information from the visible image, and the SSIM is then transformed into a weight map which is applied to the optimization method based on L2 norm to generate the final detail fusion layer. Our proposed method is evaluated and compared with 18 state-of-the-art image fusion methods, both qualitatively and quantitatively on four public datasets (i.e., CVC14 driving dataset, TNO dataset with natural scenarios, RoadScene dataset, and whole brain atlas dataset). The results show that our proposed method is generally better than the compared methods in terms of highlighting targets and retaining effective detail information.

Weighted Low-Rank Tensor Representation for Multi-View Subspace Clustering

Multi-view clustering has been deeply explored since the compatible and complementary information among views can be well captured. Recently, the low-rank tensor representation-based methods have effectively improved the clustering performance by exploring high-order correlations between multiple views. However, most of them often express the low-rank structure of the self-representative tensor by the sum of unfolded matrix nuclear norms, which may cause the loss of information in the tensor structure. In addition, the amount of effective information in all views is not consistent, and it is unreasonable to treat their contribution to clustering equally. To address the above issues, we propose a novel weighted low-rank tensor representation (WLRTR) method for multi-view subspace clustering, which encodes the low-rank structure of the representation tensor through Tucker decomposition and weights the core tensor to retain the main information of the views. Under the augmented Lagrangian method framework, an iterative algorithm is designed to solve the WLRTR method. Numerical studies on four real databases have proved that WLRTR is superior to eight state-of-the-art clustering methods.

Robust temporal low‐rank representation for traffic data recovery via fused lasso

Achieving complete and accurate traffic data as input is crucial for most intelligent transportation systems. However, due to hardware or software malfunction, traffic data is inevitably faced with missing and noise problems. Most of the existing representation-based traffic data recovery methods adopt sparse representation theory, which well models the local association properties of traffic data, but ignores their global correlation. To overcome this shortcoming, a robust low-rank representation method that incorporates temporal prior information to impute the missing traffic data is proposed. Specifically, the low-rank representation theory is first employed to model the global spatial correlation of traffic data, and then the fused lasso regularisation is utilized to fit the temporal correlation of traffic data. In addition, to make the proposed model more robust, F-norm regularisation is used to smooth the Gaussian noise of traffic data. Furthermore, an efficient optimisation algorithm based on ADMM is developed to solve the proposed model. Finally, the extensive experiments performed on real dataset validate the effectiveness of the proposed method.

Graph regularized low-rank representation for semi-supervised learning

Low-rank representation (LRR) has attracted wide attention of researchers in recent years due to its excellent performance in the exploration of high-dimensional subspace structures. However, in the existing semi-supervised learning problem based on the LRR method, graph construction and semi-supervised learning are two separate steps. Therefore, the existing label information in the data set is not well used to guide the construction of the affinity graph. Therefore, these methods do not guarantee that the final result is a global optimal solution. This paper proposes a graph regularized low-rank representation for semi-supervised learning, called GLR2S2. This method combines the construction of affinity graph with semi supervised learning and unifies them into an optimization framework. By solving the joint optimization problem, the global optimal solution can be obtained. Experimental results on several standard data sets show that the GLR2S2 method proposed in this paper is effective.

Fast and Latent Low-Rank Subspace Clustering for Hyperspectral Band Selection

This article presents a fast and latent low-rank subspace clustering (FLLRSC) method to select hyperspectral bands. The FLLRSC assumes that all the bands are sampled from a union of latent low-rank independent subspaces and formulates the self-representation property of all bands into a latent low-rank representation (LLRR) model. The assumption ensures sufficient sampling bands in representing low-rank subspaces of all bands and improves robustness to noise. The FLLRSC first implements the Hadamard random projections to reduce spatial dimensionality and lower the computational cost. It then adopts the inexact augmented Lagrange multiplier algorithm to optimize the LLRR program and estimates sparse coefficients of all the projected bands. After that, it employs a correntropy metric to measure the similarity between pairwise bands and constructs an affinity matrix based on sparse representation. The correntropy metric could better describe the nonlinear characteristics of hyperspectral bands and enhance the block-diagonal structure of the similarity matrix for correctly clustering all subspaces. The FLLRSC conducts spectral clustering on the connected graph denoted by the affinity matrix. The bands that are closest to their separate cluster centroids form the final band subset. Experimental results on three widely used hyperspectral data sets show that the FLLRSC performs better than the classical low-rank representation methods with higher classification accuracy at a low computational cost.

