学习神经网络
看不进去高深的理论，就下了个期刊小论文（基于Excel技术平台人工神经网络BP模型及应用_邹文安.pdf），配合下载的一个excel（内含vba代码实现的BP神经网络 https://wenku.baidu.com/view/167d9400eff9aef8941e0655.html?from=search ）来学习。
干什么的呢，我猜是输入给定的二进制数，输出给定的二进制数，找到这个函数关系。
1 Const N = 7, M = 5, L = 4, P = 10 2 'N为输入层节点个数, M为隐含层节点个数, L为输出层节点个数, P为训练样本 3 Const PARA_eta = 0.5, PARA_alpha = 0.5, PARA_Emin = 0.2 4 'PARA_eta为学习率, PARA_alpha动量系数, PARA_Emin总误差的精度要求 5 Const Calcu_12 = 2 6 'Calcu_12取1为(常规BP算法);取2为(增加动量项); 7 8 Dim IN_PUT(1 To N), OUT_Y(1 To M), OUT_O(1 To L), OUT_dO(1 To L) As Variant 9 'IN_PUT(1 To N)为输入向量, OUT_Y(1 To M)为隐层输出向量, OUT_O(1 To L)为输出层输出向量, 10 'OUT_dO(1 To L)为期望输出向量, 11 12 Dim PARA_12(0 To N, 1 To M), PARA_23(0 To M, 1 To L) As Variant 13 'PARA_12(0 To N, 1 To M)为输入-隐层权值, PARA_23(0 To M, 1 To L)为隐层-输出权值 14 15 Dim PARA_12d1(1 To M), PARA_23d1(1 To L) As Variant '误差δ 16 Dim PARA_12d2(0 To N, 1 To M), PARA_23d2(0 To M, 1 To L) As Variant '误差Δ 17 Dim PARA_INT(0 To N, 1 To P), PARA_OUT(1 To L, 1 To P) As Variant 18 'PARA_INT(0 To N, 1 To P)为训练样本, PARA_OUT(1 To L, 1 To P)为期望输出 19 20 Dim PARA_E, PARA_Ep As Variant 21 'PARA_E为总输出误差, PARA_Ep训练样本误差 22 23 Dim q, p_i As Integer 24 Dim PARA_P(1 To 2, 1 To P) As Variant 25 Dim int_i1, int_i2, int_i3, int_i4, int_CC, I_Res As Integer 26 Dim int_p, int_k As Integer 27 Dim para_a1, para_a2, para_a3, time_a, time_b, C_C As Variant 28 29 'AA训练与测试 30 Sub AA训练与测试() 31 I_Res = MsgBox("欢迎使用训练网络程序！可以开始训练了吗?", 4 + 64, "<训练>提示！") 32 If I_Res = 6 Then 33 BB训练程序 34 If q > 10000 Then 35 Masg_box = MsgBox("总算结束了！“训练”运行结束。 ", 0 + 16, "<结束>提示！") 36 GoTo line1 37 End If 38 I_Res = MsgBox("是否测试网络？", 4 + 48, "<测试>提示！") 39 If I_Res = 6 Then 40 C_C = 0 41 CC测试程序 42 Masg_box = MsgBox("恭喜你！“测试”运行结束。 ", 0 + 0, "<结束>提示！") 43 End If 44 GoTo line1 45 End If 46 I_Res = MsgBox("欢迎使用测试网络程序！！！" & Chr(10) & "可以开始测试了吗？", 4 + 64, "<测试>提示！") 47 If I_Res = 6 Then 48 C_C = InputBox("请辅助测试用时所需的循环次数。", "<循环次数>提示！", 0) 49 If C_C <> "" Then 50 int_i1 = Len(C_C) 51 For int_i2 = 1 To int_i1 52 If Asc(Mid(C_C, int_i2, 1)) < 48 Or Asc(Mid(C_C, int_i2, 1)) > 57 Then 53 GoTo line1 54 End If 55 Next int_i2 56 CC测试程序 57 End If 58 End If 59 line1: 60 End Sub 61 '结束AA训练与测试 62 63 'AA训练程序 64 Function BB训练程序() 65 66 Worksheets("Sheet2").Activate '激活工作表Sheet2 67 '读取训练输入距阵 68 For int_i1 = 1 To P 69 PARA_INT(0, int_i1) = -1 70 For int_i2 = 1 To N 71 PARA_INT(int_i2, int_i1) = Sheet1.Cells(int_i2 + 1, int_i1).Value 