为便于理解人工神经网络的训练过程，通过使用 VBA 编程在 Excel 中进行了人工神经网络的模拟计算。目前，该程序仅包含一个隐藏层，但各层的神经元个数及训练样本数量可以按实际场景无限制设定，各层参数及迭代数量也可自行设定。计算过程中，不仅可以实时显现迭代的中间数据，也可借助 Excel 的强大制图功能动态展示数据的迭代趋势，适合入门级学生学习。下载该程序可扫描右边二维码。[br] 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相关程序

用该程序模拟训练数据过程如下：[br][br] 单纯两类数据试验，随机选取 10 组数据（见表 2-7-1）为训练数据，以 [math]y=\frac{1}{2}x[/math]为分类界限，设定 [math]y-\frac{1}{2}x>0[/math]标记为 1 类[红色，图 2-7-7（a）分界线上方]， [math]y-\frac{1}{2}x<0[/math]标记为 0 类[蓝色，图 2-7-7（a）分界线下方]。通过该程序的 10 000 次迭代，总平均误差为 0.000 472 799。计算过程中，隐藏层的输出动态图[见图 2-7-7（b）]及输出层的动态图[见图 2-7-7（c）]也可展现。然后以 100 个随机数据作为验证值[见图 2-7-7（d）]，准确率达到 96.32%。[br][br] 表 2-7-1 随机 10 组数据表[br][img]data:image/png;base64,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[/img][br][table][tr][td][img]https://s21.ax1x.com/2025/02/17/pEMiUw8.png[/img][br][center]（a）图[/center][/td][td][img]https://s21.ax1x.com/2025/02/17/pEMiaTS.png[/img][br][center]（b）图[/center][/td][/tr][tr][td][img]https://s21.ax1x.com/2025/02/18/pEMUAsI.png[/img][br][center]（c）图[/center][/td][td][img]https://s21.ax1x.com/2025/02/18/pEMUELt.png[/img][br][center]（d）图[/center][/td][/tr][/table][br] 图 2-7-7 单纯两类分类图示