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1.
Foot Ankle Surg ; 2024 Mar 19.
Artigo em Inglês | MEDLINE | ID: mdl-38523011

RESUMO

BACKGROUND: Finite element (FE) analysis and clinical follow-up were used to evaluate the efficacy of a modified lateral column lengthening (H-LCL) for treating flexible flatfoot. METHODS: By applying inclusion and exclusion criteria, we selected patients who underwent H-LCL surgery at our institution from January 2019 to January 2023. We compared the Visual Analog Scale (VAS) scores, American Orthopaedic Foot and Ankle Society (AOFAS) scores, Pain Interference (PI), and Physical Function (PF) scores in Patient-Reported Outcomes Measurement Information System (PROMIS) between preoperative and final follow-up assessments of patients, as well as FE submodels. Furthermore, evaluate the H-LCL's biomechanical characteristics and clinical outcome before and after surgery. RESULTS: A total of 66 patients met the criteria. The average surgery time was 69.47 ± 13.22 min, and the follow-up duration was 15.18 ± 6.40 months. In the last follow-up, VAS and PI decreased compared to before surgery, while AOFAS and PF increased compared to before surgery. Meary's angle (dorsoplantar image and lateral image), calcaneal valgus angle, and talonavicular coverage angle decreased compared to before surgery, while the pitch angle increased compared to before surgery. In FE analysis, postoperative tension on the plantar fascia (PF), spring ligament (SL), and posterior tibial tendon (PTT) decreased compared to before surgery, pressure on the talonavicular joint and subtalar joints also decreased compared to before surgery, and there was no significant change in pressure on the calcaneocuboid joint. CONCLUSION: H-LCL in correcting flexible flatfoot resulted in a significant improvement of clinical outcome scores and led to good radiological correction of flatfoot deformities. It can reduce the soft tissue and interosseous pressure in maintaining the foot arch.

2.
Phys Chem Chem Phys ; 25(43): 29680-29689, 2023 Nov 08.
Artigo em Inglês | MEDLINE | ID: mdl-37882627

RESUMO

Actinides are an important component of nuclear fuel for nuclear power and affect human health, and a key process in the transport of radionuclides in the environment is adsorption on mineral surfaces. In this work, we have used density functional theory (DFT) to investigate the microscopic adsorption and diffusion mechanisms of actinyls, U(V), U(VI), Np(V), Np(VI) Pu(V), and Pu(VI), on the gibbsite (001) surface. Actinyls(VI) are attached to the gibbsite surface through two An-Os bonds, which results in a bidentate inner sphere mode, while actinyls(V) favor a monodentate inner sphere adsorption mode with the gibbsite (001) surface. The solvent effects were considered through an explicit water cluster model. All the actinyls studied can be efficiently adsorbed on the gibbsite (001) surface with binding energies ranging from -113.9 kJ mol-1 to -341.2 kJ mol-1. Electronic structure analyses indicate that the cooperation of the An-Os bonds and hydrogen bonds leads to high adsorption stability of the actinyls with the gibbsite surface. The diffusion barriers of the actinyls on the gibbsite surface were determined, and the high energy barriers indicate that this type of gas-phase diffusion process is not likely to take place.

3.
Artigo em Inglês | MEDLINE | ID: mdl-38536692

RESUMO

AdamW modifies Adam by adding a decoupled weight decay to decay network weights per training iteration. For adaptive algorithms, this decoupled weight decay does not affect specific optimization steps, and differs from the widely used l2-regularizer which changes optimization steps via changing the first- and second-order gradient moments. Despite its great practical success, for AdamW, its convergence behavior and generalization improvement over Adam and l2-regularized Adam ( l2-Adam) remain absent yet. To solve this issue, we prove the convergence of AdamW and justify its generalization advantages over Adam and l2-Adam. Specifically, AdamW provably converges but minimizes a dynamically regularized loss that combines vanilla loss and a dynamical regularization induced by decoupled weight decay, thus yielding different behaviors with Adam and l2-Adam. Moreover, on both general nonconvex problems and PL-conditioned problems, we establish stochastic gradient complexity of AdamW to find a stationary point. Such complexity is also applicable to Adam and l2-Adam, and improves their previously known complexity, especially for over-parametrized networks. Besides, we prove that AdamW enjoys smaller generalization errors than Adam and l2-Adam from the Bayesian posterior aspect. This result, for the first time, explicitly reveals the benefits of decoupled weight decay in AdamW. Experimental results validate our theory.