72 Next int_i2 73 Next int_i1 74 '结束读取训练输入距阵 75 76 '读取期望输出距阵 77 For int_i1 = 1 To P 78 For int_i2 = 1 To L 79 PARA_OUT(int_i2, int_i1) = Sheet1.Cells(int_i2 + 10, int_i1).Value 80 Next int_i2 81 Next int_i1 82 '结束期望输出距阵 83 84 '权值距阵赋初值 85 For int_i1 = 1 To M 86 For int_i2 = 0 To N 87 PARA_12(int_i2, int_i1) = (Rnd() - 0.5) 88 Next int_i2 89 Next int_i1 90 For int_i1 = 1 To L 91 For int_i2 = 0 To M 92 If int_i2 Mod 2 Then '如果行数对2取余等于1则赋值为1 93 PARA_23(int_i2, int_i1) = 1 94 Else 95 PARA_23(int_i2, int_i1) = -1 96 End If 97 Next int_i2 98 Next int_i1 99 '结束权值距阵赋初值 100 101 '清除以有的输出距阵V 102 For int_i1 = 0 To N 103 For int_i2 = 1 To M + 2 104 Sheet2.Cells(int_i1 + 5, int_i2).Value = "" 105 Next int_i2 106 Next int_i1 107 '结束清除 108 109 '清除以有的输出距阵W 110 For int_i1 = 0 To M + 2 111 For int_i2 = 1 To L 112 Sheet2.Cells(int_i1 + 14, int_i2).Value = "" 113 Next int_i2 114 Next int_i1 115 '结束清除 116 117 q = 0 118 '总训练次数归零 119 120 Sheet2.Range(Cells(2, 5), Cells(3, 7)).ClearContents 121 time_a = Now() 122 '计算开始时刻 123 124 Stude1: 125 '学习准备 126 PARA_Ep = 0 '训练样本误差 127 '随机排序训练样本 128 For int_i1 = 1 To P 129 PARA_P(1, int_i1) = int_i1 130 PARA_P(2, int_i1) = Rnd() 131 Next int_i1 132 For int_i1 = 1 To P - 1 133 For int_i2 = int_i1 + 1 To P 134 If PARA_P(2, int_i1) > PARA_P(2, int_i2) Then '如果PARA_P第二行随机数 前面的大于后面的，那么进行交换，升序排列 135 para_a1 = PARA_P(1, int_i1) 136 PARA_P(1, int_i1) = PARA_P(1, int_i2) '第一行为序号，也跟着随机数同位移动，最终随机数升序，序号随机 137 PARA_P(1, int_i2) = para_a1 138 para_a2 = PARA_P(2, int_i1) 139 PARA_P(2, int_i1) = PARA_P(2, int_i2) 140 PARA_P(2, int_i2) = para_a2 141 End If 142 Next int_i2 143 Next int_i1 144 '结束随机排序训练样本 145 '结束学习准备 146 147 '开始学习 148 For int_p = 1 To P '循环10个（随机排位的）样本 149 int_k = PARA_P(1, int_p) '随机的int_k决定取出输入样本的第int_k个，也就是PARA_INT的第 int_k 列 150 For int_i1 = 1 To N 151 IN_PUT(int_i1) = PARA_INT(int_i1, int_k) '将总样本中某个样本放入一维数组 152 Next int_i1 153 For int_i1 = 1 To L 154 OUT_dO(int_i1) = PARA_OUT(int_i1, int_k) '将对应样本对应的期望输出输入一维数组 155 Next int_i1 156 157 '计算隐层各节点输出 158 For int_i1 = 1 To M 159 para_a1 = -1 * PARA_12(0, int_i1) '这个相当于偏移的b，或则称为阈值，取第一行权重值的相反数 160 For int_i2 = 1 To N 161 para_a1 = para_a1 + IN_PUT(int_i2) * PARA_12(int_i2, int_i1) 'IN_PUT为某个输入样本， 162 Next int_i2 163 OUT_Y(int_i1) = 1 / (1 + Exp(-para_a1)) 164 Next int_i1 165 '结束计算实际隐层各节点输出 166 167 '计算输出层各节点输出 168 For int_i1 = 1 To L 169 para_a1 = -1 * PARA_23(0, int_i1) 170 For int_i2 = 1 To M 171 para_a1 = para_a1 + OUT_Y(int_i2) * PARA_23(int_i2, int_i1) 172 Next int_i2 173 OUT_O(int_i1) = 1 / (1 + Exp(-para_a1)) 174 Next int_i1 175 '结束计算输出层各节点输出 176 177 '计算误差 178 para_a1 = 0 179 For int_i1 = 1 To L 180 para_a1 = para_a1 + (OUT_dO(int_i1) - OUT_O(int_i1)) ^ 2 'para_a1为某列的样本的所有元素的误差和delta？ 