Graph Laplacian Regularization Research Articles

Learning Transferable Sparse Representations for Cross-Corpus Facial Expression Recognition

An assumption widely used in traditional facial expression recognition algorithms is that the training and testing are conducted on the same dataset. However, this assumption does not hold in practice, in which the training data and testing data are often from different datasets. In this scenario, directly deploying these algorithms would lead to severe information loss and performance degradation due to the domain shift. To address this challenging problem, in this paper, we propose a novel transferable sparse subspace representation method (TSSR) for cross-corpus facial expression recognition. Specifically, in order to reduce the cross-corpus mismatch, inspired by sparse subspace clustering, we advocate reconstructing the source and target samples using the source data points based on L1-norm sparse representation. Each data point in source and target corpora can be ideally represented as a combination of a few other source points from its own subspace. Moreover, we take into account the local geometrical information within the cross-corpus data by adopting a graph Laplacian regularizer, which can efficiently preserve the local manifold structure and better transfer knowledge between two corpora. Finally, experimental results on several facial expression datasets demonstrate the superiority of the proposed method over some state-of-the-art methods.

Hessian-based semi-supervised feature selection using generalized uncorrelated constraint

Feature selection (FS) aims to eliminate redundant features and choose the informative ones. Since labeled data are not always easily available and abundant unlabeled data are often accessible, the importance of semi-supervised FS (SSFS), which selects the informative features utilizing the labeled and unlabeled data, becomes apparent. Semi-supervised sparse FS based on graph Laplacian (GL) regularization has become a popular technique. The GL regularization biases the solution towards a constant geodesic function, has a poor extrapolating ability, and cannot preserve well the topological structure of data. Traditional ridge regression is widely utilized by the GL-based semi-supervised sparse FS, but the results cannot gain the closed-form solution and carry out the manifold structure. To tackle these problems, we propose a Hessian-based SSFS framework using the generalized uncorrelated constraint (HSFSGU) and the mixed ℓ2,p-norm (0<p≤1) regularization. We also propose a Hessian–Laplacian-based SSFS framework using the generalized uncorrelated constraint (HLSFSGU) which utilizes the combination of GL and Hessian matrices. Our frameworks use the Hessian regularization for maintaining the topological structure of data well, the ℓ2,p-norm regularization for making the projection matrix appropriate for FS, and the generalized uncorrelated constraint for preventing exceeding row sparsity of the projection matrix and providing the elegant closed-form solution for our frameworks. We also present a unified algorithm to solve the frameworks for convex and non-convex cases, and prove its convergence. The results of the experiments depict the ability of the Hessian-based frameworks under generalized uncorrelated constraint in selecting the informative features.

Multi-view clustering via matrix factorization assisted k-means

Matrix factorization based multi-view clustering algorithms has attracted much attention in recent years due to the strong interpretability and efficient implementation. In general, these approaches firstly compute the coefficient matrices of each data views, and learn a consensus matrix simultaneously. By applying the classical clustering techniques, such as k-means, on the consensus matrix, the final partition can be easily obtained. However, most of previous models work in a “step-by-step” manner, which cannot perform multi-view matrix factorization and clustering label generation simultaneously, leading to degenerated performance. In this paper, we propose a novel “one-pass” method, which integrates matrix factorization and k-means into a unified framework, named multi-view clustering via matrix factorization assisted k-means (MFK). In MFK, the generation of cluster indicator matrix and coefficient matrix learning can boost each other, leading to final improved clustering performance. Furthermore, we adopt a graph Laplacian regularization on the indicator matrix in order to capture the intrinsic geometric structure of original data. An alternating optimization strategy is designed to solve the resultant optimization problem and extensive experiments on six publicly datasets are conducted to demonstrate the superiority and effectiveness of the proposed MFK model.

Combining non-negative matrix factorization with graph Laplacian regularization for predicting drug-miRNA associations based on multi-source information fusion.

