摘要
讨论了竞技排名现行总积分法,提出了以积分数为排名判据的方案.更进一步提出了特征向量算法,即根据数据构造水平比矩阵M,根据Perron-Frobenius定理,当M为不可约非负矩阵时,算出最大特征值对应的特征向量s,以s作为排名的依据.分别采用参数法和概率法构造矩阵M,在概率法中我们用极大似然估计的思想分析了比赛结果与两队水平比的关系,给出了每种算法的排名结果.
This paper discusses competitive ranking actual total integral method, brings forward the precept of ranking based on integral scores and further more raises eigenveetor algorithm which structures level comparison matrix M based on data. According to Theorem Perron-Fmbenius, When M is an irreducible nonnegative matrix,we work out maximum eigenvalue corresponding eigenvector s which is the ranking basis. Adopting parameter method and probability method separately to structure matrix M, by using probability method we analyse the connection between competition results and two teams level comparison based on the idea of maximum likelihood estimation. Each method＇s ranking result is given.
出处
《吉林师范大学学报（自然科学版）》
2010年第3期77-81,共5页
Journal of Jilin Normal University:Natural Science Edition
基金
2009年浙江省教学团队(JTB09056)
关键词
竞技排名
数学模型
最大特征
极大似然估计
competitive ranking
mathematical model
most important feature
maximum likelihood estimation