4.
Artigo em Inglês | MEDLINE | ID: mdl-38963744

RESUMO

In deep learning, different kinds of deep networks typically need different optimizers, which have to be chosen after multiple trials, making the training process inefficient. To relieve this issue and consistently improve the model training speed across deep networks, we propose the ADAptive Nesterov momentum algorithm, Adan for short. Adan first reformulates the vanilla Nesterov acceleration to develop a new Nesterov momentum estimation (NME) method, which avoids the extra overhead of computing gradient at the extrapolation point. Then Adan adopts NME to estimate the gradient's first- and second-order moments in adaptive gradient algorithms for convergence acceleration. Besides, we prove that Adan finds an ϵ-approximate first-order stationary point within O(ϵ-3.5) stochastic gradient complexity on the non-convex stochastic problems (e.g.deep learning problems), matching the best-known lower bound. Extensive experimental results show that Adan consistently surpasses the corresponding SoTA optimizers on vision, language, and RL tasks and sets new SoTAs for many popular networks and frameworks, eg ResNet, ConvNext, ViT, Swin, MAE, DETR, GPT-2, Transformer-XL, and BERT. More surprisingly, Adan can use half of the training cost (epochs) of SoTA optimizers to achieve higher or comparable performance on ViT, GPT-2, MAE, etc, and also shows great tolerance to a large range of minibatch size, e.g.from 1k to 32k. Code is released at https://github.com/sail-sg/Adan, and has been used in multiple popular deep learning frameworks or projects.

5.
Int Immunopharmacol ; 138: 112634, 2024 Jul 05.
Artigo em Inglês | MEDLINE | ID: mdl-38971107

RESUMO

Metabolic dysfunction-associated steatohepatitis (MASH) is a severe metabolic dysfunction-associated steatotic liver disease (MASLD) characterized by abnormal hepatic steatosis and inflammation. Previous studies have shown that Patchouli alcohol (PA), the primary component of Pogostemonis Herba, can alleviate digestive system diseases. However, its protection against MASH remains unclear. This study explored the protective effects and underlying mechanism of PA against high-fat diet-induced MASH in rats. Results showed that PA considerably reduced body weight, epididymal fat, and liver index and attenuated liver histological injury in MASH rats. PA alleviated hepatic injury by inhibiting steatosis and inflammation. These effects are associated with the improvement of SREBP-1c- and PPARα-mediated lipid metabolism and inhibition of the STING-signaling pathway-mediated inflammatory response. Moreover, PA-inhibited hepatic endoplasmic reticulum (ER) stress and mitochondrial dysfunction, reducing SREBP-1c and STING expressions and enhance PPARα expression. PA treatment had the strongest effect on the regulation of mitogen fusion protein 2 (Mfn2) in inhibiting mitochondrial dysfunction. Mfn2 is an important structural protein for binding ERs and mitochondria to form mitochondria-associated ER membranes (MAMs). MASH-mediated disruption of MAMs was inhibited after PA treatment-induced Mfn2 activation. Therefore, the pharmacological effect of PA on MASH is mainly attributed to the inhibition of MAM disruption-induced hepatic steatosis and inflammation. The findings of this study may have implications for MASH treatment that do not neglect the role of Mfn2-mediated MAMs.