Increasing evidences suggest that miRNAs play a key role in the occurrence and progression of many complex human diseases. Therefore, targeting dysregulated miRNAs with small molecule drugs in the clinical has become a new treatment. Nevertheless, it is high cost and time-consuming for identifying miRNAs-targeted with drugs by biological experiments. Thus, more reliable computational method for identification associations of drugs with miRNAs urgently need to be developed. In this study, we proposed an efficient method, called GNMFDMA, to predict potential associations of drug with miRNA by combining graph Laplacian regularization with non-negative matrix factorization. We first calculated the overall similarity matrices of drugs and miRNAs according to the collected different biological information. Subsequently, the new drug-miRNA association adjacency matrix was reformulated based on the nearest neighbor profiles so as to put right the false negative associations. Finally, graph Laplacian regularization collaborative non-negative matrix factorization was used to calculate the association scores of drugs with miRNAs. In the cross validation, GNMFDMA obtains AUC of 0.9193, which outperformed the existing methods. In addition, case studies on three common drugs (i.e., 5-Aza-CdR, 5-FU and Gemcitabine), 30, 31 and 34 of the top-50 associations inferred by GNMFDMA were verified. These results reveal that GNMFDMA is a reliable and efficient computational approach for identifying the potential drug-miRNA associations.

Fast Hyperspectral Image Denoising and Destriping Method Based on Graph Laplacian Regularization

Hyperspectral images (HSIs) contain rich spatial and spectral information about the earth, and are widely used in the remote sensing field. However, an HSI is frequently corrupted by various types of noise, such as Gaussian noise, sparse noise, stripe noise, and so on, which severely limits the subsequent application of the HSI. In this paper, we propose a graph Laplacian regularizer (GLR) to exploit the low-rank information across the bands of the HSI. Compared with the traditional low-rank regularization, our graph Laplacian regularization can achieve equivalent or better performance with less time consumption. Besides, a sparse constraint and a low-rank constraint are employed to remove the sparse and stripe noise. In addition, the augmented Lagrangian multiplier is used to solve each component to restore a clean image. Finally, we have carried out experiments on the simulated and real noisy HSI data. The results show the superiority of the proposed method over state-of-the-art methods, in terms of PSNR and SSIM, time cost and visual effect. The MATLAB code is available through: https://github.com/zzhang-99/FGLR.

Large-Scale Hyperspectral Image Restoration via a Superpixel Distributed Algorithm Based on Graph Signal Processing

Hyperspectral image (HSI) is often disturbed by various kinds of noise, which brings great challenges to subsequent applications. Many of the existing restoration algorithms do not scale well for HSI with large size. This paper proposes a novel mixed-noise removal method for HSI with large size, by leveraging the superpixel segmentation-based technology and distributed algorithm based on graph signal processing. First, the underlying structure of the HSI is modeled by a two-layer architecture graph. The upper layer, called skeleton graph, is a rough graph constructed by using the modified <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -nearest-neighborhood algorithm and its nodes correspond to a series of superpixels formed by HSI segmentation. The skeleton graph can efficiently characterize the inter-correlations between superpixels, while preserving the boundary information and reducing the computational complexity. The lower layer, called detailed graph consisting of a series of local graphs which are constructed to model the similarities between pixels. Second, based on the two-layer graph architecture, the HSI restoration problem is formulated as a series of optimization problems each of which resides on a subgraph. In each optimization problem, a graph Laplacian regularization is defined and incorporated into a low-rank-based model. Third, a novel distributed algorithm is tailored for the restoration problem, by using the information interaction between the nodes of skeleton graph and subgraphs. Numerical experiments conducted on both synthetic and real-world datasets demonstrate the effectiveness of the proposed restoration algorithm compared with existing methods.

Point Cloud Sampling via Graph Balancing and Gershgorin Disc Alignment.

Point cloud (PC)-a collection of discrete geometric samples of a 3D object's surface-is typically large, which entails expensive subsequent operations. Thus, PC sub-sampling is of practical importance. Previous model-based sub-sampling schemes are ad-hoc in design and do not preserve the overall shape sufficiently well, while previous data-driven schemes are trained for specific pre-determined input PC sizes and sub-sampling rates and thus do not generalize well. Leveraging advances in graph sampling, we propose a fast PC sub-sampling algorithm of linear time complexity that chooses a 3D point subset while minimizing a global reconstruction error. Specifically, to articulate a sampling objective, we first assume a super-resolution (SR) method based on feature graph Laplacian regularization (FGLR) that reconstructs the original high-res PC, given points chosen by a sampling matrix H. We prove that minimizing a worst-case SR reconstruction error is equivalent to maximizing the smallest eigenvalue λmin of matrix HT H+ μL, where L is a symmetric, positive semi-definite matrix derived from a neighborhood graph connecting the 3D points. To arrive at a fast algorithm, instead of maximizing λmin, we maximize a lower bound λ-min(HT H+ μL) via selection of H-this translates to a graph sampling problem for a signed graph G with self-loops specified by graph Laplacian L. We tackle this general graph sampling problem in three steps. First, we approximate G with a balanced graph GB specified by Laplacian LB. Second, leveraging a recent linear algebraic theorem called Gershgorin disc perfect alignment (GDPA), we perform a similarity transform Lp = SLB S-1, so that all Gershgorin disc left-ends of Lp are aligned exactly at λmin(LB). Finally, we choose samples on GB using a previous graph sampling algorithm to maximize λ-min(HT H+ μLp) in linear time. Experimental results show that 3D points chosen by our algorithm outperformed competing schemes both numerically and visually in reconstruction quality.

