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In this work, we focus on studying the differentiable relaxations of several linear regression problems, where the original formulations are usually both nonsmooth with one nonconvex term. Unfortunately, in most cases, the standard alternating direction method of multipliers (ADMM) cannot guarantee global convergence when addressing these kinds of problems. To address this issue, by smoothing the convex term and applying a linearization technique before designing the iteration procedures, we employ nonconvex ADMM to optimize challenging nonconvex-convex composite problems. In our theoretical analysis, we prove the boundedness of the generated variable sequence and then guarantee that it converges to a stationary point. Meanwhile, a potential function is derived from the augmented Lagrange function, and we further verify that the objective function is monotonically nonincreasing. Under the Kurdyka-Łojasiewicz (KŁ) property, the global convergence is analyzed step by step. Finally, experiments on face reconstruction, image classification, and subspace clustering tasks are conducted to show the superiority of our algorithms over several state-of-the-art ones.

To enhance the effectiveness and efficiency of subspace clustering in visual tasks, this work introduces a novel approach that automatically eliminates the optimal mean, which is embedded in the subspace clustering framework of low-rank representation (LRR) methods, along with the computationally factored formulation of Schatten $p$ -norm. By addressing the issues related to meaningful computations involved in some LRR methods and overcoming biased estimation of the low-rank solver, we propose faster nonconvex subspace clustering methods through joint Schatten $p$ -norm factorization with optimal mean (JS $p$ NFOM), forming a unified framework for enhancing performance while reducing time consumption. The proposed approach employs tractable and scalable factor techniques, which effectively address the disadvantages of higher computational complexity, particularly when dealing with large-scale coefficient matrices. The resulting nonconvex minimization problems are reformulated and further iteratively optimized by multivariate weighting algorithms, eliminating the need for singular value decomposition (SVD) computations in the developed iteration procedures. Moreover, each subproblem can be guaranteed to obtain the closed-form solver, respectively. The theoretical analyses of convergence properties and computational complexity further support the applicability of the proposed methods in real-world scenarios. Finally, comprehensive experimental results demonstrate the effectiveness and efficiency of the proposed nonconvex clustering approaches compared to existing state-of-the-art methods on several publicly available databases. The demonstrated improvements highlight the practical significance of our work in subspace clustering tasks for visual data analysis. The source code for the proposed algorithms is publicly accessible at https://github.com/ZhangHengMin/TRANSUFFC.

With the growing interest in convex and nonconvex low-rank matrix learning problems, the widely used singular value thresholding (SVT) operators associated with rank relaxation functions often face higher computational complexity, particularly for large-scale data matrices. To improve the efficacy of low-rank subspace clustering and overcome the issue of high computational complexity, this work proposes an efficient and effective method that avoids the need for singular value decomposition (SVD) computations in the iteration scheme. This can be achieved through the use of a computationally efficient and compact formulation, as well as automatic removal of the optimal mean, which reduces time consumption and enhances evaluation performance. A unified clustering framework based on Schatten- $p$ norm regularized by $\ell _{2,q}$ -norm can be formulated using this processing way, where inner element suppression can be achieved by choosing appropriate $p$ , $q \in (0,1)$ . Additionally, calculating the optimal mean enhances the robustness of the proposed method in the presence of outliers. Unlike the general iteration scheme of the alternating direction method of multiplier (ADMM) algorithms that introduce auxiliary splitting variables, the proposed alternating re-weighted least square (ARwLS) algorithm uses matrix inverse and multiplication computations to obtain analytic solutions, resulting in faster processing speeds for each sub-problem. To further investigate, we provide the computational complexity of each iteration and the theoretical analysis of the convergence property, where the derived solution is a stationary point. Experimental results on synthetic data and several benchmark datasets demonstrate the promising efficiency and efficacy of the proposed clustering method compared to classical and competing algorithms.

Decomposing data matrix into low-rank plus additive matrices is a commonly used strategy in pattern recognition and machine learning. This article mainly studies the alternating direction method of multiplier (ADMM) with two dual variables, which is used to optimize the generalized nonconvex nonsmooth low-rank matrix recovery problems. Furthermore, the minimization framework with a feasible optimization procedure is designed along with the theoretical analysis, where the variable sequences generated by the proposed ADMM can be proved to be bounded. Most importantly, it can be concluded from the Bolzano–Weierstrass theorem that there must exist a subsequence converging to a critical point, which satisfies the Karush–Kuhn–Tucher (KKT) conditions. Meanwhile, we further ensure the local and global convergence properties of the generated sequence relying on constructing the potential objective function. Particularly, the detailed convergence analysis would be regarded as one of the core contributions besides the algorithm designs and the model generality. Finally, the numerical simulations and the real-world applications are both provided to verify the consistence of the theoretical results, and we also validate the superiority in performance over several mostly related solvers to the tasks of image inpainting and subspace clustering.

