Deep neural networks(DNNs)have achieved great success in many data processing applications.However,high computational complexity and storage cost make deep learning difficult to be used on resource-constrained devices...Deep neural networks(DNNs)have achieved great success in many data processing applications.However,high computational complexity and storage cost make deep learning difficult to be used on resource-constrained devices,and it is not environmental-friendly with much power cost.In this paper,we focus on low-rank optimization for efficient deep learning techniques.In the space domain,DNNs are compressed by low rank approximation of the network parameters,which directly reduces the storage requirement with a smaller number of network parameters.In the time domain,the network parameters can be trained in a few subspaces,which enables efficient training for fast convergence.The model compression in the spatial domain is summarized into three categories as pre-train,pre-set,and compression-aware methods,respectively.With a series of integrable techniques discussed,such as sparse pruning,quantization,and entropy coding,we can ensemble them in an integration framework with lower computational complexity and storage.In addition to summary of recent technical advances,we have two findings for motivating future works.One is that the effective rank,derived from the Shannon entropy of the normalized singular values,outperforms other conventional sparse measures such as the?_1 norm for network compression.The other is a spatial and temporal balance for tensorized neural networks.For accelerating the training of tensorized neural networks,it is crucial to leverage redundancy for both model compression and subspace training.展开更多
Based on the characteristics of high-end products,crowd-sourcing user stories can be seen as an effective means of gathering requirements,involving a large user base and generating a substantial amount of unstructured...Based on the characteristics of high-end products,crowd-sourcing user stories can be seen as an effective means of gathering requirements,involving a large user base and generating a substantial amount of unstructured feedback.The key challenge lies in transforming abstract user needs into specific ones,requiring integration and analysis.Therefore,we propose a topic mining-based approach to categorize,summarize,and rank product requirements from user stories.Specifically,after determining the number of story categories based on py LDAvis,we initially classify“I want to”phrases within user stories.Subsequently,classic topic models are applied to each category to generate their names,defining each post-classification user story category as a requirement.Furthermore,a weighted ranking function is devised to calculate the importance of each requirement.Finally,we validate the effectiveness and feasibility of the proposed method using 2966 crowd-sourced user stories related to smart home systems.展开更多
The RPL(IPv6 Routing Protocol for Low-Power and Lossy Networks)protocol is essential for efficient communi-cation within the Internet of Things(IoT)ecosystem.Despite its significance,RPL’s susceptibility to attacks r...The RPL(IPv6 Routing Protocol for Low-Power and Lossy Networks)protocol is essential for efficient communi-cation within the Internet of Things(IoT)ecosystem.Despite its significance,RPL’s susceptibility to attacks remains a concern.This paper presents a comprehensive simulation-based analysis of the RPL protocol’s vulnerability to the decreased rank attack in both static andmobilenetwork environments.We employ the Random Direction Mobility Model(RDM)for mobile scenarios within the Cooja simulator.Our systematic evaluation focuses on critical performance metrics,including Packet Delivery Ratio(PDR),Average End to End Delay(AE2ED),throughput,Expected Transmission Count(ETX),and Average Power Consumption(APC).Our findings illuminate the disruptive impact of this attack on the routing hierarchy,resulting in decreased PDR and throughput,increased AE2ED,ETX,and APC.These results underscore the urgent need for robust security measures to protect RPL-based IoT networks.Furthermore,our study emphasizes the exacerbated impact of the attack in mobile scenarios,highlighting the evolving security requirements of IoT networks.展开更多
