【作者】 刘阳；

【导师】 郭东伟；

【作者基本信息】 吉林大学 ， 计算机应用技术， 2018， 硕士

【摘要】 复杂性和复杂系统是21世纪的中间研究课题之一。复杂网络概括了复杂系统的特征。很久以来,许多学者认为典型的网络是由许多个节点和连接这些节点的边组成,网络是点和边的集合,用随机图来表示。后来,这种想法发生了根本性的变化,主要归功于计算机对数据的处理、运算能力的迅猛发展。于是人们开始研究复杂网络的统计特性和的拓扑结构特性,经研究发现,尽管许多网络具有非常明显的随机性和复杂性,但是也会出现可以用数学或统计语言来描述的模式和规律,其中最重要的就是小世界效应。近些年来,人们已经认识到人工神经网络模型与大脑神经网络存在着差距,生物神经网络既不是规则网络也不是随机网络,它是介于规则网络与随机网络之间的一种复杂的网络结构。小世界网络它既具有规则网络的较大的聚类系数,又具有随机网络的较小的平均路径长度,因此小世界网络的优越性引起了人们的关注。由于在BP算法误差反向传播的过程中,权值修正阶段很容易陷入到局部极小点,而且传统的BP算法收敛速度较慢。因此本文优化了BP算法,提高了网络的收敛速度并且减少了网络陷入局部极小的可能性。由于全连接的网络中隐节点过多,节点间连接过于紧密,因此会存在过度拟合的问题。换句话说,对于不在训练样本中的数据,网络的学习能力不强,导致网络的实用价值下降,因此我们亟待找到一个合适的网络结构。长期以来,人们往往凭经验来确定网络的结构,为了保障精度常常偏向于冗余。因此不但网络训练的过程所需时间变长、增加了学习算法在学习速度上的负担,而且所得到所谓网络的高精度很有可能是冗余节点所导致的,会出现过拟合的现象,具体表现为对于训练样本之外的数据其网络训练的精度急剧下降、网路的泛化能力比较弱。本文提出一个基于E指数信息熵多层前馈小世界网络的修剪算法。基于信息熵的原理,计算每个隐节点的熵值,将那些熵值没有明显变化或者熵值变化小于阈值的隐节点进行修剪,通过不断地训练网络直至网络趋于稳定。实验结果表明,使用修剪算法的网络相比于未修剪的网络在准确率方面有明显的提高,在误差方面也做到了相应的控制,并且在一定程度上改善了过拟合的问题。更多还原

【Abstract】 Complexity and complex systems are one of the middle research topics of the twenty-first Century.Complex networks generalize the characteristics of complex systems.Slowly,as the rapid development of computer data processing and computing,the fundamental change has taken place in this case.Slowly,because of the rapid development of computer data processing and computing power,this situation has changed radically.People began to study the topology of large-scale complex networks.The research found that although many networks have obvious complexity and randomness,there will be clear patterns and rules that can be described in mathematical and statistical languages,and the most important is the small world effect.In recent years,it has been recognized that the there is a gapbetween artificial neural network and the brain neural network.The biological neural network is neither a random network nor a regular network,it is a network structure between the two.While the small world network has both a larger clustering coefficient of a regular network and a smaller average path length of a random network,so the superiority of the small world network has aroused people’s attention.As the BP algorithm converges slowly in the process of error back propagation,it is easy to fall into the local minimum point in the modified weight stage,so this paper Optimizes the BP algorithm to improve the convergence rate of the network and improve the problem that the network is easy to fall into the local minimal.The connection between nodes is too close because there are too many hidden nodes,as a result,the problem of overfitting is arisen.In other words,as for data that are not in the training sample,the learning ability of the network is not strong,resulting in a decrease in the practical value of the network.So we need to find a suitable network structure.For a long time,the structure of the network by experience,in order to ensure the accuracy is often biased in favor of redundancy,so the network training process required a longer time,increase the burden of learning algorithm in the training speed,and high accuracy of the resulting network is likely to be the result of the existence of redundant nodes,there have been fitted,as for the training sample data outside the accuracy declined sharply,the network generalization ability weak.In this paper,a pruning algorithm based on E exponent information entropy multi-layer feedforward small world network is proposed.Based on the principle of information entropy,we calculate the entropy value of each hidden node,prune the hidden nodes that have no significant change in entropy or entropy change is less than the threshold value,and constantly train the network until the network tends to be stable.Experimental results show that compared with unpruned networks,the pruning algorithm improves the accuracy significantly,and achieves the corresponding control in terms of error,and improves the over fitting problem to a certain extent.更多还原