Unified Framework for Faster Clustering via Joint Schatten p-Norm Factorization With Optimal Mean.

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.

Toughening Ceramics down to Cryogenic Temperatures by Reentrant Strain-Glass Transition.

Ceramics, often exhibiting important functional properties like piezoelectricity, superconductivity, and magnetism, are usually mechanically brittle at room temperature and even more brittle at low temperature due to their ionic or covalent bonding nature. The brittleness in their working temperature range (mostly from room down to cryogenic temperatures) has been a limiting factor for the usefulness of these ceramics. In this Letter, we report a surprising "low-temperature toughening" phenomenon in a La-doped CaTiO_{3} perovskite ceramic, where a 2.5× increase of fracture toughness K_{IC} from 1.9 to 4.8 MPa m^{1/2} occurs when cooling from above room temperature (323 K) down to a cryogenic temperature of 123 K, the lowest temperature our experiment can reach. In situ microscopic observations in combination with macroscopic characterizations show that this desired but counterintuitive phenomenon stems from a reentrant strain-glass transition, during which nanosized orthorhombic ferroelastic domains gradually emerge from the existing tetragonal ferroelastic matrix. The temperature stability of this unique microstructure and its stress-induced transition into the macroscopic orthorhombic phase provide a low-temperature toughening mechanism over a wide temperature range and explain the observed phenomenon. Our finding may open a way to design tough ceramics with a wide temperature range and shed light on the nature of reentrant transitions in other ferroic systems.

Generalized Nonconvex Nonsmooth Low-Rank Matrix Recovery Framework With Feasible Algorithm Designs and Convergence Analysis.

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.

Proprotein Convertase Subtilisin/Kexin 9 (PCSK9) Promotes Macrophage Activation via LDL Receptor-Independent Mechanisms.

BACKGROUND: Activated macrophages contribute to the pathogenesis of vascular disease. Vein graft failure is a major clinical problem with limited therapeutic options. PCSK9 (proprotein convertase subtilisin/kexin 9) increases low-density lipoprotein (LDL)-cholesterol levels via LDL receptor (LDLR) degradation. The role of PCSK9 in macrophage activation and vein graft failure is largely unknown, especially through LDLR-independent mechanisms. This study aimed to explore a novel mechanism of macrophage activation and vein graft disease induced by circulating PCSK9 in an LDLR-independent fashion. METHODS: We used Ldlr-/- mice to examine the LDLR-independent roles of circulating PCSK9 in experimental vein grafts. Adeno-associated virus (AAV) vector encoding a gain-of-function mutant of PCSK9 (rAAV8/D377Y-mPCSK9) induced hepatic PCSK9 overproduction. To explore novel inflammatory targets of PCSK9, we used systems biology in Ldlr-/- mouse macrophages. RESULTS: In Ldlr-/- mice, AAV-PCSK9 increased circulating PCSK9, but did not change serum cholesterol and triglyceride levels. AAV-PCSK9 promoted vein graft lesion development when compared with control AAV. In vivo molecular imaging revealed that AAV-PCSK9 increased macrophage accumulation and matrix metalloproteinase activity associated with decreased fibrillar collagen, a molecular determinant of atherosclerotic plaque stability. AAV-PCSK9 induced mRNA expression of the pro-inflammatory mediators IL-1ß (interleukin-1 beta), TNFα (tumor necrosis factor alpha), and MCP-1 (monocyte chemoattractant protein-1) in peritoneal macrophages underpinned by an in vitro analysis of Ldlr-/- mouse macrophages stimulated with endotoxin-free recombinant PCSK9. A combination of unbiased global transcriptomics and new network-based hyperedge entanglement prediction analysis identified the NF-κB (nuclear factor-kappa B) signaling molecules, lectin-like oxidized LOX-1 (LDL receptor-1), and SDC4 (syndecan-4) as potential PCSK9 targets mediating pro-inflammatory responses in macrophages. CONCLUSIONS: Circulating PCSK9 induces macrophage activation and vein graft lesion development via LDLR-independent mechanisms. PCSK9 may be a potential target for pharmacologic treatment for this unmet medical need.

Global Convergence Guarantees of (A)GIST for a Family of Nonconvex Sparse Learning Problems.