6.
Front Microbiol ; 15: 1403849, 2024.
Artigo em Inglês | MEDLINE | ID: mdl-38808276

RESUMO

Soil microorganisms can be used as one of the important indicators of wetland ecosystem restoration. To study the effects of different restoration stages on soil microbial community composition and diversity in Naolihe Wetland, we employed a "time and space parallel" method. Four restoration stages, namely corn field (Corn), short-term restoration wetland (2 years, ST), long-term restoration wetland (8 years, LT) and natural wetland (>25 years, NW), were selected to represent the restoration time and geographical location in Naolihe Nature Wetland. We investigated the composition and diversity of soil microbial communities in different restoration wetland (from corn fields to natural wetlands) by using 16S rRNA and ITS rRNA gene sequencing. We also performed chemical experiments to measure soil enzyme activity and physicochemical properties at each sampling site. The results showed that soil physicochemical properties and enzyme activities significantly differed with the extension of wetland restoration years (p < 0.05). Proteobacteria, Acidobacteria, and Actinobacteria are the most dominant phyla in bacterial. The alpha diversity of soil bacteria was the highest in the corn field (Corn), and ST-LT-NW first decreased and then increased with the extension of wetland restoration years. There are two most dominant phyla (Ascomycota and Mucoromycota) in fungal. However, the alpha diversity of soil fungi was the lowest in the Corn and LT stage, and ST-LT-NW first decreased and then increased with the extension of wetland restoration years. The research findings indicated that the changes in soil physicochemical properties with the extension of wetland restoration years play a significant role in shaping the structure and diversity changes of soil microbial communities. Through the analyses of bacterial and fungal functions using the FUNGuild and FAPROTAX databases, the results showed that the abundance of aerobic bacteria in the soil increased more than that of anaerobic bacteria as the wetland restoration years prolonged, while the abundance of saprotrophic, symbiotic, and pathogenic fungi in the soil significantly decreased with the prolonged wetland restoration years. This study will help us better understand the process of restoration after farmland abandonment, providing valuable reference information for the implementation of a series of wetland ecological restoration projects in the future.

7.
Eur J Pharmacol ; 968: 176433, 2024 Apr 05.
Artigo em Inglês | MEDLINE | ID: mdl-38369273

RESUMO

The promotion of excess low-density lipoprotein (LDL) clearance stands as an effective clinical approach for treating hyperlipidemia. Tetrahydroberberine, a metabolite of berberine, exhibits superior bioavailability compared to berberine and demonstrates a pronounced hypolipidemic effect. Despite these characteristics, the impact of tetrahydroberberine on improving excessive LDL clearance in hyperlipidemia has remained unexplored. Thus, this study investigates the potential effects of tetrahydroberberine on high-fat diet-induced hyperlipidemia in mice. The findings reveal that tetrahydroberberine exerts a more potent lipid-lowering effect than berberine, particularly concerning LDL-cholesterol in hyperlipidemic mice. Notably, tetrahydroberberine significantly reduces serum levels of upstream lipoproteins, including intermediate-density lipoprotein (IDL) and very low-density lipoprotein, by promoting their conversion to LDL. This reduction is further facilitated by the upregulation of hepatic LDL receptor expression induced by tetrahydroberberine. Intriguingly, tetrahydroberberine enhances the apolipoprotein E (ApoE)/apolipoprotein B100 (ApoB100) ratio, influencing lipoprotein assembly in the serum. This effect is achieved through the activation of the efflux of ApoE-containing cholesterol in the liver. The ApoE/ApoB100 ratio exhibits a robust negative correlation with serum levels of LDL and IDL, indicating its potential as a diagnostic indicator for hyperlipidemia. Moreover, tetrahydroberberine enhances hepatic lipid clearance without inducing lipid accumulation in the liver and alleviates existing liver lipid content. Importantly, no apparent hepatorenal toxicity is observed following tetrahydroberberine treatment for hyperlipidemia. In summary, tetrahydroberberine demonstrates a positive impact against hyperlipidemia by modulating lipoprotein assembly-induced clearance of LDL and IDL. The ApoE/ApoB100 ratio emerges as a promising diagnostic indicator for hyperlipidemia, showcasing the potential clinical significance of tetrahydroberberine in lipid management.


Assuntos
Berberina , Berberina/análogos & derivados , Hiperlipidemias , Camundongos , Animais , Lipoproteínas IDL/metabolismo , Berberina/farmacologia , Berberina/uso terapêutico , Dieta Hiperlipídica/efeitos adversos , Triglicerídeos , Colesterol/metabolismo , Apolipoproteínas E/genética , LDL-Colesterol , Fígado/metabolismo
8.
Artigo em Inglês | MEDLINE | ID: mdl-37018253

RESUMO

Breast cancer was the most commonly diagnosed cancer among women worldwide in 2020. Recently, several deep learning-based classification approaches have been proposed to screen breast cancer in mammograms. However, most of these approaches require additional detection or segmentation annotations. Meanwhile, some other image-level label-based methods often pay insufficient attention to lesion areas, which are critical for diagnosis. This study designs a novel deep-learning method for automatically diagnosing breast cancer in mammography, which focuses on the local lesion areas and only utilizes image-level classification labels. In this study, we propose to select discriminative feature descriptors from feature maps instead of identifying lesion areas using precise annotations. And we design a novel adaptive convolutional feature descriptor selection (AFDS) structure based on the distribution of the deep activation map. Specifically, we adopt the triangle threshold strategy to calculate a specific threshold for guiding the activation map to determine which feature descriptors (local areas) are discriminative. Ablation experiments and visualization analysis indicate that the AFDS structure makes the model easier to learn the difference between malignant and benign/normal lesions. Furthermore, since the AFDS structure can be regarded as a highly efficient pooling structure, it can be easily plugged into most existing convolutional neural networks with negligible effort and time consumption. Experimental results on two publicly available INbreast and CBIS-DDSM datasets indicate that the proposed method performs satisfactorily compared with state-of-the-art methods.

