中文摘要：

量子群作为经典李群、李代数的基本对称概念的推广,有着丰富的代数、几何及物理性质.本文基于量子群的基本理论,结合药物分子设计中的分子对接问题,在李群机器学习的基础上提出了一个基于量子群的分子对接药物设计方法,从而进一步丰富了李群机器学习理论.本文首先建立了基于量子群的分子对接模型,并设计了基于量子群生成元的分子匹配算法,运用此算法对小分子数据库中的分子进行对接,并将试验结果与Autodock4.0、分子动力学算法的对接时间和精度进行比较和分析.实例测试表明了量子群的理论与药物分子对接相结合的合理性及有效性.

英文摘要：

People have investigated quantum group in certain aspects for a long time. However, most of them limited themselves to pure grouptheoretical or physical approaches, so many proterties of quantum group haven＇t been explored until now. As a generalization of classical Lie group and basic symmetrical conceptions of Lie algebra, quantum group has abundant algebraic, geometrical and physical properties, and shows its particular advantages in solving non commutative and non-symmetrical problems in machine learning. On the other hand, molecular docking is becoming more and more important in drug design. So many methods and algorithms are used in molecular docking. Thus, in this paper we introduce quantum group into machine learning and propose a quantum group based molecular docking. We first design molecular docking model based on quantum grouple, and present a quantum group generators based molecular docking algorithm. We compare the accuracy and the time required with well known and commonly used molecular docking methods like Autodock and molucular dynamics based algorithm. We show that our algorithm is accurate, because of flexibility of its adopting quantum group generators to control the search space. In addition, this paper further enriches the theories of Lie group machine learning. Finally, we conclude that group theory is an emerging new direction in machine learning.