Roux-en-Y gastric bypass (RYGB) surgery reduces weight in obese patients. A marked decrease in blood glucose levels occurs before weight loss; however, key molecules that improve the glycemic profile remain largely unknown. Using a murine RYGB surgery model, we performed multiorgan proteomics and bioinformatics to monitor the proteins and molecular pathways that change in this early glycemic response. Multiplexed proteomic kinetics data analysis revealed that the Roux limb, biliopancreatic limb, liver, and pancreas each exhibited unique temporal and molecular responses to the RYGB surgery. In addition, protein–protein network analysis indicated that the changes to the microbial environment in the intestine may play a crucial role in the beneficial effects of RYGB surgery. Furthermore, insulin-like growth factor binding protein 7 (Igfbp7) was identified as an early induced protein in the Roux limb. Known secretory properties of Igfbp7 prompted us to further investigate its role as a remote organ regulator of glucose metabolism. Igfbp7 overexpression decreased blood glucose levels in diet-induced obese mice and attenuated gluconeogenic gene expression in the liver. Secreted Igfbp7 appeared to mediate these beneficial effects. These results demonstrate that organs responded differentially to RYGB surgery and indicate that Igfbp7 may play an important role in improving blood glucose levels.

Recently, there is a rapidly increasing attraction for the efficient recovery of low-rank matrix in computer vision and machine learning. The popular convex solution of rank minimization is nuclear norm-based minimization (NNM), which usually leads to a biased solution since NNM tends to overshrink the rank components and treats each rank component equally. To address this issue, some nonconvex nonsmooth rank (NNR) relaxations have been exploited widely. Different from these convex and nonconvex rank substitutes, this paper first introduces a general and flexible rank relaxation function named weighted NNR relaxation function, which is actually derived from the initial double NNR (DNNR) relaxations, i.e., DNNR relaxation function acts on the nonconvex singular values function (SVF). An iteratively reweighted SVF optimization algorithm with continuation technology through computing the supergradient values to define the weighting vector is devised to solve the DNNR minimization problem, and the closed-form solution of the subproblem can be efficiently obtained by a general proximal operator, in which each element of the desired weighting vector usually satisfies the nondecreasing order. We next prove that the objective function values decrease monotonically, and any limit point of the generated subsequence is a critical point. Combining the Kurdyka–Łojasiewicz property with some milder assumptions, we further give its global convergence guarantee. As an application in the matrix completion problem, experimental results on both synthetic data and real-world data can show that our methods are competitive with several state-of-the-art convex and nonconvex matrix completion methods. [ABSTRACT FROM AUTHOR]

The recent studies have found that the nonconvex relaxation functions usually perform better than the convex counterparts in the $l_{0}$ -norm and rank function minimization problems. However, due to the absence of convexity in these nonconvex problems, developing efficient algorithms with convergence guarantee becomes very challenging. Inspired by the basic ideas of both the Jacobian alternating direction method of multipliers (JADMMs) for solving linearly constrained problems with separable objectives and the proximal gradient methods (PGMs) for optimizing the unconstrained problems with one variable, this paper focuses on extending the PGMs to the proximal Jacobian iteration methods (PJIMs) for handling with a family of nonconvex composite optimization problems with two splitting variables. To reduce the total computational complexity by decreasing the number of iterations, we devise the accelerated version of PJIMs through the well-known Nesterov’s acceleration strategy and further extend both to solve the multivariable cases. Most importantly, we provide a rigorous convergence analysis, in theory, to show that the generated variable sequence globally converges to a critical point by exploiting the Kurdyka–Łojasiewica (KŁ) property for a broad class of functions. Furthermore, we also establish the linear and sublinear convergence rates of the obtained variable sequence in the objective function. As the specific application to the nonconvex sparse and low-rank recovery problems, several numerical experiments can verify that the newly proposed algorithms not only keep fast convergence speed but also have high precision. [ABSTRACT FROM AUTHOR]