Hyperspectral image denoising and destriping based on sparse representation, graph Laplacian regularization and stripe low-rank property

During the acquisition of a hyperspectral image (HSI), it is easily corrupted by many kinds of noises, which limits the subsequent applications. For decades, numerous HSI denoising methods have been proposed. However, these methods rarely consider the stripe noise as an independent component, thus cannot effectively remove the stripe noise. In this paper, we propose a mixed noise removal algorithm to destripe an HSI by taking advantage of the low-rank property of stripe noise. In the meantime, sparse representation and graph Laplacian regularization are utilized to remove Gaussian and sparse noise. Roughly speaking, the sparse representation helps achieve the approximation of the original image. A graph Laplacian regularization term can ensure the non-local spatial similarity of an HSI. Separate constraints on the sparse coefficient matrix and stripe noise components can help remove different types of noises. Experimental results on both simulated and real data demonstrate the effectiveness of the proposed method for HSI restoration.

Statistical inference using GLEaM model with spatial heterogeneity and correlation between regions

A better understanding of various patterns in the coronavirus disease 2019 (COVID-19) spread in different parts of the world is crucial to its prevention and control. Motivated by the previously developed Global Epidemic and Mobility (GLEaM) model, this paper proposes a new stochastic dynamic model to depict the evolution of COVID-19. The model allows spatial and temporal heterogeneity of transmission parameters and involves transportation between regions. Based on the proposed model, this paper also designs a two-step procedure for parameter inference, which utilizes the correlation between regions through a prior distribution that imposes graph Laplacian regularization on transmission parameters. Experiments on simulated data and real-world data in China and Europe indicate that the proposed model achieves higher accuracy in predicting the newly confirmed cases than baseline models.

Robust unsupervised feature selection via sparse and minimum-redundant subspace learning with dual regularization

Unsupervised feature selection, one of the important dimensionality reduction methods for high-dimensional data, has been paid more and more attention by researchers due to its effectiveness of processing the data without labels. However, most unsupervised feature selection methods do not take into account the fact that real data tends to be mixed with noise or outliers, or only consider the sensitivity of the model to them. In addition, the local manifold structure of data is usually preserved by a simple graph based on fixed k nearest neighbors. On the one hand, the different sample distributions of different data are considered without distinction. On the other hand, simple graph can not well capture the inherent relations between samples when facing multi-modal data. In view of the above problems, a robust unsupervised feature selection algorithm, sparse and minimum-redundant subspace learning with dual regularization (SMRSDR), is proposed in this paper. Specifically, a self-paced learning regularization based on soft weight allocation is introduced into SMRSDR to strictly control the samples’ entry into model learning. Normal samples are allowed to enter model learning in order of their importance, while noise or outliers are strictly blocked out of model learning. Besides, considering the difference in sample distribution and the multimodal nature of data, the traditional simple graph Laplacian regularization is replaced by the hypergraph Laplacian regularization based on adaptive nearest neighbors selection. Furthermore, the sparsity and minimum-redundancy constraints are imposed on the subspace learning framework so that the most representative and minimum-redundant features can be selected. Finally, the objective function of SMRSDR is solved by an alternating iterative optimization algorithm. And a series of experiments are performed to comprehensively prove the effectiveness and superiority of SMRSDR.

Coupled Tensor Block Term Decomposition with Superpixel-Based Graph Laplacian Regularization for Hyperspectral Super-Resolution

Hyperspectral image (HSI) super-resolution aims at improving the spatial resolution of HSI by fusing a high spatial resolution multispectral image (MSI). To preserve local submanifold structures in HSI super-resolution, a novel superpixel graph-based super-resolution method is proposed. Firstly, the MSI is segmented into superpixel blocks to form two-directional feature tensors, then two graphs are created using spectral–spatial distance between the unfolded feature tensors. Secondly, two graph Laplacian terms involving underlying BTD factors of high-resolution HSI are developed, which ensures the inheritance of the spatial geometric structures. Finally, by incorporating graph Laplacian priors with the coupled BTD degradation model, a HSI super-resolution model is established. Experimental results demonstrate that the proposed method achieves better fused results compared with other advanced super-resolution methods, especially on the improvement of the spatial structure.

