Partial least squares(PLS) regression is an important linear regression method that efficiently addresses the multiple correlation problem by combining principal component analysis and multiple regression. In this pap...Partial least squares(PLS) regression is an important linear regression method that efficiently addresses the multiple correlation problem by combining principal component analysis and multiple regression. In this paper, we present a quantum partial least squares(QPLS) regression algorithm. To solve the high time complexity of the PLS regression, we design a quantum eigenvector search method to speed up principal components and regression parameters construction. Meanwhile, we give a density matrix product method to avoid multiple access to quantum random access memory(QRAM)during building residual matrices. The time and space complexities of the QPLS regression are logarithmic in the independent variable dimension n, the dependent variable dimension w, and the number of variables m. This algorithm achieves exponential speed-ups over the PLS regression on n, m, and w. In addition, the QPLS regression inspires us to explore more potential quantum machine learning applications in future works.展开更多
Boreal forests play an important role in global environment systems. Understanding boreal forest ecosystem structure and function requires accurate monitoring and estimating of forest canopy and biomass. We used parti...Boreal forests play an important role in global environment systems. Understanding boreal forest ecosystem structure and function requires accurate monitoring and estimating of forest canopy and biomass. We used partial least square regression （PLSR） models to relate forest parameters, i.e. canopy closure density and above ground tree biomass, to Landsat ETM＋ data. The established models were optimized according to the variable importance for projection （VIP） criterion and the bootstrap method, and their performance was compared using several statistical indices. All variables selected by the VIP criterion passed the bootstrap test （p〈0.05）. The simplified models without insignificant variables （VIP 〈1） performed as well as the full model but with less computation time. The relative root mean square error （RMSE%） was 29% for canopy closure density, and 58% for above ground tree biomass. We conclude that PLSR can be an effective method for estimating canopy closure density and above ground biomass.展开更多
为解决多级制造过程关键质量特性识别中多质量特性之间的相关性问题,将偏最小二乘回归方法(Partial Least Squares Regression,PLSR)引入模型构建与分析中。首先应用状态空间方法建立多级制造过程关键质量特性识别模型,进而利用PLSR方...为解决多级制造过程关键质量特性识别中多质量特性之间的相关性问题,将偏最小二乘回归方法(Partial Least Squares Regression,PLSR)引入模型构建与分析中。首先应用状态空间方法建立多级制造过程关键质量特性识别模型,进而利用PLSR方法解决质量特性间的多重共线性问题并进行模型分析,识别关键质量特性,最后以卷烟生产过程为例介绍了该方法的应用。实例表明,该方法不仅可以有效识别多级制造过程关键质量特性,而且能够建立各级过程的输出质量对最终产品质量的影响及其质量特性之间相互关系的模型,反映多级生产过程的结构特征和各级过程质量特性之间的因果关系,为多级制造过程质量分析与控制提供依据。展开更多
基金Project supported by the Fundamental Research Funds for the Central Universities, China (Grant No. 2019XD-A02)the National Natural Science Foundation of China (Grant Nos. U1636106, 61671087, 61170272, and 92046001)+2 种基金Natural Science Foundation of Beijing Municipality, China (Grant No. 4182006)Technological Special Project of Guizhou Province, China (Grant No. 20183001)the Foundation of Guizhou Provincial Key Laboratory of Public Big Data (Grant Nos. 2018BDKFJJ016 and 2018BDKFJJ018)。
文摘Partial least squares(PLS) regression is an important linear regression method that efficiently addresses the multiple correlation problem by combining principal component analysis and multiple regression. In this paper, we present a quantum partial least squares(QPLS) regression algorithm. To solve the high time complexity of the PLS regression, we design a quantum eigenvector search method to speed up principal components and regression parameters construction. Meanwhile, we give a density matrix product method to avoid multiple access to quantum random access memory(QRAM)during building residual matrices. The time and space complexities of the QPLS regression are logarithmic in the independent variable dimension n, the dependent variable dimension w, and the number of variables m. This algorithm achieves exponential speed-ups over the PLS regression on n, m, and w. In addition, the QPLS regression inspires us to explore more potential quantum machine learning applications in future works.
基金supported by the 948 Program of the State Forestry Administration (2009-4-43)the National Natura Science Foundation of China (No.30870420)
文摘Boreal forests play an important role in global environment systems. Understanding boreal forest ecosystem structure and function requires accurate monitoring and estimating of forest canopy and biomass. We used partial least square regression （PLSR） models to relate forest parameters, i.e. canopy closure density and above ground tree biomass, to Landsat ETM＋ data. The established models were optimized according to the variable importance for projection （VIP） criterion and the bootstrap method, and their performance was compared using several statistical indices. All variables selected by the VIP criterion passed the bootstrap test （p〈0.05）. The simplified models without insignificant variables （VIP 〈1） performed as well as the full model but with less computation time. The relative root mean square error （RMSE%） was 29% for canopy closure density, and 58% for above ground tree biomass. We conclude that PLSR can be an effective method for estimating canopy closure density and above ground biomass.
文摘为解决多级制造过程关键质量特性识别中多质量特性之间的相关性问题,将偏最小二乘回归方法(Partial Least Squares Regression,PLSR)引入模型构建与分析中。首先应用状态空间方法建立多级制造过程关键质量特性识别模型,进而利用PLSR方法解决质量特性间的多重共线性问题并进行模型分析,识别关键质量特性,最后以卷烟生产过程为例介绍了该方法的应用。实例表明,该方法不仅可以有效识别多级制造过程关键质量特性,而且能够建立各级过程的输出质量对最终产品质量的影响及其质量特性之间相互关系的模型,反映多级生产过程的结构特征和各级过程质量特性之间的因果关系,为多级制造过程质量分析与控制提供依据。