Most existing regression based classification methods for robust face recognition usually characterize the representation error using L 1 -norm or Frobenius-norm for the pixel-level noise or nuclear norm for the image-level noise, and code the coefficients vector by l 1 -norm or l 2 -norm. To our best knowledge, nuclear norm can be used to describe the low-rank structural information but may lead to the suboptimal solution, while l 1 -norm or l 2 -norm can promote the sparsity or cooperativity but may neglect the prior information (e.g., the locality and similarity relationship) among data. To solve these drawbacks, we propose two weighted sparse coding regularized nonconvex matrix regression models including w eighted s parse coding regularized matrix γ -norm based m atrix r egression (WS γ MR) for the structural noise and w eighted s parse coding regularized matrix γ -norm plus m inimax concave plus (MCP) function based m atrix r egression (WS γ M 2 R) for the mixed noise (e.g, structural noise plus sparse noise). The MCP induced nonconvex function can overcome the imbalanced penalization of different singular values and entries of the error image matrix, and the weighted sparse coding can consider the prior information by borrowing a novel distance metric. The variants of inexact augmented Lagrange multiplier (iALM) algorithm including nonconvex iALM (NCiALM) and majorization-minimization iALM (MMiALM) are developed to solve the proposed models, respectively. The matrix γ -norm based classifier is devised for classification. Finally, experiments on four popular face image databases can validate the superiority of our methods compared with the-state-of-the-art regression methods. [ABSTRACT FROM AUTHOR]

Supplemental Digital Content is available in the text.

Compressive sensing (CS) based computed tomography (CT) image reconstruction aims at reducing the radiation risk through sparse-view projection data. However, it is challenging to achieve satisfying image quality from incomplete projections. Recent works demonstrate the promising potential of nonconvex L 1 / 2 -norm in CS problem, while the applications on medical imaging are constrained by its nonconvexity. In this paper, we develop an L 1 / 2 -regularized nonlocal self-similarity (NSS) denoiser based CT reconstruction model, which combines with low-rank approximation and group sparse coding (GSC) framework. Concretely, we firstly split the CT reconstruction problem into two subproblems, then improve CT image quality furtherly using our proposed denoiser. Instead of optimizing the nonconvex problem under the perspective of GSC, we particularly reconstruct CT image via low-rank minimization based on two simple yet essential schemes, which build the equivalent relationship between GSC based denoiser and low-rank minimization. Furtherly, the weighted singular value thresholding (WSVT) operator is utilized to optimize the resulting nonconvex L 1 / 2 minimization problem. Following this, our proposed denoiser is integrated with the CT reconstruction problem by alternating direction method of multipliers (ADMM) framework. Extensive experimental results on typical clinical CT images have demonstrated that our approach can further achieve better performance than popular approaches. [ABSTRACT FROM AUTHOR]

Abstract: Under the most elementary conditions on stochastic differential equations and some milder conditions on backward stochastic differential equations with finite or infinite time intervals and linear-growth generators, a representation theorem of generators and a converse comparison theorem of solutions are established in this paper. [Copyright &y& Elsevier]

Tissue injury in mammals triggers both inflammatory and repair responses that, in some contexts, results in fibrosis. Fibrosis is characterized by the persistence of activated myofibroblasts, ineffective re-epithelialization, and variable degrees of inflammation within injured tissues. The protein kinase inhibitor (PKI), imatinib mesylate, has been proposed as a potential antifibrotic therapeutic agent. In this study, the efficacy of imatinib mesylate to modulate fibrogenic responses, both in vitro and in vivo, was examined. In an in vitro fibroblast culture model, imatinib inhibits platelet-derived growth factor receptor activation and fibroblast proliferation but not the stably differentiated myofibroblast phenotype. Furthermore, imatinib inhibits lung epithelial cell proliferation and survival but not the induction of epithelial-mesenchymal transition. Imatinib does not alter transforming growth factor-beta/SMAD3 signaling in either cell type. In a murine model of lung fibrosis, bleomycin-induced injury to the pulmonary epithelium provokes an early inflammatory response with more delayed fibrosis during the late reparative phase of lung injury. Imatinib mesylate (10 mg/kg/day by i.p. injection or oral gavage), administered during the postinjury repair phase, failed to significantly alter fibrogenic responses assessed by histopathology, collagen content, and the accumulation of myofibroblasts within the injured lung. These studies indicate that the capacity of a PKI to inhibit fibroblast proliferation may be insufficient to mediate significant antifibrotic effects in late stages of tissue injury repair. Pharmacologic agents that modulate the activities and fate of differentiated (myo)fibroblasts, without interfering with the regenerative capacity of epithelial cells, are likely to be more effective for treatment of nonresolving, progressive fibrotic disorders.

