Principal Component Analysis(PCA)is one of the most important feature extraction methods,and Kernel Principal Component Analysis(KPCA)is a nonlinear extension of PCA based on kernel methods.In real world,each input da...Principal Component Analysis(PCA)is one of the most important feature extraction methods,and Kernel Principal Component Analysis(KPCA)is a nonlinear extension of PCA based on kernel methods.In real world,each input data may not be fully assigned to one class and it may partially belong to other classes.Based on the theory of fuzzy sets,this paper presents Fuzzy Principal Component Analysis(FPCA)and its nonlinear extension model,i.e.,Kernel-based Fuzzy Principal Component Analysis(KFPCA).The experimental results indicate that the proposed algorithms have good performances.展开更多
Tensor robust principal component analysis has received a substantial amount of attention in various fields.Most existing methods,normally relying on tensor nuclear norm minimization,need to pay an expensive computati...Tensor robust principal component analysis has received a substantial amount of attention in various fields.Most existing methods,normally relying on tensor nuclear norm minimization,need to pay an expensive computational cost due to multiple singular value decompositions at each iteration.To overcome the drawback,we propose a scalable and efficient method,named parallel active subspace decomposition,which divides the unfolding along each mode of the tensor into a columnwise orthonormal matrix(active subspace)and another small-size matrix in parallel.Such a transformation leads to a nonconvex optimization problem in which the scale of nuclear norm minimization is generally much smaller than that in the original problem.We solve the optimization problem by an alternating direction method of multipliers and show that the iterates can be convergent within the given stopping criterion and the convergent solution is close to the global optimum solution within the prescribed bound.Experimental results are given to demonstrate that the performance of the proposed model is better than the state-of-the-art methods.展开更多
旋转机械的剩余使用寿命(remaining useful life, RUL)预测对工业设备预测和健康管理的具有重要意义。该文针对多传感器冗余数据导致旋转机械退化信息提取困难、剩余使用寿命预测效果差的问题,提出了一种基于核主成分分析-长短期记忆网...旋转机械的剩余使用寿命(remaining useful life, RUL)预测对工业设备预测和健康管理的具有重要意义。该文针对多传感器冗余数据导致旋转机械退化信息提取困难、剩余使用寿命预测效果差的问题,提出了一种基于核主成分分析-长短期记忆网络(kernel principal component analysis-long short term memory, KPCA-LSTM)的方法对旋转机械剩余使用寿命预测。首先,分析旋转机械的多维退化数据,选择可以表征旋转机械退化的数据;其次,对退化数据进行(kernel principal component analysis, KPCA)融合及特征提取,将降维融合的特征作为预测模型的输入;然后构建旋转机械的健康指标,并通过多阶微分划分旋转机械的不同健康状态,建立KPCA-LSTM模型对旋转机械的剩余使用寿命进行预测;最后,在实验室搭建的矿用减速器平台上进行了试验验证。试验结果表明:该文所提方法与LSTM、粒子群优化LSTM的方法比较,该方法预测效果优于其他两种模型,并降低模型训练的复杂性,减少预测用时。展开更多
Principal component analysis(PCA)is employed to extract the principal components(PCs)present in nuclear mass models for the first time.The effects from different nuclear mass models are reintegrated and reorganized in...Principal component analysis(PCA)is employed to extract the principal components(PCs)present in nuclear mass models for the first time.The effects from different nuclear mass models are reintegrated and reorganized in the extracted PCs.These PCs are recombined to build new mass models,which achieve better accuracy than the original theoretical mass models.This comparison indicates that using the PCA approach,the effects contained in different mass models can be collaborated to improve nuclear mass predictions.展开更多
Principal component analysis(PCA)is a widely used tool in machine learning algorithms,but it can be computationally expensive.In 2014,Lloyd,Mohseni&Rebentrost proposed a quantum PCA(qPCA)algorithm[Nat.Phys.10,631(...Principal component analysis(PCA)is a widely used tool in machine learning algorithms,but it can be computationally expensive.In 2014,Lloyd,Mohseni&Rebentrost proposed a quantum PCA(qPCA)algorithm[Nat.Phys.10,631(2014)]that has not yet been experimentally demonstrated due to challenges in preparing multiple quantum state copies and implementing quantum phase estimations.In this study,we presented a hardware-efficient approach for qPCA,utilizing an iterative approach that effectively resets the relevant qubits in a nuclear magnetic resonance(NMR)quantum processor.Additionally,we introduced a quantum scattering circuit that efficiently determines the eigenvalues and eigenvectors(principal components).As an important application of PCA,we focused on classifying thoracic CT images from COVID-19 patients and achieved high accuracy in image classification using the qPCA circuit implemented on the NMR system.Our experiment highlights the potential of near-term quantum devices to accelerate qPCA,opening up new avenues for practical applications of quantum machine learning algorithms.展开更多
水泥生产过程中,分解炉出口温度是非常重要的工艺参数,为了应对出口温度变量的多样性,文章提出一种核主成分分析(kernel principal component analysis,KPCA)与双向长短期记忆(bidirectional long short-term memory,BiLSTM)神经网络相...水泥生产过程中,分解炉出口温度是非常重要的工艺参数,为了应对出口温度变量的多样性,文章提出一种核主成分分析(kernel principal component analysis,KPCA)与双向长短期记忆(bidirectional long short-term memory,BiLSTM)神经网络相结合的温度预测组合模型用来预测分解炉的出口温度。通过KPCA筛选出影响因素的主成分从而达到数据降维目的,将降维后的主成分作为BiLSTM神经网络的输入,分解炉出口温度作为BiLSTM神经网络的输出。经BiLSTM神经网络训练,得到分解炉出口温度预测模型。通过对比验证表明,使用KPCA-BiLSTM相结合的温度预测模型具有较好的预测精度。展开更多
文摘Principal Component Analysis(PCA)is one of the most important feature extraction methods,and Kernel Principal Component Analysis(KPCA)is a nonlinear extension of PCA based on kernel methods.In real world,each input data may not be fully assigned to one class and it may partially belong to other classes.Based on the theory of fuzzy sets,this paper presents Fuzzy Principal Component Analysis(FPCA)and its nonlinear extension model,i.e.,Kernel-based Fuzzy Principal Component Analysis(KFPCA).The experimental results indicate that the proposed algorithms have good performances.