In recent years, most of the studies have shown that the generalized iterated shrinkage thresholdings (GISTs) have become the commonly used first-order optimization algorithms in sparse learning problems. The nonconvex relaxations of the l0 -norm usually achieve better performance than the convex case (e.g., l1 -norm) since the former can achieve a nearly unbiased solver. To increase the calculation efficiency, this work further provides an accelerated GIST version, that is, AGIST, through the extrapolation-based acceleration technique, which can contribute to reduce the number of iterations when solving a family of nonconvex sparse learning problems. Besides, we present the algorithmic analysis, including both local and global convergence guarantees, as well as other intermediate results for the GIST and AGIST, denoted as (A)GIST, by virtue of the Kurdyka-Lojasiewica (KL) property and some milder assumptions. Numerical experiments on both synthetic data and real-world databases can demonstrate that the convergence results of objective function accord to the theoretical properties and nonconvex sparse learning methods can achieve superior performance over some convex ones.

Joint Optimal Transport With Convex Regularization for Robust Image Classification.

The critical step of learning the robust regression model from high-dimensional visual data is how to characterize the error term. The existing methods mainly employ the nuclear norm to describe the error term, which are robust against structure noises (e.g., illumination changes and occlusions). Although the nuclear norm can describe the structure property of the error term, global distribution information is ignored in most of these methods. It is known that optimal transport (OT) is a robust distribution metric scheme due to that it can handle correspondences between different elements in the two distributions. Leveraging this property, this article presents a novel robust regression scheme by integrating OT with convex regularization. The OT-based regression with L2 norm regularization (OTR) is first proposed to perform image classification. The alternating direction method of multipliers is developed to handle the model. To further address the occlusion problem in image classification, the extended OTR (EOTR) model is then presented by integrating the nuclear norm error term with an OTR model. In addition, we apply the alternating direction method of multipliers with Gaussian back substitution to solve EOTR and also provide the complexity and convergence analysis of our algorithms. Experiments were conducted on five benchmark datasets, including illumination changes and various occlusions. The experimental results demonstrate the performance of our robust regression model on biometric image classification against several state-of-the-art regression-based classification methods.

Systems Approach to Discovery of Therapeutic Targets for Vein Graft Disease: PPARα Pivotally Regulates Metabolism, Activation, and Heterogeneity of Macrophages and Lesion Development.

BACKGROUND: Vein graft failure remains a common clinical challenge. We applied a systems approach in mouse experiments to discover therapeutic targets for vein graft failure. METHODS: Global proteomics and high-dimensional clustering on multiple vein graft tissues were used to identify potential pathogenic mechanisms. The PPARs (peroxisome proliferator-activated receptors) pathway served as an example to substantiate our discovery platform. In vivo mouse experiments with macrophage-targeted PPARα small interfering RNA, or the novel, selective activator pemafibrate demonstrate the role of PPARα in the development and inflammation of vein graft lesions. In vitro experiments further included metabolomic profiling, quantitative polymerase chain reaction, flow cytometry, metabolic assays, and single-cell RNA sequencing on primary human and mouse macrophages. RESULTS: We identified changes in the vein graft proteome associated with immune responses, lipid metabolism regulated by the PPARs, fatty acid metabolism, matrix remodeling, and hematopoietic cell mobilization. PPARα agonism by pemafibrate retarded the development and inflammation of vein graft lesions in mice, whereas gene silencing worsened plaque formation. Pemafibrate also suppressed arteriovenous fistula lesion development. Metabolomics/lipidomics, functional metabolic assays, and single-cell analysis of cultured human macrophages revealed that PPARα modulates macrophage glycolysis, citrate metabolism, mitochondrial membrane sphingolipid metabolism, and heterogeneity. CONCLUSIONS: This study explored potential drivers of vein graft inflammation and identified PPARα as a novel potential pharmacological treatment for this unmet medical need.

Multiorgan Systems Study Reveals Igfbp7 as a Suppressor of Gluconeogenesis after Gastric Bypass Surgery.

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.

Low-Rank Matrix Recovery via Modified Schatten-p Norm Minimization with Convergence Guarantees.

In recent years, low-rank matrix recovery problems have attracted much attention in computer vision and machine learning. The corresponding rank minimization problems are both combinational and NP-hard in general, which are mainly solved by both nuclear norm and Schatten-p (0

Efficient Recovery of Low-Rank Matrix via Double Nonconvex Nonsmooth Rank Minimization.

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-Lojasiewicz 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.