Robust High-Order Manifold Constrained Low Rank Representation for Subspace Clustering

Due to the effectiveness in learning the subspace structures, low-rank representation (LRR) and its variations have been widely applied in various fields, such as computer vision and pattern recognition. However, in real applications, it is a challenge to handle the complex noises. To address this problem, we propose a novel robust LRR method based on kernel risk-sensitive loss (KRSL) with high-order manifold constraint, called RHLRR, in which the KRSL is introduced to deal with the noises and the multiple hypergraph regularization term is used as a high order manifold constraint to effectively capture the locality, similarity and the intrinsic geometric information in data. Besides, an iterative algorithm based on the half-quadratic (HQ) and the accelerated block coordinate update (BCU) is developed. The experimental results demonstrate that the proposed method can outperform other state-of-the-art LRR variants.

Label Enhancement with Sample Correlations via Low-Rank Representation

Compared with single-label and multi-label annotations, label distribution describes the instance by multiple labels with different intensities and accommodates to more-general conditions. Nevertheless, label distribution learning is unavailable in many real-world applications because most existing datasets merely provide logical labels. To handle this problem, a novel label enhancement method, Label Enhancement with Sample Correlations via low-rank representation, is proposed in this paper. Unlike most existing methods, a low-rank representation method is employed so as to capture the global relationships of samples and predict implicit label correlation to achieve label enhancement. Extensive experiments on 14 datasets demonstrate that the algorithm accomplishes state-of-the-art results as compared to previous label enhancement baselines.

Research of Low-Rank Representation and Discriminant Correlation Analysis for Alzheimer's Disease Diagnosis.

As population aging is becoming more common worldwide, applying artificial intelligence into the diagnosis of Alzheimer's disease (AD) is critical to improve the diagnostic level in recent years. In early diagnosis of AD, the fusion of complementary information contained in multimodality data (e.g., magnetic resonance imaging (MRI), positron emission tomography (PET), and cerebrospinal fluid (CSF)) has obtained enormous achievement. Detecting Alzheimer's disease using multimodality data has two difficulties: (1) there exists noise information in multimodal data; (2) how to establish an effective mathematical model of the relationship between multimodal data? To this end, we proposed a method named LDF which is based on the combination of low-rank representation and discriminant correlation analysis (DCA) to fuse multimodal datasets. Specifically, the low-rank representation method is used to extract the latent features of the submodal data, so the noise information in the submodal data is removed. Then, discriminant correlation analysis is used to fuse the submodal data, so the complementary information can be fully utilized. The experimental results indicate the effectiveness of this method.

Block-Constraint Laplacian-Regularized Low-Rank Representation and Its Application for Cancer Sample Clustering Based on Integrated TCGA Data

Low-Rank Representation (LRR) is a powerful subspace clustering method because of its successful learning of low-dimensional subspace of data. With the breakthrough of “OMics” technology, many LRR-based methods have been proposed and used to cancer clustering based on gene expression data. Moreover, studies have shown that besides gene expression data, some other genomic data in TCGA also contain important information for cancer research. Therefore, these genomic data can be integrated as a comprehensive feature source for cancer clustering. How to establish an effective clustering model for comprehensive analysis of integrated TCGA data has become a key issue. In this paper, we develop the traditional LRR method and propose a novel method named Block-constraint Laplacian-Regularized Low-Rank Representation (BLLRR) to model multigenome data for cancer sample clustering. The proposed method is dedicated to extracting more abundant subspace structure information from multiple genomic data to improve the accuracy of cancer sample clustering. Considering the heterogeneity of different genome data, we introduce the block-constraint idea into our method. In BLLRR decomposition, we treat each genome data as a data block and impose different constraints on different data blocks. In addition, graph Laplacian is also introduced into our method to better learn the topological structure of data by preserving the local geometric information. The experiments demonstrate that the BLLRR method can effectively analyze integrated TCGA data and extract more subspace structure information from multigenome data. It is a reliable and efficient clustering algorithm for cancer sample clustering.