181 Next int_i1 182 '训练样本误差的平方， 一个样本就是一列数。 PARA_E为总输出误差 183 PARA_Ep = PARA_Ep + para_a1 184 '累加 - 训练样本误差的平方 185 '结束计算误差 186 187 '计算δ 求PARA_23d1 188 For int_i1 = 1 To L 189 PARA_23d1(int_i1) = (OUT_dO(int_i1) - OUT_O(int_i1)) * (1 - OUT_O(int_i1)) * OUT_O(int_i1) 'deltajk 190 Next int_i1 191 ' 求 PARA_12d1 192 For int_i1 = 1 To M '权值动量项 193 para_a1 = 0 194 For int_i2 = 1 To L 195 para_a1 = para_a1 + PARA_23d1(int_i2) * PARA_23(int_i1, int_i2) 'ADD（deltajk*Wjk） 196 Next int_i2 197 PARA_12d1(int_i1) = para_a1 * (1 - OUT_Y(int_i1)) * OUT_Y(int_i1) 198 Next int_i1 199 '结束计算δ 200 201 Select Case Calcu_12 '取1为(常规BP算法);取2为(增加动量项); 202 Case 1 203 '权值调整(常规BP算法) 204 For int_i1 = 1 To L 205 PARA_23(0, int_i1) = PARA_23(0, int_i1) + PARA_eta * PARA_23d1(int_i1) * (-1) 206 For int_i2 = 1 To M 207 PARA_23(int_i2, int_i1) = PARA_23(int_i2, int_i1) + PARA_eta * PARA_23d1(int_i1) * OUT_Y(int_i2) 208 Next int_i2 209 Next int_i1 210 For int_i1 = 1 To M 211 PARA_12(0, int_i1) = PARA_12(0, int_i1) + PARA_eta * PARA_12d1(int_i1) * (-1) 212 For int_i2 = 1 To N 213 PARA_12(int_i2, int_i1) = PARA_12(int_i2, int_i1) + PARA_eta * PARA_12d1(int_i1) * IN_PUT(int_i2) 214 Next int_i2 215 Next int_i1 216 '结束权值调整(常规BP算法) 217 Case 2 218 '权值调整(增加动量项) 219 For int_i1 = 1 To L 220 PARA_23(0, int_i1) = PARA_23(0, int_i1) + PARA_eta * PARA_23d1(int_i1) * (-1) 221 PARA_23(0, int_i1) = PARA_23(0, int_i1) + PARA_alpha * PARA_23d2(0, int_i1) 222 PARA_23d2(0, int_i1) = PARA_eta * PARA_23d1(int_i1) * (-1) 223 For int_i2 = 1 To M 224 PARA_23(int_i2, int_i1) = PARA_23(int_i2, int_i1) + PARA_eta * PARA_23d1(int_i1) * OUT_Y(int_i2) 225 PARA_23(int_i2, int_i1) = PARA_23(int_i2, int_i1) + PARA_alpha * PARA_23d2(int_i2, int_i1) 226 PARA_23d2(int_i2, int_i1) = PARA_eta * PARA_23d1(int_i1) * OUT_Y(int_i2) 227 Next int_i2 228 Next int_i1 229 For int_i1 = 1 To M 230 PARA_12(0, int_i1) = PARA_12(0, int_i1) + PARA_eta * PARA_12d1(int_i1) * (-1) 231 PARA_12(0, int_i1) = PARA_12(0, int_i1) + PARA_alpha * PARA_12d2(0, int_i1) 232 PARA_12d2(0, int_i1) = PARA_eta * PARA_12d1(int_i1) * (-1) 233 For int_i2 = 1 To N 234 PARA_12(int_i2, int_i1) = PARA_12(int_i2, int_i1) + PARA_eta * PARA_12d1(int_i1) * IN_PUT(int_i2) 235 PARA_12(int_i2, int_i1) = PARA_12(int_i2, int_i1) + PARA_alpha * PARA_12d2(int_i2, int_i1) 236 PARA_12d2(int_i2, int_i1) = PARA_eta * PARA_12d1(int_i1) * IN_PUT(int_i2) 237 Next int_i2 238 Next int_i1 239 '结束权值调整(增加动量项) 240 End Select 241 242 q = q + 1 243 Sheet2.Cells(3, 1).Value = q 244 '输出总训练次数 245 246 If q > 10000 Then 247 GoTo Fin_Calcu 248 End If 249 '输出总训练次数超过一万次，误差未达到精度要求，结束训练。 250 251 '训练一次完毕,取下一个训练样本 252 Next int_p 253 '结束学习 254 255 PARA_E = Sqr(PARA_Ep / P) 256 '总输出误差 257 Sheet2.Cells(3, 2).Value = PARA_E 258 259 If PARA_E > PARA_Emin Then '检查误差是否达到精度要求 PARA_E为总输出误差 260 GoTo Stude1 '误差未达到精度要求,返回“学习准备”-“开始学习” 261 End If 262 263 Fin_Calcu: 264 265 time_b = Now() 266 '计算结束时刻 267 268 Sheet2.Cells(2, 5) = "用时" 269 Sheet2.Cells(3, 5) = time_b - time_a 270 Sheet2.Cells(2, 6) = "开始" 271 Sheet2.Cells(3, 6) = time_a 272 Sheet2.Cells(2, 7) = "结束" 273 Sheet2.Cells(3, 7) = time_b 274 '输出计算用时情况 275 276 '输出PARA_12距阵的值 277 For int_i1 = 0 To N 278 For int_i2 = 1 To M 279 Sheet2.Cells(int_i1 + 5, int_i2).Value = PARA_12(int_i1, int_i2) 280 Next int_i2 281 Next int_i1 282 '结束输出PARA_12距阵的值 283 284 '输出PARA_23距阵的值 285 For int_i1 = 0 To M 286 For int_i2 = 1 To L 287 Sheet2.Cells(int_i1 + 14, int_i2).Value = PARA_23(int_i1, int_i2) 288 Next int_i2 289 Next int_i1 290 '结束输出PARA_23距阵的值 291 292 End Function 293 'FIN AA训练程序 294 295 Function CC测试程序() 296 297 Worksheets("Sheet3").Activate '激活工作表Sheet3 298 299 '读取输入矩阵 300 For int_i1 = 1 To P 301 PARA_INT(0, int_i1) = -1 302 For int_i2 = 1 To N 303 PARA_INT(int_i2, int_i1) = Sheet1.Cells(int_i2 + 1, int_i1).Value 304 Next int_i2 305 Next int_i1 306 '结束读取输入矩阵 307 308 '读取权值矩阵 309 For int_i1 = 1 To M 310 For int_i2 = 0 To N 311 PARA_12(int_i2, int_i1) = Sheet2.Cells(int_i2 + 5, int_i1).Value 'V 312 Next int_i2 313 Next int_i1 314 For int_i1 = 1 To L 315 For int_i2 = 0 To M 316 PARA_23(int_i2, int_i1) = Sheet2.Cells(int_i2 + 14, int_i1).Value 'M 317 Next int_i2 318 Next int_i1 319 '结束权值距阵赋初值 320 321 Sheet3.Range(Cells(16, 3), Cells(17, 5)).ClearContents 322 time_a = Now() 323 '测试开始时刻 324 325 '辅助测试用时 326 Sheet3.Cells(16, 2) = "" 327 Sheet3.Cells(17, 2) = "" 328 If C_C = 0 Then 329 GoTo PION_100A 330 End If 331 Sheet3.Cells(16, 2) = "循环次数" 332 Sheet3.Cells(17, 2) = C_C 333 For int_CC = 1 To C_C 334 int_k = 0 