DNA序列分类的数学模型  

The Mathematical Models on the Classification of The DNA Sequences

作　　者：吕金翅[1] 马小龙[1] 曹芳[1] 陶大程[1] 

机构地区：[1]中国科学技术大学,合肥230026

出　　处：《数学的实践与认识》2001年第1期46-53,共8页Mathematics in Practice and Theory

摘　　要：本文从三个不同的角度分别论述了如何对 DNA序列进行分类的问题 ,依据这三个角度分别建立了三类模型 .首先 ,从生物学背景和几何对称观点出发 ,建立了 DNA序列的三维空间曲线的表达形式 .建立了初步数学模型 -积分模型 ,并且通过模型函数计算得到了 1到 2 0号 DNA序列的分类结果 ,发现与题目所给分类结果相同 ,然后我们又对后 2 0个 DNA序列进行了分类 .然后 ,从人工神经网络的角度出发 ,得到了第二类数学模型 -人工神经网络模型 .并且选择了三种适用于模式分类的基本网络 ,即感知机模型 ,多层感知机 ( BP网络 )模型以及 LVQ矢量量化学习器 ,同时就本问题提出了对 BP网络的改进 (改进型多层感知机 ) ,最后采用多种训练方案 ,均得到了较理想的分类结果 .同时也发现了通过人工神经网络的方法得到的分类结果与积分模型得到的分类结果是相同的 (前四十个 ) .最后 ,我们对碱基赋予几何意义 :A.C.G.T分别表示右 .下 .左 .上 .用 DNA序列控制平面上点的移动 ,每个序列得到一个游动曲线 ,提取游动方向趋势作为特征 ,建立起了模型函数 ,同时也得到了后二十个 DNA序列的分类结果 ,而且发现结果与上述两个模型所得到的分类结果几乎相同 (其中有一个不同 ,在本模型中表示为不可分的 ) .此模型保留的信息量更多 。This paper deals with the problem of how to classify the DNA sequences from three different angles and accordingly establishes three kinds of models. Firstly,on the point of biological background and geometrical symmetry,we established a descriptive model of 3- dimensional space curve on the DNA sequence,by which we got a rudimentary mathematical model- Calculus model.Through the integration of the model function, we have acquired the classification results of the DNA sequences from 1 to 2 0 ,and found them identical to the classification results given by the problem.Then we classified the latter2 0 DNA sequences. Then,on the view of the artificial neural networks,a second model- The Artificial neural networks model was established.We chosen three kinds of basic networks,which well fit into the classification atlast.And by the same time,we proposed the improvementofthe BPnetwork, and finally procured comparatively ideal classification results by various training programmes. also,we found the results identical to what we have got by Calculus model. By the end,we endowed A,C,G,T with geometrical meaning:A indicates right,while C as down,G as up,T as left.We got a mobile curve from each sequence with the points of the plain moving according to the controlling of the DNA sequence.By following the feature of the moving direction,the model function was established.By the way we acquired the classification results of the latter2 0 DNA sequences and found them practically identical to the results of the two above models(One of results differently showed in this model is regarded as indivisible) .This model contains more information,and is more stable

关 键 词：DNA序列 分类 数学模型 积分模型 神经网络模型 

分 类 号：Q-332[生物学]