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
In this paper, we propose two weighted learning methods for the construction of single hidden layer feedforward neural networks. Both methods incorporate weighted least squares. Our idea is to allow the training insta...In this paper, we propose two weighted learning methods for the construction of single hidden layer feedforward neural networks. Both methods incorporate weighted least squares. Our idea is to allow the training instances nearer to the query to offer bigger contributions to the estimated output. By minimizing the weighted mean square error function, optimal networks can be obtained. The results of a number of experiments demonstrate the effectiveness of our proposed methods.展开更多
SF_(6)电气设备内部的分解组分可以通过可调谐吸收光谱技术进行检测,其中CO_(2)浓度反映了设备内部的绝缘缺陷情况。因此,通过准确测量CO_(2)浓度可以及时发现设备潜在的绝缘故障。为克服传统最小二乘法浓度反演模型稳定性较差的问题,...SF_(6)电气设备内部的分解组分可以通过可调谐吸收光谱技术进行检测,其中CO_(2)浓度反映了设备内部的绝缘缺陷情况。因此,通过准确测量CO_(2)浓度可以及时发现设备潜在的绝缘故障。为克服传统最小二乘法浓度反演模型稳定性较差的问题,文中基于改进的旗鱼优化算法(Improved Sailed Fish Optimizer,ISFO)与核极限学习机(Kernel Based Extreme Learning Machine,KELM)建立了ISFO-KELM气体浓度反演模型。利用多策略初始化方法、Levy随机步长、柯西变异和自适应t分布变异等技术提升了旗鱼优化算法寻优能力和跳出局部最优解能力。实验结果表明,该模型具有高精度和鲁棒性,并且在稳定性和泛化能力方面优于最小二乘法、极限学习机、反向传播(Back Propagation,BP)神经网络等传统方法,对评估SF_(6)电气设备运行状态具有重要意义。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 NSC under Grant No.NSC-100-2221-E-110-083-MY3 and NSC-101-2622-E-110-011-CC3"Aim for the Top University Plan"of the National Sun-Yat-Sen University and Ministry of Education
文摘In this paper, we propose two weighted learning methods for the construction of single hidden layer feedforward neural networks. Both methods incorporate weighted least squares. Our idea is to allow the training instances nearer to the query to offer bigger contributions to the estimated output. By minimizing the weighted mean square error function, optimal networks can be obtained. The results of a number of experiments demonstrate the effectiveness of our proposed methods.
文摘SF_(6)电气设备内部的分解组分可以通过可调谐吸收光谱技术进行检测,其中CO_(2)浓度反映了设备内部的绝缘缺陷情况。因此,通过准确测量CO_(2)浓度可以及时发现设备潜在的绝缘故障。为克服传统最小二乘法浓度反演模型稳定性较差的问题,文中基于改进的旗鱼优化算法(Improved Sailed Fish Optimizer,ISFO)与核极限学习机(Kernel Based Extreme Learning Machine,KELM)建立了ISFO-KELM气体浓度反演模型。利用多策略初始化方法、Levy随机步长、柯西变异和自适应t分布变异等技术提升了旗鱼优化算法寻优能力和跳出局部最优解能力。实验结果表明,该模型具有高精度和鲁棒性,并且在稳定性和泛化能力方面优于最小二乘法、极限学习机、反向传播(Back Propagation,BP)神经网络等传统方法,对评估SF_(6)电气设备运行状态具有重要意义。