9.
IEEE Trans Pattern Anal Mach Intell ; 45(3): 3604-3616, 2023 Mar.
Artigo em Inglês | MEDLINE | ID: mdl-35687620

RESUMO

To reveal the mystery behind deep neural networks (DNNs), optimization may offer a good perspective. There are already some clues showing the strong connection between DNNs and optimization problems, e.g., under a mild condition, DNN's activation function is indeed a proximal operator. In this paper, we are committed to providing a unified optimization induced interpretability for a special class of networks-equilibrium models, i.e., neural networks defined by fixed point equations, which have become increasingly attractive recently. To this end, we first decompose DNNs into a new class of unit layer that is the proximal operator of an implicit convex function while keeping its output unchanged. Then, the equilibrium model of the unit layer can be derived, we name it Optimization Induced Equilibrium Networks (OptEq). The equilibrium point of OptEq can be theoretically connected to the solution of a convex optimization problem with explicit objectives. Based on this, we can flexibly introduce prior properties to the equilibrium points: 1) modifying the underlying convex problems explicitly so as to change the architectures of OptEq; and 2) merging the information into the fixed point iteration, which guarantees to choose the desired equilibrium point when the fixed point set is non-singleton. We show that OptEq outperforms previous implicit models even with fewer parameters.

10.
World J Clin Cases ; 11(27): 6523-6530, 2023 Sep 26.
Artigo em Inglês | MEDLINE | ID: mdl-37900222

RESUMO

BACKGROUND: Eosinophilic granulomatosis with polyangiitis (EGPA), formerly known as Churg-Strauss syndrome, is a rare form of anti-neutrophil cytoplasmic antibody-associated vasculitis characterized by asthma, vasculitis, and eosinophilia. CASE SUMMARY: We report an atypical case of EGPA in a 20-year-old female patient. Unlike previously reported cases of EGPA, this patient's initial symptom was asthma associated with a respiratory infection. This was followed by Loeffler endocarditis and cardiac insufficiency. She received treatment with methylprednisolone sodium succinate, low molecular weight heparin, recombinant human brain natriuretic peptide, furosemide, cefoperazone sodium/sulbactam sodium, and acyclovir. Despite prophylactic anticoagulation, she developed a large right ventricular thrombus. EGPA diagnosis was confirmed based on ancillary test results and specialty consultations. Subsequent treatment included mycophenolate mofetil. Her overall condition improved significantly after treatment, as evidenced by decreased peripheral blood eosinophils and cardiac markers. She was discharged after 17 d. Her most recent follow-up showed normal peripheral blood eosinophil levels, restored cardiac function, and a reduced cardiac mural thrombus size. CONCLUSION: This case illustrates the swift progression of EGPA and underscores the significance of early detection and immediate intervention to ensure a favorable prognosis.

11.
Contrast Media Mol Imaging ; 2022: 6884308, 2022.
Artigo em Inglês | MEDLINE | ID: mdl-35965621

RESUMO

In order to prove that SOX9 in keratinocytes regulates claudin 2 transcription during skin aging, the skin of 8-week-old and 24-month-old mice is sequenced to obtain a differentially expressed gene SOX9. The gene is mainly expressed in keratinocytes, and it increases first and then decreases from newborn to aging. Six core sequences of SOX9 and claudin 2 are predicted from Jaspar. The double Luciferase Report shows that overexpression of SOX9 induces the full-length promoter of claudin 2 significantly and has no effect on the mutation and cleavage plasmid without SOX9 response. Claudin 2 is consistent with SOX9 in the skin of mice of different ages, and SOX9 is strongly positively correlated with claudin 2. Finally, overexpression of SOX9 and claudin 2 will delay PM2.5-induced keratinocyte senescence. The silencing of claudin 2 leads to the loss of SOX9 function. It is clearly evident that SOX9 can affect the transcription of claudin 2, which increases first and then decreases in the process of mice from newborn to aging. SOX9 inhibits proinflammatory mediators, increases antioxidant capacity, and restores keratin differentiation. It can effectively prevent melanin deposition and delay aging.