Progressive fibrotic diseases involving diverse organ systems are associated with the persistence of fibroblasts/myofibroblasts in injured tissues. Activation of focal adhesion kinase (FAK) and protein kinase B (PKB/Akt) by transforming growth factor-β1 mediate stable induction of myofibroblast differentiation and survival. In this report, we demonstrate that transforming growth factor-β1-induced activation of both PKB/Akt and FAK are dose dependently inhibited by the protein kinase inhibitor, AG1879, in cultured human lung fibroblasts. In a murine model of intratracheal bleomycin-induced lung fibrosis, regions of active fibrogenesis demonstrate elevated expression of PKB/Akt and FAK phosphorylation in vivo, effects that are attenuated in mice receiving daily intraperitoneal injections of AG1879 (bleomycin-AG1879) versus a chemically inactive analog (bleomycin-control). PKB/Akt and FAK phosphorylation are elevated in fibroblasts isolated from lungs of bleomycin-injured mice, effects that are inhibited in bleomycin-AG1879 mice. Accumulation of α-smooth muscle actin-expressing myofibroblasts is markedly reduced in lungs of bleomycin-AG1879 mice. The numbers of recruited inflammatory cells were not significantly different between these groups. Bleomycin-AG1879 mice are protected from lung fibrosis as evidenced by histopathology, trichrome staining, and biochemical analysis for collagen. Thus, targeting of prosurvival signaling pathways in fibroblasts/myofibroblasts may provide a novel and effective strategy for anti-fibrotic therapy of treatment-unresponsive fibrotic disorders.

Introduction:Hemodialysis access by arteriovenous fistulas (AVF) remain the primary lifeline for chronic renal failure patients. AVF failure rates, however, are unacceptably high with no effective medical therapy and underlying mechanisms remain unclear. By closely mimicking the clinical AVF creation in mice, we have taken a proteomics-assisted systems approach to target discovery for AVF failure.Methods:We created AVF in Ldlr-/- mice via surgical anastomosis between the distal end of the left external jugular vein (EJV) and the post arteriotomy lateral aspect of the left mid-common carotid artery. Functional fistulas validated by Color Doppler (Vevo2100, Fujifilm-Visualsonics) at 1-week post-op were used for this study. AVF tissues and their paired right non-surgically modified EJVs (normal veins) were harvested at 2, 4, and 6-weeks post-surgery (n=3-4). Each AVF and EJV tissue was divided into 3 equal lengths, and each segment was then processed for histology and LC-MS/MS. Pathway enrichment and network analysis of the proteome provided biological insights on temporal and regional changes during the arterialization of AVF. Putative key regulators of the AVF disease were identified through a multi-step network objects prioritization strategy.Results:As early as 2 weeks after surgery, proteins related to macrophage immune response and cytoskeleton protein regulation increased in the proximal third of the venous segment (to the anastomosis) relative to the middle and distal third segments. At 4 weeks, these increases in predominant proteins moved to the middle third contiguous segment, with ~50% of this proteome remaining elevated in the proximal third while ~50% decline in abundance. Interactome analysis of this spatiotemporal movement of the AVF proteome from proximal to distal portions over time, accompanied by changes in Doppler and histologic features, revealed putative key regulators in the process of AVF failure (e.g., EGF receptor, karyopherins ?1 and ?2, ELAV-like protein 1, FAM21A).Conclusions:We propose that the first ever network analysis of the AVF proteome revealed early pathologic tissue changes in a mouse model and identified potential therapeutic targets for this devastating maladaptive venous disease.

Linear regression-based and extended methods have been widely used in pattern classification. These methods can be roughly divided into two categories: reconstruction error-based methods and discriminative methods. The reconstruction error-based methods search the target label by learning the representation coefficients to compute the minimal reconstruction error. The goal of the discriminative methods is to learn the projection matrix to predict the target label of the image. To combine the advantages of these two kinds of regression-based methods, this paper presents a dual robust regression framework (DualRR) for pattern classification. In the training stage, a double low-rank robust regression model (DLR) is proposed to learn the projection matrix. In DLR, low-rank robust regression motivates us to model the data as the sum of a low-rank clean data and sparse noise matrix. The low-rank is further used to constrain the projection matrix to enhance the discriminative performance. In the testing stage, the proposed framework employs a robust regression representation model to learn the optimal representation coefficients and obtain the reconstruction sample to approximate the test sample. We thus apply the reconstruction sample to search the classification label by using the projection matrix learned in the training stage. Extensive experiments are conducted on six public available databases, namely, LFW, FRGC, CUHK Sketch, PolyU Palm, NUST-RF and Caltech 101, demonstrating the merits of the proposed model over state-of-the-art regression-based classification methods. [ABSTRACT FROM AUTHOR]