Discriminative dimensionality reduction for sensor drift compensation in electronic nose: A robust, low-rank, and sparse representation method

Sensor drift, which is a critical issue in the field of sensor measurements, has plagued the sensor community in the past several decades. How to tackle the sensor drift problem using expert and intelligent systems has gained increasing attention. Most sensor drift compensation methods ignore the sparse and low-rank characteristics of sensor signals. In this paper, we propose a discriminative dimensionality reduction method for sensor drift compensation in the electronic nose. The proposed method consists of four major components. (1) The distribution discrepancy between source data and target data is alleviated via projecting all the data into a common subspace. (2) A sparse and low-rank reconstruction coefficient matrix is employed to preserve the global and local structures of sensor signals. (3) An error matrix is introduced to deal with outliers. (4) The source data label information is taken into consideration to avoid overlapping of samples with different labels in the common subspace. The formulated minimization problem with constraints can be solved in an iterative manner. The effectiveness of the proposed method has been verified by conducting experiments on two sensor drift datasets. The proposed method may provide new insights into the gas sensor drift compensation systems or other expert and intelligent systems.

Hyperspectral Anomaly Detection via Tensor- Based Endmember Extraction and Low-Rank Decomposition

Due to the limited resolution of hyperspectral sensors, anomalous targets expressed with subpixels are often mixed with nonhomogeneous backgrounds. This fact makes anomalies difficult to distinguish from the surrounding background. From this perspective, a novel hyperspectral anomaly detection (AD) algorithm based on endmember extraction and low-rank representation (LRR) is proposed. For the characteristics of pixels in hyperspectral images (HSIs), the proposed algorithm employs an endmember extraction technology to yield an abundance matrix for AD, thereby gathering more feature information compared with the direct use of a raw image. In addition, a dictionary construction strategy based on Tucker decomposition, and the ${k}$ -means++ clustering method is proposed to make the dictionary more stable and discriminative. An LRR method based on the dictionary is applied to obtain a sparse residual matrix. Finally, anomalies can be determined by the response of the residual matrix. Experiments on three hyperspectral data sets validate the performance of the proposed algorithm.

Multi-cancer samples clustering via graph regularized low-rank representation method under sparse and symmetric constraints

BackgroundIdentifying different types of cancer based on gene expression data has become hotspot in bioinformatics research. Clustering cancer gene expression data from multiple cancers to their own class is a significance solution. However, the characteristics of high-dimensional and small samples of gene expression data and the noise of the data make data mining and research difficult. Although there are many effective and feasible methods to deal with this problem, the possibility remains that these methods are flawed.ResultsIn this paper, we propose the graph regularized low-rank representation under symmetric and sparse constraints (sgLRR) method in which we introduce graph regularization based on manifold learning and symmetric sparse constraints into the traditional low-rank representation (LRR). For the sgLRR method, by means of symmetric constraint and sparse constraint, the effect of raw data noise on low-rank representation is alleviated. Further, sgLRR method preserves the important intrinsic local geometrical structures of the raw data by introducing graph regularization. We apply this method to cluster multi-cancer samples based on gene expression data, which improves the clustering quality. First, the gene expression data are decomposed by sgLRR method. And, a lowest rank representation matrix is obtained, which is symmetric and sparse. Then, an affinity matrix is constructed to perform the multi-cancer sample clustering by using a spectral clustering algorithm, i.e., normalized cuts (Ncuts). Finally, the multi-cancer samples clustering is completed.ConclusionsA series of comparative experiments demonstrate that the sgLRR method based on low rank representation has a great advantage and remarkable performance in the clustering of multi-cancer samples.

Tensor Low-Rank Representation for Data Recovery and Clustering.

Multi-way or tensor data analysis has attracted increasing attention recently, with many important applications in practice. This article develops a tensor low-rank representation (TLRR) method, which is the first approach that can exactly recover the clean data of intrinsic low-rank structure and accurately cluster them as well, with provable performance guarantees. In particular, for tensor data with arbitrary sparse corruptions, TLRR can exactly recover the clean data under mild conditions; meanwhile TLRR can exactly verify their true origin tensor subspaces and hence cluster them accurately. TLRR objective function can be optimized via efficient convex programing with convergence guarantees. Besides, we provide two simple yet effective dictionary construction methods, the simple TLRR (S-TLRR) and robust TLRR (R-TLRR), to handle slightly and severely corrupted data respectively. Experimental results on two computer vision data analysis tasks, image/video recovery and face clustering, clearly demonstrate the superior performance, efficiency and robustness of our developed method over state-of-the-arts including the popular LRR and SSC methods.