Purpose:The quantitative rankings of over 55,000 institutions and their institutional programs are based on the individual rankings of approximately 30 million scholars determined by their productivity,impact,and qual...Purpose:The quantitative rankings of over 55,000 institutions and their institutional programs are based on the individual rankings of approximately 30 million scholars determined by their productivity,impact,and quality.Design/methodology/approach:The institutional ranking process developed here considers all institutions in all countries and regions,thereby including those that are established,as well as those that are emerging in scholarly prowess.Rankings of individual scholars worldwide are first generated using the recently introduced,fully indexed ScholarGPS database.The rankings of individual scholars are extended here to determine the lifetime and last-five-year Top 20 rankings of academic institutions over all Fields of scholarly endeavor,in 14 individual Fields,in 177 Disciplines,and in approximately 350,000 unique Specialties.Rankings associated with five specific Fields(Medicine,Engineering&Computer Science,Life Sciences,Physical Sciences&Mathematics,and Social Sciences),and in two Disciplines(Chemistry,and Electrical&Computer Engineering)are presented as examples,and changes in the rankings over time are discussed.Findings:For the Fields considered here,the Top 20 institutional rankings in Medicine have undergone the least change(lifetime versus last five years),while the rankings in Engineering&Computer Science have exhibited significant change.The evolution of institutional rankings over time is largely attributed to the recent emergence of Chinese academic institutions,although this emergence is shown to be highly Field-and Discipline-dependent.Practical implementations:Existing rankings of academic institutions have:(i)often been restricted to pre-selected institutions,clouding the potential discovery of scholarly activity in emerging institutions and countries;(ii)considered only broad areas of research,limiting the ability of university leadership to act on the assessments in a concrete manner,or in contrast;(iii)have considered only a narrow area of research for comparison,diminishing the broader applicability and impact of the assessment.In general,existing institutional rankings depend on which institutions are included in the ranking process,which areas of research are considered,the breadth(or granularity)of the research areas of interest,and the methodologies used to define and quantify research performance.In contrast,the methods presented here can provide important data over a broad range of granularity to allow responsible individuals to gauge the performance of any institution from the Overall(all Fields)level,to the level of the Specialty.The methods may also assist identification of the root causes of shifts in institution rankings,and how these shifts vary across hundreds of thousands of Fields,Disciplines,and Specialties of scholarly endeavor.Originality/value:This study provides the first ranking of all academic institutions worldwide over Fields,Disciplines,and Specialties based on a unique methodology that quantifies the productivity,impact,and quality of individual scholars.展开更多
In software testing,the quality of test cases is crucial,but manual generation is time-consuming.Various automatic test case generation methods exist,requiring careful selection based on program features.Current evalu...In software testing,the quality of test cases is crucial,but manual generation is time-consuming.Various automatic test case generation methods exist,requiring careful selection based on program features.Current evaluation methods compare a limited set of metrics,which does not support a larger number of metrics or consider the relative importance of each metric to the final assessment.To address this,we propose an evaluation tool,the Test Case Generation Evaluator(TCGE),based on the learning to rank(L2R)algorithm.Unlike previous approaches,our method comprehensively evaluates algorithms by considering multiple metrics,resulting in a more reasoned assessment.The main principle of the TCGE is the formation of feature vectors that are of concern by the tester.Through training,the feature vectors are sorted to generate a list,with the order of the methods on the list determined according to their effectiveness on the tested assembly.We implement TCGE using three L2R algorithms:Listnet,LambdaMART,and RFLambdaMART.Evaluation employs a dataset with features of classical test case generation algorithms and three metrics—Normalized Discounted Cumulative Gain(NDCG),Mean Average Precision(MAP),and Mean Reciprocal Rank(MRR).Results demonstrate the TCGE’s superior effectiveness in evaluating test case generation algorithms compared to other methods.Among the three L2R algorithms,RFLambdaMART proves the most effective,achieving an accuracy above 96.5%,surpassing LambdaMART by 2%and Listnet by 1.5%.Consequently,the TCGE framework exhibits significant application value in the evaluation of test case generation algorithms.展开更多
