求解最小闭包球问题改进的SMO-型算法-计算机工程与应用.PDFVIP

Computer Engineering and Applications 计算机工程与应用 2013 ，49 （3 ） 1 ⦾博士论坛⦾ 求解最小闭包球问题改进的SMO-型算法 1 2 丛伟杰 ，刘红卫 1 2 CONG Weijie , LIU Hongwei 1.西安邮电大学 理学院，西安 710121 2.西安电子科技大学 理学院，西安 710071 1.School of Science, Xi ’an University of Posts and Telecommunications, Xi ’an 710121, China 2.School of Science, Xidian University, Xi ’an 710071, China CONG Weijie, LIU Hongwei. Modified SMO-type algorithm for solving minimum enclosing ball problem. Computer En- gineering and Applications, 2013, 49 （3 ）：1-3. Abstract ：To study the Minimum Enclosing Ball （MEB ）problem of m points in n dimensions. By incorporating the technique of identification and elimination of interior points into Sequential Minimal Optimization （SMO）method, a modified SMO-type algorithm for the MEB problem is presented. This algorithm has the linear convergence. The numerical results show that the CPU time of the modified algorithm may improve by more than a speed-up factor of 10 on some large-scale date sets where m n . In particular, when n equals 100 and m equals 100 000, the modified SMO-type algorithm only needs to run about 8 s. In addition, it also takes only about 150 s for the large-scale data sets in which n equals 10 000 and m equals 1 000. Key words ：Minimum Enclosing Ball （MEB ）; identification and elimination of interior points; sequential minimal optimiza- tion; linear convergence; large-scale data sets n m 摘 要：研究 维空间中 个点的最小闭包球（MEB ）问题。通过结合确定并删除内部点的技术到序列最小最优化（SMO ） 方法中，提出一种近似求解MEB 问题的改进的SMO-型算法。证明了该算法具有线性收敛性。数值结果表明对于一些 m n n m 的大规模数据集，改进的算法与原算法相比速度可以提高10倍以上。尤其，当 等于100且 等于100 000 时，改进 n m 的SMO-型算