This paper deals with the calculation of a vector of reliable weights of decision alternatives on the basis of interval pairwise comparison judgments of experts. These weights are used to construct the ranking of deci...This paper deals with the calculation of a vector of reliable weights of decision alternatives on the basis of interval pairwise comparison judgments of experts. These weights are used to construct the ranking of decision alternatives and to solve selection problems, problems of ratings construction, resources allocation problems, scenarios evaluation problems, and other decision making problems. A comparative analysis of several popular models, which calculate interval weights on the basis of interval pairwise comparison matrices (IPCMs), was performed. The features of these models when they are applied to IPCMs with different inconsistency levels were identified. An algorithm is proposed which contains the stages for analyzing and increasing the IPCM inconsistency, calculating normalized interval weights, and calculating the ranking of decision alternatives on the basis of the resulting interval weights. It was found that the property of weak order preservation usually allowed identifying order-related intransitive expert pairwise comparison judgments. The correction of these elements leads to the removal of contradictions in resulting weights and increases the accuracy and reliability of results.展开更多
Supervised learning often requires a large number of labeled examples,which has become a critical bottleneck in the case that manual annotating the class labels is costly.To mitigate this issue,a new framework called ...Supervised learning often requires a large number of labeled examples,which has become a critical bottleneck in the case that manual annotating the class labels is costly.To mitigate this issue,a new framework called pairwise comparison(Pcomp)classification is proposed to allow training examples only weakly annotated with pairwise comparison,i.e.,which one of two examples is more likely to be positive.The previous study solves Pcomp problems by minimizing the classification error,which may lead to less robust model due to its sensitivity to class distribution.In this paper,we propose a robust learning framework for Pcomp data along with a pairwise surrogate loss called Pcomp-AUC.It provides an unbiased estimator to equivalently maximize AUC without accessing the precise class labels.Theoretically,we prove the consistency with respect to AUC and further provide the estimation error bound for the proposed method.Empirical studies on multiple datasets validate the effectiveness of the proposed method.展开更多
We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to c...We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to clarify one of the important properties of sequences of pairwise NQD random variables,so that we can point out some mistakes that have appeared in recent published papers.展开更多
部分和之和在实际问题如随机游动、时间序列分析、破产理论中有着广泛的应用.研究同分布和不同分布情况下,两两NQD随机变量序列部分和之和Tn=(sum from i=1 to n)Si的弱大数定律,其中Sn=(sum from i=1 to n)Xi,将两两NQD随机变量序列部...部分和之和在实际问题如随机游动、时间序列分析、破产理论中有着广泛的应用.研究同分布和不同分布情况下,两两NQD随机变量序列部分和之和Tn=(sum from i=1 to n)Si的弱大数定律,其中Sn=(sum from i=1 to n)Xi,将两两NQD随机变量序列部分和的弱大数定律推广到了部分和之和的情形.展开更多
Clustering is widely exploited in data mining.It has been proved that embedding weak label prior into clustering is effective to promote its performance.Previous researches mainly focus on only one type of prior.Howev...Clustering is widely exploited in data mining.It has been proved that embedding weak label prior into clustering is effective to promote its performance.Previous researches mainly focus on only one type of prior.However,in many real scenarios,two kinds of weak label prior information,e.g.,pairwise constraints and cluster ratio,are easily obtained or already available.How to incorporate them to improve clustering performance is important but rarely studied.We propose a novel constrained Clustering with Weak Label Prior method(CWLP),which is an integrated framework.Within the unified spectral clustering model,the pairwise constraints are employed as a regularizer in spectral embedding and label proportion is added as a constraint in spectral rotation.To approximate a variant of the embedding matrix more precisely,we replace a cluster indicator matrix with its scaled version.Instead of fixing an initial similarity matrix,we propose a new similarity matrix that is more suitable for deriving clustering results.Except for the theoretical convergence and computational complexity analyses,we validate the effectiveness of CWLP through several benchmark datasets,together with its ability to discriminate suspected breast cancer patients from healthy controls.The experimental evaluation illustrates the superiority of our proposed approach.展开更多
文摘This paper deals with the calculation of a vector of reliable weights of decision alternatives on the basis of interval pairwise comparison judgments of experts. These weights are used to construct the ranking of decision alternatives and to solve selection problems, problems of ratings construction, resources allocation problems, scenarios evaluation problems, and other decision making problems. A comparative analysis of several popular models, which calculate interval weights on the basis of interval pairwise comparison matrices (IPCMs), was performed. The features of these models when they are applied to IPCMs with different inconsistency levels were identified. An algorithm is proposed which contains the stages for analyzing and increasing the IPCM inconsistency, calculating normalized interval weights, and calculating the ranking of decision alternatives on the basis of the resulting interval weights. It was found that the property of weak order preservation usually allowed identifying order-related intransitive expert pairwise comparison judgments. The correction of these elements leads to the removal of contradictions in resulting weights and increases the accuracy and reliability of results.
基金Natural Science Foundation of Jiangsu Province,China(BK20222012,BK20211517)National Key R&D Program of China(2020AAA0107000)National Natural Science Foundation of China(Grant No.62222605)。
文摘Supervised learning often requires a large number of labeled examples,which has become a critical bottleneck in the case that manual annotating the class labels is costly.To mitigate this issue,a new framework called pairwise comparison(Pcomp)classification is proposed to allow training examples only weakly annotated with pairwise comparison,i.e.,which one of two examples is more likely to be positive.The previous study solves Pcomp problems by minimizing the classification error,which may lead to less robust model due to its sensitivity to class distribution.In this paper,we propose a robust learning framework for Pcomp data along with a pairwise surrogate loss called Pcomp-AUC.It provides an unbiased estimator to equivalently maximize AUC without accessing the precise class labels.Theoretically,we prove the consistency with respect to AUC and further provide the estimation error bound for the proposed method.Empirical studies on multiple datasets validate the effectiveness of the proposed method.
基金Supported by the National Natural Science Foundation of China (10671149)
文摘We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to clarify one of the important properties of sequences of pairwise NQD random variables,so that we can point out some mistakes that have appeared in recent published papers.
文摘部分和之和在实际问题如随机游动、时间序列分析、破产理论中有着广泛的应用.研究同分布和不同分布情况下,两两NQD随机变量序列部分和之和Tn=(sum from i=1 to n)Si的弱大数定律,其中Sn=(sum from i=1 to n)Xi,将两两NQD随机变量序列部分和的弱大数定律推广到了部分和之和的情形.
基金supported by the National Key R&D Program(No.2022ZD0114803)the National Natural Science Foundation of China(Grant Nos.62136005,61922087).
文摘Clustering is widely exploited in data mining.It has been proved that embedding weak label prior into clustering is effective to promote its performance.Previous researches mainly focus on only one type of prior.However,in many real scenarios,two kinds of weak label prior information,e.g.,pairwise constraints and cluster ratio,are easily obtained or already available.How to incorporate them to improve clustering performance is important but rarely studied.We propose a novel constrained Clustering with Weak Label Prior method(CWLP),which is an integrated framework.Within the unified spectral clustering model,the pairwise constraints are employed as a regularizer in spectral embedding and label proportion is added as a constraint in spectral rotation.To approximate a variant of the embedding matrix more precisely,we replace a cluster indicator matrix with its scaled version.Instead of fixing an initial similarity matrix,we propose a new similarity matrix that is more suitable for deriving clustering results.Except for the theoretical convergence and computational complexity analyses,we validate the effectiveness of CWLP through several benchmark datasets,together with its ability to discriminate suspected breast cancer patients from healthy controls.The experimental evaluation illustrates the superiority of our proposed approach.