Objective:The objective of this study was to investigate the alterations and potential implications of the Osteoprotegerin(OPG)/Receptor Activator of Nuclear Factor-kappa B Ligand(RANKL)/Receptor Activator of Nuclear ...Objective:The objective of this study was to investigate the alterations and potential implications of the Osteoprotegerin(OPG)/Receptor Activator of Nuclear Factor-kappa B Ligand(RANKL)/Receptor Activator of Nuclear Factor-kappa B(RANK)signaling pathway factors in a murine model of sepsis-associated acute kidney injury(SA-AKI).This research aimed to offer novel insights into the mechanistic exploration of SA-AKI.Methods:The SA-AKI model group(CLP group)was established through cecal ligation and puncture surgery(CLP),while the control group consisted of sham-operated animals(Sham group)subjected only to laparotomy without cecal ligation and puncture.Blood samples were collected 24 h post-surgery,and murine kidney tissues were harvested upon euthanasia.Serum levels of Serum Creatinine(Scr)and Blood Urea Nitrogen(BUN)were quantified using assay kits.Furthermore,serum levels of interleukin-6(IL-6),tumor necrosis factor-alpha(TNF-α),and interleukin-1 beta(IL-1β)were assessed through enzyme-linked immunosorbent assay(ELISA).Renal tissue pathological alterations were examined employing hematoxylin-eosin staining(HE),and the mRNA and protein levels of OPG,RANKL,and RANK in murine kidney tissues were determined via reverse transcription-quantitative polymerase chain reaction(RT-qPCR)and Western blotting.Results:Comparative analysis revealed that,in comparison to the Sham group,the CLP group demonstrated a significant elevation in the levels of Scr,BUN,IL-6,TNF-α,and IL-1β,with statistically significant disparities(all P<0.05).Histopathological examination of the CLP group's kidneys unveiled glomerular congestion,edema,partial ischemic wrinkling,enlargement of interstitial spaces,the presence of necrotic epithelial cells in select renal tubules,tubular luminal dilation,varying degrees of interstitial edema,and infiltration by a limited number of inflammatory cells.In parallel,relative to the Sham group,the CLP group exhibited substantial upregulation in mRNA expression of OPG and RANK in renal tissues,while RANKL mRNA expression experienced marked downregulation,with statistically significant distinctions(all P<0.05).Moreover,in comparison with the Sham group,the CLP group demonstrated an elevation in protein expression of OPG and RANK in kidney tissues,whereas RANKL protein expression displayed significant downregulation,with statistically significant differences(all P<0.05).Conclusion:In a murine sepsis model,augmented expression of OPG and RANK,coupled with diminished RANKL expression,suggests the potential involvement of the OPG/RANKL/RANK signaling pathway in the pathophysiological progression of SA-AKI.展开更多
Multi-view Subspace Clustering (MVSC) emerges as an advanced clustering method, designed to integrate diverse views to uncover a common subspace, enhancing the accuracy and robustness of clustering results. The signif...Multi-view Subspace Clustering (MVSC) emerges as an advanced clustering method, designed to integrate diverse views to uncover a common subspace, enhancing the accuracy and robustness of clustering results. The significance of low-rank prior in MVSC is emphasized, highlighting its role in capturing the global data structure across views for improved performance. However, it faces challenges with outlier sensitivity due to its reliance on the Frobenius norm for error measurement. Addressing this, our paper proposes a Low-Rank Multi-view Subspace Clustering Based on Sparse Regularization (LMVSC- Sparse) approach. Sparse regularization helps in selecting the most relevant features or views for clustering while ignoring irrelevant or noisy ones. This leads to a more efficient and effective representation of the data, improving the clustering accuracy and robustness, especially in the presence of outliers or noisy data. By incorporating sparse regularization, LMVSC-Sparse can effectively handle outlier sensitivity, which is a common challenge in traditional MVSC methods relying solely on low-rank priors. Then Alternating Direction Method of Multipliers (ADMM) algorithm is employed to solve the proposed optimization problems. Our comprehensive experiments demonstrate the efficiency and effectiveness of LMVSC-Sparse, offering a robust alternative to traditional MVSC methods.展开更多
Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Anal...Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Analysis (RPCA) addresses these limitations by decomposing data into a low-rank matrix capturing the underlying structure and a sparse matrix identifying outliers, enhancing robustness against noise and outliers. This paper introduces a novel RPCA variant, Robust PCA Integrating Sparse and Low-rank Priors (RPCA-SL). Each prior targets a specific aspect of the data’s underlying structure and their combination allows for a more nuanced and accurate separation of the main data components from outliers and noise. Then RPCA-SL is solved by employing a proximal gradient algorithm for improved anomaly detection and data decomposition. Experimental results on simulation and real data demonstrate significant advancements.展开更多
A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with...A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.展开更多
基金supported by the National Natural Science Foundation of China(62171088,U19A2052,62020106011)the Medico-Engineering Cooperation Funds from University of Electronic Science and Technology of China(ZYGX2021YGLH215,ZYGX2022YGRH005)。
文摘Deep neural networks(DNNs)have achieved great success in many data processing applications.However,high computational complexity and storage cost make deep learning difficult to be used on resource-constrained devices,and it is not environmental-friendly with much power cost.In this paper,we focus on low-rank optimization for efficient deep learning techniques.In the space domain,DNNs are compressed by low rank approximation of the network parameters,which directly reduces the storage requirement with a smaller number of network parameters.In the time domain,the network parameters can be trained in a few subspaces,which enables efficient training for fast convergence.The model compression in the spatial domain is summarized into three categories as pre-train,pre-set,and compression-aware methods,respectively.With a series of integrable techniques discussed,such as sparse pruning,quantization,and entropy coding,we can ensemble them in an integration framework with lower computational complexity and storage.In addition to summary of recent technical advances,we have two findings for motivating future works.One is that the effective rank,derived from the Shannon entropy of the normalized singular values,outperforms other conventional sparse measures such as the?_1 norm for network compression.The other is a spatial and temporal balance for tensorized neural networks.For accelerating the training of tensorized neural networks,it is crucial to leverage redundancy for both model compression and subspace training.
基金supported by the National Natural Science Foundation of China(71690233,71901214)。
文摘Based on the characteristics of high-end products,crowd-sourcing user stories can be seen as an effective means of gathering requirements,involving a large user base and generating a substantial amount of unstructured feedback.The key challenge lies in transforming abstract user needs into specific ones,requiring integration and analysis.Therefore,we propose a topic mining-based approach to categorize,summarize,and rank product requirements from user stories.Specifically,after determining the number of story categories based on py LDAvis,we initially classify“I want to”phrases within user stories.Subsequently,classic topic models are applied to each category to generate their names,defining each post-classification user story category as a requirement.Furthermore,a weighted ranking function is devised to calculate the importance of each requirement.Finally,we validate the effectiveness and feasibility of the proposed method using 2966 crowd-sourced user stories related to smart home systems.
文摘The RPL(IPv6 Routing Protocol for Low-Power and Lossy Networks)protocol is essential for efficient communi-cation within the Internet of Things(IoT)ecosystem.Despite its significance,RPL’s susceptibility to attacks remains a concern.This paper presents a comprehensive simulation-based analysis of the RPL protocol’s vulnerability to the decreased rank attack in both static andmobilenetwork environments.We employ the Random Direction Mobility Model(RDM)for mobile scenarios within the Cooja simulator.Our systematic evaluation focuses on critical performance metrics,including Packet Delivery Ratio(PDR),Average End to End Delay(AE2ED),throughput,Expected Transmission Count(ETX),and Average Power Consumption(APC).Our findings illuminate the disruptive impact of this attack on the routing hierarchy,resulting in decreased PDR and throughput,increased AE2ED,ETX,and APC.These results underscore the urgent need for robust security measures to protect RPL-based IoT networks.Furthermore,our study emphasizes the exacerbated impact of the attack in mobile scenarios,highlighting the evolving security requirements of IoT networks.
