| 求解岭回归问题的加速增广投影算法 |
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| 引用本文： | 邱志红,潘宝珍,顾传青.求解岭回归问题的加速增广投影算法[J].高等学校计算数学学报,2020(2):133-147. |
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| 作者姓名： | 邱志红 潘宝珍 顾传青 |
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| 作者单位： | 上海大学理学院 |
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| 基金项目： | 国家自然科学基金资助项目(11371243);上海市重点学科资助项目(S30104)。 |
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| 摘 要： | 1引言考虑求解岭回归或者Tikhonov正则化最小二乘回归问题■这里X是一个m×n的复矩阵,β是一个n维未知向量,y是一个m维的复向量,λ是正则化参数,‖·‖2表示向量的欧拉范数.岭回归问题对病态数据的拟合效果要强于最小二乘法.目前,岭回归问题已广泛应用于数据分析、机器学习、电网等领域.近年来,一系列随机算法被用来求解大规模线性系统.
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| 关 键 词： | TIKHONOV正则化 岭回归 未知向量 最小二乘法 复矩阵 最小二乘回归 投影算法 随机算法 |
AN ACCELERATED AUGMENTED PROJECTION ALGORITHM FOR RIDGE REGRESSION PROBLEM |
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| Qiu Zhihong,Pan Baozhen,Gu Chuanqing.AN ACCELERATED AUGMENTED PROJECTION ALGORITHM FOR RIDGE REGRESSION PROBLEM[J].Numerical Mathematics A Journal of Chinese Universities,2020(2):133-147. |
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| Authors: | Qiu Zhihong Pan Baozhen Gu Chuanqing |
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| Institution: | (College of Sciences,Shanghai University,Shanghai 200444) |
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| Abstract: | In this paper,we proposed a new algorithm,an accelerated augmented projection(AIZ)algorithm to solve ridge regression problem or Tikhonov regularized least-squares problem.The algorithm is in augmented projection algorithm with random coordinate descent method to speed up.We prove the convergence of the accelerated augmented projection algorithm,and some numerical results are given to show that the algorithm has certain advantages. |
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| Keywords: | ridge regression problem randomized Kaczmarz algorithm Nesterov’s accelerated coordinate descent method |
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