Assuntos
Fatores de Transcrição SOX9/metabolismo , Envelhecimento da Pele , Animais , Claudina-2/genética , Queratinócitos/metabolismo , Camundongos , Regiões Promotoras Genéticas , Fatores de Transcrição SOX9/genética , Transcrição Gênica
12.
Acta Cir Bras ; 37(10): e371002, 2022.
Artigo em Inglês | MEDLINE | ID: mdl-36542040

RESUMO

PURPOSE: The active melanocytes in the skin were affected by hormones and ultraviolet (UV) irradiation. Licorice zinc has a whitening effect, which may have a prominent potential in the treatment of pigmented skin disease. METHODS: Modeling chloasma C57BL/6J mice by daily progesterone injection (15 mg/kg) and ultraviolet B (UVB) irradiation (λ = 312 nm, 2 h/day) for 30 days. Then, mice were given 0.65, 1.3, and 2.6 (g/kg) of licorice zinc and tranexamic acid 250 mg daily by oral administration for 14 days, respectively. Hematoxylin and eosin and Fontana-Masson staining, and Western blotting (WB) were performed to test the inhibitory of melanogenesis and activation of c-Jun-N-terminal (JNK)/p38 mitogen-activated protein kinases (MAPK) for licorice zinc. Melanogenesis was induced by α-melanocyte-stimulating hormone in vitro. Cell counting kit-8, melanin content determination, and WB were performed to verify the inhibitory effect of licorice zinc on melanogenesis. RESULTS: The present study showed that licorice zinc decreased melanin formation, cutaneous tissue injury, and the phosphorylation of JNK and P38MAPK, which was caused by UVB irradiation in vivo. In vitro, licorice zinc showed opposite effects from JNK/p38 activator. Meanwhile, tyrosinase-related protein-1, tyrosinase, and microphthalmia-associated transcription factor were decreased too. CONCLUSIONS: Licorice zinc induced a decrease in melanin synthesis by inhibiting the JNK and the P38MAPK signaling pathway, suggesting licorice zinc is a potential agent of anti-chloasma.


Assuntos
Glycyrrhiza , Melaninas , Animais , Camundongos , Melaninas/metabolismo , Melaninas/farmacologia , Sistema de Sinalização das MAP Quinases , Proteínas Quinases p38 Ativadas por Mitógeno , Glycyrrhiza/metabolismo , Zinco/farmacologia , Camundongos Endogâmicos C57BL , Linhagem Celular Tumoral
13.
Zhongguo Xiu Fu Chong Jian Wai Ke Za Zhi ; 35(1): 70-75, 2021 Jan 15.
Artigo em Zh | MEDLINE | ID: mdl-33448202

RESUMO

OBJECTIVE: To investigate the effectiveness of anatomical reconstruction of the anterior talofibular ligament by partial peroneal brevis tendon combined with double intra-fix screws. METHODS: A clinical data of 46 patients with the anterior talofibular ligament rupture admitted between September 2015 and October 2019 and met the selection criteria were retrospectively analyzed. All anterior talofibular ligaments were reconstructed with partial peroneal brevis tendon and fixed with double intra-fix screws. There were 22 males and 24 females, with an average age of 28.1 years (range, 16-52 years). Forty cases had a history of ankle sprain, 1 case was injured by a heavy object, and 5 cases were suffered from falls. There were 17 cases on the left side and 29 cases on the right side. The disease duration ranged from 3 months to 10 years (median, 20.3 months). The visual analogue scale (VAS) score, American Orthopaedic Foot and Ankle Society (AOFAS) ankle-hindfoot score, varus angle of ankle, and the difference of the anterior talar translation between healthy and affected sides (looseness, similarity, tightness) were recorded before and after operation; 23 patients were evaluated by Patient-Reported Outcomes Measurement Information System (PROMIS) score, including pain interference (PI) and physical function (PF) scores. RESULTS: The operation time was 39-179 minutes, with an average of 65.8 minutes. All incisions healed by first intention. All patients were followed up 12-30 months (mean, 23 months). The VAS score, AOFAS ankle-hindfoot score, varus angle of ankle, difference of the anterior talar translation between healthy and affected sides, and PI and PF scores of PROMIS at 6 months and last follow-up significantly improved when compared with those before operation ( P<0.05). There was no significant difference in VAS score, PI score of PROMIS, and AOFAS ankle-hindfoot score between at 6 months and at last follow-up ( P>0.05). However, the PF score of PROMIS, the difference of the anterior talar translation between healthy and affected sides, and the varus angle of ankle were significant ( P<0.05). CONCLUSION: Anatomical reconstruction of the anterior talofibular ligament by partial peroneal brevis tendon and double intra-fix screws has the advantages of small incision, convenient tendon removal, and firm graft fixation. The postoperative patients recover quickly and the effectiveness is satisfactory.