文摘Purpose:The quantitative rankings of over 55,000 institutions and their institutional programs are based on the individual rankings of approximately 30 million scholars determined by their productivity,impact,and quality.Design/methodology/approach:The institutional ranking process developed here considers all institutions in all countries and regions,thereby including those that are established,as well as those that are emerging in scholarly prowess.Rankings of individual scholars worldwide are first generated using the recently introduced,fully indexed ScholarGPS database.The rankings of individual scholars are extended here to determine the lifetime and last-five-year Top 20 rankings of academic institutions over all Fields of scholarly endeavor,in 14 individual Fields,in 177 Disciplines,and in approximately 350,000 unique Specialties.Rankings associated with five specific Fields(Medicine,Engineering&Computer Science,Life Sciences,Physical Sciences&Mathematics,and Social Sciences),and in two Disciplines(Chemistry,and Electrical&Computer Engineering)are presented as examples,and changes in the rankings over time are discussed.Findings:For the Fields considered here,the Top 20 institutional rankings in Medicine have undergone the least change(lifetime versus last five years),while the rankings in Engineering&Computer Science have exhibited significant change.The evolution of institutional rankings over time is largely attributed to the recent emergence of Chinese academic institutions,although this emergence is shown to be highly Field-and Discipline-dependent.Practical implementations:Existing rankings of academic institutions have:(i)often been restricted to pre-selected institutions,clouding the potential discovery of scholarly activity in emerging institutions and countries;(ii)considered only broad areas of research,limiting the ability of university leadership to act on the assessments in a concrete manner,or in contrast;(iii)have considered only a narrow area of research for comparison,diminishing the broader applicability and impact of the assessment.In general,existing institutional rankings depend on which institutions are included in the ranking process,which areas of research are considered,the breadth(or granularity)of the research areas of interest,and the methodologies used to define and quantify research performance.In contrast,the methods presented here can provide important data over a broad range of granularity to allow responsible individuals to gauge the performance of any institution from the Overall(all Fields)level,to the level of the Specialty.The methods may also assist identification of the root causes of shifts in institution rankings,and how these shifts vary across hundreds of thousands of Fields,Disciplines,and Specialties of scholarly endeavor.Originality/value:This study provides the first ranking of all academic institutions worldwide over Fields,Disciplines,and Specialties based on a unique methodology that quantifies the productivity,impact,and quality of individual scholars.
文摘In software testing,the quality of test cases is crucial,but manual generation is time-consuming.Various automatic test case generation methods exist,requiring careful selection based on program features.Current evaluation methods compare a limited set of metrics,which does not support a larger number of metrics or consider the relative importance of each metric to the final assessment.To address this,we propose an evaluation tool,the Test Case Generation Evaluator(TCGE),based on the learning to rank(L2R)algorithm.Unlike previous approaches,our method comprehensively evaluates algorithms by considering multiple metrics,resulting in a more reasoned assessment.The main principle of the TCGE is the formation of feature vectors that are of concern by the tester.Through training,the feature vectors are sorted to generate a list,with the order of the methods on the list determined according to their effectiveness on the tested assembly.We implement TCGE using three L2R algorithms:Listnet,LambdaMART,and RFLambdaMART.Evaluation employs a dataset with features of classical test case generation algorithms and three metrics—Normalized Discounted Cumulative Gain(NDCG),Mean Average Precision(MAP),and Mean Reciprocal Rank(MRR).Results demonstrate the TCGE’s superior effectiveness in evaluating test case generation algorithms compared to other methods.Among the three L2R algorithms,RFLambdaMART proves the most effective,achieving an accuracy above 96.5%,surpassing LambdaMART by 2%and Listnet by 1.5%.Consequently,the TCGE framework exhibits significant application value in the evaluation of test case generation algorithms.