Predicting Multiple Types of Associations Between miRNAs and Diseases Based on Graph Regularized Weighted Tensor Decomposition.

Many studies have indicated miRNAs lead to the occurrence and development of diseases through a variety of underlying mechanisms. Meanwhile, computational models can save time, minimize cost, and discover potential associations on a large scale. However, most existing computational models based on a matrix or tensor decomposition cannot recover positive samples well. Moreover, the high noise of biological similarity networks and how to preserve these similarity relationships in low-dimensional space are also challenges. To this end, we propose a novel computational framework, called WeightTDAIGN, to identify potential multiple types of miRNA–disease associations. WeightTDAIGN can recover positive samples well and improve prediction performance by weighting positive samples. WeightTDAIGN integrates more auxiliary information related to miRNAs and diseases into the tensor decomposition framework, focuses on learning low-rank tensor space, and constrains projection matrices by using the L 2,1 norm to reduce the impact of redundant information on the model. In addition, WeightTDAIGN can preserve the local structure information in the biological similarity network by introducing graph Laplacian regularization. Our experimental results show that the sparser datasets, the more satisfactory performance of WeightTDAIGN can be obtained. Also, the results of case studies further illustrate that WeightTDAIGN can accurately predict the associations of miRNA–disease-type.

Depth Map Super-Resolution Based on Dual Normal-Depth Regularization and Graph Laplacian Prior

The edge information plays a key role in the restoration of a depth map. Most conventional methods assume that the color image and depth map are consistent in edge areas. However, complex texture regions in the color image do not match exactly with edges in the depth map. In this paper, firstly, we point out that in most cases the consistency between normal map and depth map is much higher than that between RGB-D pairs. Then we propose a dual normal-depth regularization term to guide the restoration of depth map, which constrains the edge consistency between normal map and depth map back and forth. Moreover, considering the bimodal characteristic of weight distribution that exists in depth discontinuous areas, a reweighted graph Laplacian regularizer is proposed to promote this bimodal characteristic. And this regularization is incorporated into a unified optimization framework to effectively protect the piece-wise smoothness(PWS) characteristics of depth map. By treating depth image as graph signal, the weight between two nodes is adapted according to its content. The proposed method is tested for both noise-free and noisy cases, and is compared against the state-of-the-art methods on both synthesis and real captured datasets. Extensive experimental results demonstrate the superior performance of our method compared with most state-of-the-art works in terms of both objective and subjective quality evaluations. Specifically, our method is more effective on edge areas and more robust to noises.

Infrared small target detection using kernel low-rank approximation and regularization terms for constraints

The robust detection of infrared (IR) small targets remains a challenging task. When targets are submerged in heavy clutter or disturbed by strong edge, it is difficult to extract targets and suppress background clutter simultaneously. In this paper, we present a kernel robust principal component analysis model for IR small target detection. Firstly, to overcome the interference of heavy clutter and strong edge, the kernel low-rank approximation is proposed to estimate the background component; Then, to further improve detection performance, the lp-norm is adopted to recover the sparse component, the total variation regularization is employed to smooth the background, and the graph Laplacian regularization is utilized as a sparse constraint to constrain the homogeneous target region. Finally, we derive an effective method to solve the proposed model based on the alternating direction method of multipliers. Experimental results not only show the proposed method can robustly and effectively detect IR small targets even when the targets are submerged in strong clutter or seriously disturbed by strong edge, but also confirm the proposed method is competitive with the state-of-the-art methods.

Globality constrained adaptive graph regularized non‐negative matrix factorization for data representation

Benefiting from the good physical interpretations and low computational complexity, non-negative matrix factorization (NMF) has attracted wide attentions in data representation learning tasks. Some graph-based NMF approaches make the learned representation encode the topological structure by the local graph Laplacian regularizer, which improves the discriminant ability of data representation. However, the performance of graph-based NMF methods depend heavily on the quality of the predefined graph and the complexity of models is high. Here, a globality constrained adaptive graph regularized non-negative matrix factorization for data representation (GCAG-NMF) model is proposed, which not only uses the self-representation characteristics of data to learn an adaptive graph to describe the sample relationship more accurately, but also proposes a graph factorization technique to reduce the complexity of the model and improve the discriminative ability of data representation. Then, an iterative optimizing strategy with low complexity and strict convergence guarantee is developed to optimize the objective function. Experimental results on some databases demonstrate the effectiveness of the proposed model.