Rapidly and exactly determining postharvest dry soybean seed quality based on machine vision technology

The development of machine vision-based technologies to replace human labor for rapid and exact detection of agricultural product quality has received extensive attention. In this study, we describe a low-rank representation of jointly multi-modal bag-of-feature (JMBoF) classification framework for inspecting the appearance quality of postharvest dry soybean seeds. Two categories of speeded-up robust features and spatial layout of L*a*b* color features are extracted to characterize the dry soybean seed kernel. The bag-of-feature model is used to generate a visual dictionary descriptor from the above two features, respectively. In order to exactly represent the image characteristics, we introduce the low-rank representation (LRR) method to eliminate the redundant information from the long joint two kinds of modal dictionary descriptors. The multiclass support vector machine algorithm is used to classify the encoding LRR of the jointly multi-modal bag of features. We validate our JMBoF classification algorithm on the soybean seed image dataset. The proposed method significantly outperforms the state-of-the-art single-modal bag of features methods in the literature, which could contribute in the future as a significant and valuable technology in postharvest dry soybean seed classification procedure.

Anomaly Detection in Hyperspectral Imagery Based on Low-Rank Representation Incorporating a Spatial Constraint

Hyperspectral imagery contains abundant spectral information. Each band contains some specific characteristics closely related to target objects. Therefore, using these characteristics, hyperspectral imagery can be used for anomaly detection. Recently, with the development of compressed sensing, low-rank-representation-based methods have been applied to hyperspectral anomaly detection. In this study, novel low-rank representation methods were developed for anomaly detection from hyperspectral images based on the assumption that hyperspectral pixels can be effectively decomposed into a low-rank component (for background) and a sparse component (for anomalies). In order to improve detection performance, we imposed a spatial constraint on the low-rank representation coefficients, and single or multiple local window strategies was applied to smooth the coefficients. Experiments on both simulated and real hyperspectral datasets demonstrated that the proposed approaches can effectively improve hyperspectral anomaly detection performance.

Dual Pursuit for Subspace Learning

In general, low-rank representation (LRR) aims to find the lowest rank representation with respect to a dictionary. In fact, the dictionary is a key aspect of low-rank representation. However, a lot of low-rank representation methods usually use the data itself as a dictionary (i.e., a fixed dictionary), which may degrade their performances due to the lack of clustering ability of a fixed dictionary. To this end, we propose learning a locality-preserving dictionary instead of the fixed dictionary for low-rank representation, where the locality-preserving dictionary is constructed by using a graph regularization technique to capture the intrinsic geometric structure of the dictionary and, hence, the locality-preserving dictionary has an underlying clustering ability. In this way, the obtained low-rank representation via the locality-preserving dictionary has a better grouping-effect representation. Inversely, a better grouping-effect representation can help to learn a good dictionary. The locality-preserving dictionary and the grouping-effect representation interact with each other, where dual pursuit is called. The proposed method, namely, Dual Pursuit for Subspace Learning, provides us with a robust method for clustering and classification simultaneously, and compares favorably with the other state-of-the-art methods.

A Low-Rank Representation Method Regularized by Dual-Hypergraph Laplacian for Selecting Differentially Expressed Genes

Differentially expressed genes selection becomes a hotspot and difficulty in recent molecular biology. Low-rank representation (LRR) uniting graph Laplacian regularization has gained good achievement in the above field. However, the co-expression information of data cannot be captured well by graph regularization. Therefore, a novel low-rank representation method regularized by dual-hypergraph Laplacian is proposed to reveal the intrinsic geometrical structures hidden in the samples and genes direction simultaneously, which is called dual-hypergraph Laplacian regularized LRR (DHLRR). Finally, a low-rank matrix and a sparse perturbation matrix can be recovered from genomic data by DHLRR. Based on the sparsity of differentially expressed genes, the sparse disturbance matrix can be applied to extracting differentially expressed genes. In our experiments, two gene analysis tools are used to discuss the experimental results. The results on two real genomic data and an integrated dataset prove that DHLRR is efficient and effective in finding differentially expressed genes.