Assuntos
Ligamentos Laterais do Tornozelo , Adolescente , Adulto , Articulação do Tornozelo/cirurgia , Parafusos Ósseos , Feminino , Humanos , Ligamentos Laterais do Tornozelo/cirurgia , Masculino , Pessoa de Meia-Idade , Estudos Retrospectivos , Tendões , Resultado do Tratamento , Adulto Jovem
14.
IEEE Trans Vis Comput Graph ; 26(11): 3255-3270, 2020 Nov.
Artigo em Inglês | MEDLINE | ID: mdl-31180892

RESUMO

Point cloud is the primary source from 3D scanners and depth cameras. It usually contains more raw geometric features, as well as higher levels of noise than the reconstructed mesh. Although many mesh denoising methods have proven to be effective in noise removal, they hardly work well on noisy point clouds. We propose a new multi-patch collaborative method for point cloud denoising, which is solved as a low-rank matrix recovery problem. Unlike the traditional single-patch based denoising approaches, our approach is inspired by the geometric statistics which indicate that a number of surface patches sharing approximate geometric properties always exist within a 3D model. Based on this observation, we define a rotation-invariant height-map patch (HMP) for each point by robust Bi-PCA encoding bilaterally filtered normal information, and group its non-local similar patches together. Within each group, all patches are geometrically similar, while suffering from noise. We pack the height maps of each group into an HMP matrix, whose initial rank is high, but can be significantly reduced. We design an improved low-rank recovery model, by imposing a graph constraint to filter noise. Experiments on synthetic and raw datasets demonstrate that our method outperforms state-of-the-art methods in both noise removal and feature preservation.

15.
IEEE Trans Vis Comput Graph ; 25(10): 2910-2926, 2019 Oct.
Artigo em Inglês | MEDLINE | ID: mdl-30106734

RESUMO

Mesh denoising is a classical, yet not well-solved problem in digital geometry processing. The challenge arises from noise removal with the minimal disturbance of surface intrinsic properties (e.g., sharp features and shallow details). We propose a new patch normal co-filter (PcFilter) for mesh denoising. It is inspired by the geometry statistics which show that surface patches with similar intrinsic properties exist on the underlying surface of a noisy mesh. We model the PcFilter as a low-rank matrix recovery problem of similar-patch collaboration, aiming at removing different levels of noise, yet preserving various surface features. We generalize our model to pursue the low-rank matrix recovery in the kernel space for handling the nonlinear structure contained in the data. By making use of the block coordinate descent minimization and the specifics of a proximal based coordinate descent method, we optimize the nonlinear and nonconvex objective function efficiently. The detailed quantitative and qualitative results on synthetic and real data show that the PcFilter competes favorably with the state-of-the-art methods in surface accuracy and noise-robustness.

16.
IEEE Trans Image Process ; 27(1): 477-489, 2018 Jan.
Artigo em Inglês | MEDLINE | ID: mdl-29053462

RESUMO

While current block diagonal constrained subspace clustering methods are performed explicitly on the original data space, in practice, it is often more desirable to embed the block diagonal prior into the reproducing kernel Hilbert feature space by kernelization techniques, as the underlying data structure in reality is usually nonlinear. However, it is still unknown how to carry out the embedding and kernelization in the models with block diagonal constraints. In this paper, we shall take a step in this direction. First, we establish a novel model termed implicit block diagonal low-rank representation (IBDLR), by incorporating the implicit feature representation and block diagonal prior into the prevalent low-rank representation method. Second, mostly important, we show that the model in IBDLR could be kernelized by making use of a smoothed dual representation and the specifics of a proximal gradient-based optimization algorithm. Finally, we provide some theoretical analyses for the convergence of our optimization algorithm. Comprehensive experiments on synthetic and real-world data sets demonstrate the superiorities of our IBDLR over state-of-the-art methods.

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