计算机科学 ›› 2017, Vol. 44 ›› Issue (12): 42-47.doi: 10.11896/j.issn.1002-137X.2017.12.008
王梅,王莎莎,孙莺萁,宋考平,田枫,廖士中
WANG Mei, WANG Sha-sha, SUN Ying-qi, SONG Kao-ping, TIAN Feng and LIAO Shi-zhong
摘要： 正则化路径算法是数值求解支持向量回归机(Support Vector Regression,SVR)的有效方法。根据SVR正则化路径的分段线性性质,该类算法可在相当于一次SVR求解的时间复杂度内求得正则化参数的所有可能取值及对应SVR的解。由于在解路径建立过程中需要求解线性方程组,已有的精确计算方法难以处理大规模的样本数据,因此研究了正则化路径近似算法,并提出了SVR正则化路径近似算法SVRRPMCC。首先,应用Monte Carlo方法实现线性方程组系数矩阵的随机采样,求得近似系数矩阵； 然后,应用Cholesky分解方法实现快速求解系数逆矩阵；进一步,分析了SVRRPMCC算法的近似误差和计算复杂性；最后,在标准数据集上的实验验证了SVRRPMCC算法的合理性和较高的计算效率。
| [1] CHENG X Q,JIN X L,et al.Survey on Big Data System and Analytic Technology[J].Journal of Software,2014,5(9):1889-1908.(in Chinese) 程学旗,靳小龙,等.大数据系统和分析技术综述[J].软件学报,2014,5(9):1889-1908. [2] HUANG Y H.Research Progress on Big Data Machine Lear-ning System[J].Big Data Research,2015,1:1-20.(in Chinese) 黄宜华.大数据机器学习系统研究进展[J].大数据,2015,1:1-20. [3] HE Q,LI N,et al.A Survey of Machine Learning Algorithms for Big Data[J].Pattern Recognition and Artificial Intelligence,2014,7(4):327-335.(in Chinese) 何清,李宁,等.大数据下的机器学习算法综述[J].模式识别与人工智能,2014,7(4):327-335. [4] EFRON B,HASTIE T,JOHNSTONE I,et al.Least angle regression [J].The Annals of Statistics,2004,2(2):407-499. [5] HASTIE T,ROSSET S,Tibshirani R,et al.The entire regularization path for the support vector machine [J].Journal of Machine Learning Research,2004,5:1391-1415. [6] GUNTER L,ZHU J.Efficient computation and model selection for the support vector regression [J].Neural Computation,2007,9(6):1633-1655. [7] ROSSET S,ZHU J.Piecewise linear regularized solution paths [J].The Annals of Statistics,2007,5(3):1012-1030. [8] KARASUYAMA M,TAKEUCHI I.Suboptimal solution path algorithm for support vector machine [C]∥Proc.of the 28th Int.Conf.on Machine Learning.New York:Association for Computing Machinery,2011. [9] ONG C J,SHAO S Y,YANG J B.An improved algorithm for the solution of the regularization path of support vector machine [J].IEEE Transactions on Neural Networks,2010,1(3):451-462. [10] LIAO S Z,WANG M,ZHAO Z H.Regularization Path Algorithm of SVM via Positive Definite Matrix[J].Journal of Computer Research and Development,2013,0(11):2253-2261.(in Chinese) 廖士中,王梅,赵志辉.正定矩阵支持向量机正则化路径算法[J].计算机研究与发展,2013,0(11):2253-2261. [11] DING L Z,LIAO S Z.Approximate model selection on regularization path for support vector machines[J].Journal of Computer Research and Development,2012,9(6):1248-1255.(in Chinese) 丁立中,廖士中.基于正则化路径的支持向量机近似模型选择[J].计算机研究与发展,2012,9(6):1248-1255. [12] WANG L F,SHEN X T.Multi-category support vector ma-chines,feature selection and solution path [J].Statistica Sinica,2006,6(2):617-633. [13] RAKOTOMAMONJY A,DAVY M.One-class SVM regularization path and comparison with alpha seeding [C]∥Proc.of European Symp.on Artificial Neural Networks.Belgium:D-Facto Publications,2007:271-276. [14] ZAPIEN K,GRTNER T,GASSO G,et al.Regularisation path for ranking SVM [C]∥Proc.of European Symp.on Artificial Neural Networks.Belgium:D-Facto Publications,2008:415-420. [15] KARASUYAMA M,TAKEUCHI I.Nonlinear regularizationpath for quadratic loss support vector machines [J].IEEE Transactions on Neural Networks,2011,2(10):1613-1625. [16] LOOSLI G,GASSO G,CANU S.Regularization paths forv-SVM and v-SVR [C]∥Proc of the 4th International Sympo-sium on Neural Network.Heidelberg:Springer,2007:486-496. [17] GASSO G,ZAPIEN K,CANU S.Sparsity regularization path for semi-supervised SVM [C]∥The 6th Int Conf on Machine Learning and Applications.Los Alamitos,CA:IEEE Computer Society,2007:25-30. [18] WANG G,WANG F,CHEN T,et al.Solution path for manifold regularized semisupervised classification [J].IEEE Transactions on Systems,Man,and Cybernetics,Part B:Cybernetics,2012,42(2):308-319. [19] BACH F R,THIBAUX R,JORDAN M I.Computing regularization paths for learning multiple kernels [M]∥Advances in Neural Information Processing Systems 17.Cambridge,MA:MIT Press,2004:41-48. [20] BLOMBERG N,ROJAS C R,BO W.Approximate Regularization Path for Nuclear Norm Based H2 Model Reduction[J].Decision & Control,2015,5:3637-3641. [21] WANG M.Model Combination of SVM on Regularization Path [D].Tianjin:Tianjin University,2013.(in Chinese) 王梅.正则化路径上支持向量机模型组合[D].天津:天津大学,2013. [22] HASTIE T,TIBSHIRANI R,FRIEDMAN J H.The Elements of Statistical Learning:Data Mining,Inference,and Prediction [M].New York:Springer,2001. [23] BERROUBB C,GLAVIEUX A,THITIMASHIMA P.NearShannon limit error-correcting coding and decoding:Turbo codes[C]∥IEEE Int Conf on Communications.NewYork:IEEE,1993:1064-1071. [24] WEI C J,ZHANG C S,LIU J.A new method of solving inverse matrix based on Cholesky matrix [J].Electronic Design Engineering,2014,2(1):159-164.(in Chinese) 魏婵娟,张春水,刘健.一种基于Cholesky分解的快速矩阵求逆方法设计[J].电子设计工程,2014,2(1):159-164. [25] HORN R,JOHNSON C.Matrix Analysis [M].Cambridge,UK:Cambridge University Press,1985. |
| No related articles found! |
|
||
首页