基金Natural Science Foundation of Xinjiang Uygur Autonomous Region(No.2022D01C604)。
文摘Objective:The objective of this study was to investigate the alterations and potential implications of the Osteoprotegerin(OPG)/Receptor Activator of Nuclear Factor-kappa B Ligand(RANKL)/Receptor Activator of Nuclear Factor-kappa B(RANK)signaling pathway factors in a murine model of sepsis-associated acute kidney injury(SA-AKI).This research aimed to offer novel insights into the mechanistic exploration of SA-AKI.Methods:The SA-AKI model group(CLP group)was established through cecal ligation and puncture surgery(CLP),while the control group consisted of sham-operated animals(Sham group)subjected only to laparotomy without cecal ligation and puncture.Blood samples were collected 24 h post-surgery,and murine kidney tissues were harvested upon euthanasia.Serum levels of Serum Creatinine(Scr)and Blood Urea Nitrogen(BUN)were quantified using assay kits.Furthermore,serum levels of interleukin-6(IL-6),tumor necrosis factor-alpha(TNF-α),and interleukin-1 beta(IL-1β)were assessed through enzyme-linked immunosorbent assay(ELISA).Renal tissue pathological alterations were examined employing hematoxylin-eosin staining(HE),and the mRNA and protein levels of OPG,RANKL,and RANK in murine kidney tissues were determined via reverse transcription-quantitative polymerase chain reaction(RT-qPCR)and Western blotting.Results:Comparative analysis revealed that,in comparison to the Sham group,the CLP group demonstrated a significant elevation in the levels of Scr,BUN,IL-6,TNF-α,and IL-1β,with statistically significant disparities(all P<0.05).Histopathological examination of the CLP group's kidneys unveiled glomerular congestion,edema,partial ischemic wrinkling,enlargement of interstitial spaces,the presence of necrotic epithelial cells in select renal tubules,tubular luminal dilation,varying degrees of interstitial edema,and infiltration by a limited number of inflammatory cells.In parallel,relative to the Sham group,the CLP group exhibited substantial upregulation in mRNA expression of OPG and RANK in renal tissues,while RANKL mRNA expression experienced marked downregulation,with statistically significant distinctions(all P<0.05).Moreover,in comparison with the Sham group,the CLP group demonstrated an elevation in protein expression of OPG and RANK in kidney tissues,whereas RANKL protein expression displayed significant downregulation,with statistically significant differences(all P<0.05).Conclusion:In a murine sepsis model,augmented expression of OPG and RANK,coupled with diminished RANKL expression,suggests the potential involvement of the OPG/RANKL/RANK signaling pathway in the pathophysiological progression of SA-AKI.
文摘Multi-view Subspace Clustering (MVSC) emerges as an advanced clustering method, designed to integrate diverse views to uncover a common subspace, enhancing the accuracy and robustness of clustering results. The significance of low-rank prior in MVSC is emphasized, highlighting its role in capturing the global data structure across views for improved performance. However, it faces challenges with outlier sensitivity due to its reliance on the Frobenius norm for error measurement. Addressing this, our paper proposes a Low-Rank Multi-view Subspace Clustering Based on Sparse Regularization (LMVSC- Sparse) approach. Sparse regularization helps in selecting the most relevant features or views for clustering while ignoring irrelevant or noisy ones. This leads to a more efficient and effective representation of the data, improving the clustering accuracy and robustness, especially in the presence of outliers or noisy data. By incorporating sparse regularization, LMVSC-Sparse can effectively handle outlier sensitivity, which is a common challenge in traditional MVSC methods relying solely on low-rank priors. Then Alternating Direction Method of Multipliers (ADMM) algorithm is employed to solve the proposed optimization problems. Our comprehensive experiments demonstrate the efficiency and effectiveness of LMVSC-Sparse, offering a robust alternative to traditional MVSC methods.
文摘Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Analysis (RPCA) addresses these limitations by decomposing data into a low-rank matrix capturing the underlying structure and a sparse matrix identifying outliers, enhancing robustness against noise and outliers. This paper introduces a novel RPCA variant, Robust PCA Integrating Sparse and Low-rank Priors (RPCA-SL). Each prior targets a specific aspect of the data’s underlying structure and their combination allows for a more nuanced and accurate separation of the main data components from outliers and noise. Then RPCA-SL is solved by employing a proximal gradient algorithm for improved anomaly detection and data decomposition. Experimental results on simulation and real data demonstrate significant advancements.
文摘A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.
