【作者】 刘向阳；

【导师】 王如云；

【作者基本信息】 河海大学 ， 应用数学， 2003， 硕士

【摘要】 考虑到在很多情况下，人们更关心预报模型的预报值与实际值的相对误差情况，从而本文采用实际输出与希望输出的相对误差的平方和作为目标函数，给出了一种基于相对误差平方和为最小的BP算法。考虑到网络的实际输出值介于0到1之间，对实际问题的理想输出值给出了一种规范化处理方法。通过大量算例检验证实，在基于相对误差平方和为检验标准前提下，利用所给算法求得的拟合值或预报结果优于传统的基于绝对误差平方和作为目标函数的BP算法所得结果。 由于评价人工神经网络最终学习效果是通过累积误差来进行的，从而我们直接瞄准累积误差来研究多层人工神经网络快速学习的算法。我们首先简单介绍基于累积误差的梯形下降法，在此基础上，给出了一种自适应学习速率的调整方案。经过大量算例检验，在相同的精度要求下，本文算法的收敛速度大大加快，并有效地克服了一般的基于累积误差的梯形下降法在学习过程中所具有的震荡性。 基于误差逆传播算法对图像进行压缩的工作已有很多，但存在着人工神经网络训练时间较长，精度偏低等问题。考虑到利用三层及三层以上BP网络对图像压缩，其有效信息是中间层单元上的输出值和中间层与输出层之间的连接权，而输入层与中间层的连接权是冗余的，以至于对学习速度和压缩质量有负面影响。基于此我们提出了新型二层误差逆传播网络拓扑结构和算法，为进一步提高图像压缩的压缩比和压缩质量，我们提出了新型三层误差逆传播网络拓扑结构和算法。经过上机压缩测试，相对于三层BP网络、三层以上BP网络以及嵌套BP网络图像压缩的压缩比、学习速度和压缩质量都有很大提高，取得了很好的效果。更多还原

【Abstract】 As in many cases, people pay more attention to the relative error between actual output values and the idea output values, in this paper, an improved BP algorithm based on the smallest square sum of the relative error is proposed, which looks on the square sum of relative error between the idea output and the actual output as the object function. Because the network’s actual output values are between 0 and 1, a method of standardization management is given to the idea output of actual problem in this paper. It has been proved in many examples that the BP algorithm based in the square sum of the relative error is better than the conventional BP method.Since we value the learning effect of neural networks by cumulative error, the paper pay direct attention to it to study the BP algorithm. First, we introduce the trapezoid drop method based on cumulative error, and give a study way of adaptation. It has been proved in many examples that in the same precision need our algorithm get a good result in the convergence speed, and has effectively solved the convergence shake of algorithm study in generic trapezoid drop method.There has been many techniques of image compression based upon back propagationarithmetic, but they all have their own limits, the long study speed and lower compression quality. In the process of image compression, Considering that the three or more layers BP networks have some redundancies in the weights between input layer and meddle layer so as to effect the network’s study speed and compression quality, we bring forward a new two layers back propagation networks and it’s arithmetic. To get the much more quality and rate of image compression, we bring forward another new three layers back propagation networks and it’s arithmetic. It has been proved in many examples that the new networks get a good result in the compression rate, study speed and compression quality of image compression than other back propagations.更多还原