335 For int_p = 1 To P 336 For int_i1 = 1 To N 337 IN_PUT(int_i1) = PARA_INT(int_i1, int_p) 338 Next int_i1 339 '计算隐层各节点输出 340 For int_i1 = 1 To M 341 para_a1 = -1 * PARA_12(0, int_i1) 342 For int_i2 = 1 To N 343 para_a1 = para_a1 + IN_PUT(int_i2) * PARA_12(int_i2, int_i1) 344 Next int_i2 345 OUT_Y(int_i1) = 1 / (1 + Exp(-para_a1)) 346 Next int_i1 347 '结束计算实际隐层各节点输出 348 349 '计算输出层各节点输出 350 For int_i1 = 1 To L 351 para_a1 = -1 * PARA_23(0, int_i1) 352 For int_i2 = 1 To M 353 para_a1 = para_a1 + OUT_Y(int_i2) * PARA_23(int_i2, int_i1) 354 Next int_i2 355 OUT_O(int_i1) = 1 / (1 + Exp(-para_a1)) 356 Next int_i1 357 '结束计算输出层各节点输出 358 359 '计算十进制结果 360 para_a1 = 0 361 For int_i1 = 1 To L 362 OUT_O(int_i1) = Round(OUT_O(int_i1)) 363 para_a1 = para_a1 + OUT_O(int_i1) * 2 ^ (L - int_i1) 364 Next int_i1 365 '结束计算十进制结果 366 Next int_p 367 Next int_CC 368 '结束辅助测试用时 369 PION_100A: 370 371 int_k = 0 372 For int_p = 1 To P 373 For int_i1 = 1 To N 374 IN_PUT(int_i1) = PARA_INT(int_i1, int_p) '在10个样本中取出一个样本（一列） 375 Next int_i1 376 '计算隐层各节点输出 377 For int_i1 = 1 To M 378 para_a1 = -1 * PARA_12(0, int_i1) 379 For int_i2 = 1 To N 380 para_a1 = para_a1 + IN_PUT(int_i2) * PARA_12(int_i2, int_i1) 381 Next int_i2 382 OUT_Y(int_i1) = 1 / (1 + Exp(-para_a1)) 383 Next int_i1 384 '结束计算实际隐层各节点输出 385 386 '计算输出层各节点输出 387 For int_i1 = 1 To L 388 para_a1 = -1 * PARA_23(0, int_i1) 389 For int_i2 = 1 To M 390 para_a1 = para_a1 + OUT_Y(int_i2) * PARA_23(int_i2, int_i1) 391 Next int_i2 392 OUT_O(int_i1) = 1 / (1 + Exp(-para_a1)) 393 Next int_i1 394 '结束计算输出层各节点输出 395 396 '输出结果 397 para_a1 = 0 398 For int_i1 = 1 To L 399 OUT_O(int_i1) = Round(OUT_O(int_i1)) '将OUT_O四舍五入，要么是0，要么是1 400 Sheet3.Cells(int_p + 2, int_i1).Value = OUT_O(int_i1) 'sheet3中输出一行 401 para_a1 = para_a1 + OUT_O(int_i1) * 2 ^ (L - int_i1) '将二进制化为十进制 402 Next int_i1 403 Sheet3.Cells(int_p + 2, 6).Value = para_a1 404 '结束输出结果 405 406 If (para_a1 + 1) = int_p Then 407 int_k = int_k + 1 408 End If 409 410 Next int_p 411 412 413 Sheet3.Cells(13, 3).Value = 10 * int_k 414 415 time_b = Now() 416 '测试结束时刻 417 418 Sheet3.Cells(16, 3) = "测试用时" 419 Sheet3.Cells(17, 3) = time_b - time_a 420 Sheet3.Cells(16, 4) = "开始" 421 Sheet3.Cells(17, 4) = time_a 422 Sheet3.Cells(16, 5) = "结束" 423 Sheet3.Cells(17, 5) = time_b 424 '输出测试用时情况 425 426 427 End Function 428 'FIN BB测试程序
比较正式的教程：https://zhuanlan.zhihu.com/p/21930884?refer=intelligentunit