基金the HKRGC GRF 12306616,12200317,12300218 and 12300519,and HKU Grant 104005583.
文摘Tensor robust principal component analysis has received a substantial amount of attention in various fields.Most existing methods,normally relying on tensor nuclear norm minimization,need to pay an expensive computational cost due to multiple singular value decompositions at each iteration.To overcome the drawback,we propose a scalable and efficient method,named parallel active subspace decomposition,which divides the unfolding along each mode of the tensor into a columnwise orthonormal matrix(active subspace)and another small-size matrix in parallel.Such a transformation leads to a nonconvex optimization problem in which the scale of nuclear norm minimization is generally much smaller than that in the original problem.We solve the optimization problem by an alternating direction method of multipliers and show that the iterates can be convergent within the given stopping criterion and the convergent solution is close to the global optimum solution within the prescribed bound.Experimental results are given to demonstrate that the performance of the proposed model is better than the state-of-the-art methods.
文摘旋转机械的剩余使用寿命(remaining useful life, RUL)预测对工业设备预测和健康管理的具有重要意义。该文针对多传感器冗余数据导致旋转机械退化信息提取困难、剩余使用寿命预测效果差的问题,提出了一种基于核主成分分析-长短期记忆网络(kernel principal component analysis-long short term memory, KPCA-LSTM)的方法对旋转机械剩余使用寿命预测。首先,分析旋转机械的多维退化数据,选择可以表征旋转机械退化的数据;其次,对退化数据进行(kernel principal component analysis, KPCA)融合及特征提取,将降维融合的特征作为预测模型的输入;然后构建旋转机械的健康指标,并通过多阶微分划分旋转机械的不同健康状态,建立KPCA-LSTM模型对旋转机械的剩余使用寿命进行预测;最后,在实验室搭建的矿用减速器平台上进行了试验验证。试验结果表明:该文所提方法与LSTM、粒子群优化LSTM的方法比较,该方法预测效果优于其他两种模型,并降低模型训练的复杂性,减少预测用时。
基金supported by the State Key Laboratory of Nuclear Physics and Technology,Peking University(Grant No.NPT2023KFY02)the China Postdoctoral Science Foundation(Grant No.2021M700256)+2 种基金the National Key R&D Program of China(Grant No.2018YFA0404400)the National Natural Science Foundation of China(Grant Nos.11935003,11975031,12141501,and 12070131001)the High-performance Computing Platform of Peking University。
文摘Principal component analysis(PCA)is employed to extract the principal components(PCs)present in nuclear mass models for the first time.The effects from different nuclear mass models are reintegrated and reorganized in the extracted PCs.These PCs are recombined to build new mass models,which achieve better accuracy than the original theoretical mass models.This comparison indicates that using the PCA approach,the effects contained in different mass models can be collaborated to improve nuclear mass predictions.
基金supported by the National Key Research and Development Program of China(No.2019YFA0308100)the National Natural Science Foundation of China(Nos.12075110 and 12104213)+3 种基金the Science,Technology and Innovation Commission of Shenzhen Municipality(Nos.KQTD20190929173815000 and JCYJ20200109140803865)Pengcheng Scholars,Guangdong Innovative and Entrepreneurial Research Team Program(No.2019ZT08C044)Guangdong Provincial Key Laboratory(No.2019B121203002)Guangdong Basic and Applied Basic Research Foundation(No.2020A1515110987).
文摘Principal component analysis(PCA)is a widely used tool in machine learning algorithms,but it can be computationally expensive.In 2014,Lloyd,Mohseni&Rebentrost proposed a quantum PCA(qPCA)algorithm[Nat.Phys.10,631(2014)]that has not yet been experimentally demonstrated due to challenges in preparing multiple quantum state copies and implementing quantum phase estimations.In this study,we presented a hardware-efficient approach for qPCA,utilizing an iterative approach that effectively resets the relevant qubits in a nuclear magnetic resonance(NMR)quantum processor.Additionally,we introduced a quantum scattering circuit that efficiently determines the eigenvalues and eigenvectors(principal components).As an important application of PCA,we focused on classifying thoracic CT images from COVID-19 patients and achieved high accuracy in image classification using the qPCA circuit implemented on the NMR system.Our experiment highlights the potential of near-term quantum devices to accelerate qPCA,opening up new avenues for practical applications of quantum machine learning algorithms.
文摘水泥生产过程中,分解炉出口温度是非常重要的工艺参数,为了应对出口温度变量的多样性,文章提出一种核主成分分析(kernel principal component analysis,KPCA)与双向长短期记忆(bidirectional long short-term memory,BiLSTM)神经网络相结合的温度预测组合模型用来预测分解炉的出口温度。通过KPCA筛选出影响因素的主成分从而达到数据降维目的,将降维后的主成分作为BiLSTM神经网络的输入,分解炉出口温度作为BiLSTM神经网络的输出。经BiLSTM神经网络训练,得到分解炉出口温度预测模型。通过对比验证表明,使用KPCA-BiLSTM相结合的温度预测模型具有较好的预测精度。