DeepVir: Graphical Deep Matrix Factorization for In Silico Antiviral Repositioning-Application to COVID-19.

This study formulates antiviral repositioning as a matrix completion problem wherein the antiviral drugs are along the rows and the viruses are along the columns. The input matrix is partially filled, with ones in positions where the antiviral drug has been known to be effective against a virus. The curated metadata for antivirals (chemical structure and pathways) and viruses (genomic structure and symptoms) are encoded into our matrix completion framework as graph Laplacian regularization. We then frame the resulting multiple graph regularized matrix completion (GRMC) problem as deep matrix factorization. This is solved by using a novel optimization method called HyPALM (Hybrid Proximal Alternating Linearized Minimization). Results of our curated RNA drug-virus association data set show that the proposed approach excels over state-of-the-art GRMC techniques. When applied to in silico prediction of antivirals for COVID-19, our approach returns antivirals that are either used for treating patients or are under trials for the same.

An improved graph Laplacian regularization method for identifying biomarkers of Alzheimer's disease

Alzheimer's disease (AD) is one of the most common dementia, and its pathogenesis has not been clarified. The failure of amyloid targeted therapy has led us to rethink the pathogenesis of AD. There is growing evidence that complex diseases usually involve the impairment of multiple biological functions, rather than focus on several single genes. Protein-protein interaction network (PPIN) has been recognized as an important tool for identifying and predicting disease biomarkers. It is a great challenge to design network-based classification method for identifying effective, stable and interpretable biomarkers to distinguish the disease phenotype based on gene expression profile data. In this study, we used graph Laplacian regularization method to introduce topology information of PPIN, which can reveal the damaged networks involved in disease from heterogeneous gene expression profile data and identify disease-related biomarkers. The results in three AD datasets showed that the biomarkers identified by our method can not only distinguish the sample categories more accurately, but also help researchers understand the biological meaning behind complex diseases.

Improvement for Single Image Super-resolution and Image Segmentation by Graph Laplacian Regularizer Based on Differences of Neighboring Pixels

Improvement for Single Image Super-resolution and Image Segmentation by Graph Laplacian Regularizer Based on Differences of Neighboring Pixels

Pointwise Mutual Information-Based Graph Laplacian Regularized Sparse Unmixing

Sparse unmixing (SU) aims to express the observed image signatures as a linear combination of pure spectra known <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> and has become a very popular technique with promising results in analyzing hyperspectral images (HSIs) over the past ten years. In SU, utilizing the spatial–contextual information allows for more realistic abundance estimation. To make full use of the spatial–spectral information, in this letter, we propose a pointwise mutual information (PMI)-based graph Laplacian (GL) regularization for SU. Specifically, we construct the affinity matrices via PMI by modeling the association between neighboring image features through a statistical framework and then we use them in the GL regularizer. We also adopt a double reweighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula> norm minimization scheme to promote the sparsity of fractional abundances. Experimental results on simulated and real datasets prove the effectiveness of the proposed method and its superiority over competing algorithms in the literature.

Generic Reversible Visible Watermarking via Regularized Graph Fourier Transform Coding.

Reversible visible watermarking (RVW) is an active copyright protection mechanism. It not only transparently superimposes copyright patterns on specific positions of digital images or video frames to declare the copyright ownership information, but also completely erases the visible watermark image and thus enables restoring the original host image without any distortion. However, existing RVW algorithms mostly construct the reversible mapping mechanism for a specific visible watermarking scheme, which is not versatile. Hence, we propose a generic RVW framework to accommodate various visible watermarking schemes. In particular, we obtain a reconstruction data packet-the compressed difference image between the watermarked image and the original host image, which is embedded into the watermarked image via any conventional reversible data hiding method to facilitate the blind recovery of the host image. The key is to achieve compact compression of the difference image for efficient embedding of the reconstruction data packet. To this end, we propose regularized Graph Fourier Transform (GFT) coding, where the difference image is smoothed via the graph Laplacian regularizer for more efficient compression and then encoded by multi-resolution GFTs in an approximately optimal manner. Experimental results show that the proposed framework has much better versatility than state-of-the-art methods. Due to the small amount of auxiliary information to be embedded, the visual quality of the watermarked image is also higher.