本文主要講如何不依賴TenserFlow等高級(jí)API實(shí)現(xiàn)一個(gè)簡(jiǎn)單的神經(jīng)網(wǎng)絡(luò)來做分類，所有的代碼都在下面；在構(gòu)造的數(shù)據(jù)（通過程序構(gòu)造）上做了驗(yàn)證，經(jīng)過1個(gè)小時(shí)的訓(xùn)練分類的準(zhǔn)確率可以達(dá)到97%。

完整的結(jié)構(gòu)化代碼見于：鏈接地址

先來說說原理

網(wǎng)絡(luò)構(gòu)造

上面是一個(gè)簡(jiǎn)單的三層網(wǎng)絡(luò)；輸入層包含節(jié)點(diǎn)X1 , X2；隱層包含H1，H2；輸出層包含O1。
輸入節(jié)點(diǎn)的數(shù)量要等于輸入數(shù)據(jù)的變量數(shù)目。
隱層節(jié)點(diǎn)的數(shù)量通過經(jīng)驗(yàn)來確定。
如果只是做分類，輸出層一般一個(gè)節(jié)點(diǎn)就夠了。

從輸入到輸出的過程

1.輸入節(jié)點(diǎn)的輸出等于輸入，X1節(jié)點(diǎn)輸入x1時(shí)，輸出還是x1.
2. 隱層和輸出層的輸入I為上層輸出的加權(quán)求和再加偏置，輸出為f(I) ， f為激活函數(shù)，可以取sigmoid。H1的輸出為 sigmoid(w1x1 + w2x2 + b)

誤差反向傳播的過程

Python實(shí)現(xiàn)

構(gòu)造測(cè)試數(shù)據(jù)

# -*- coding: utf-8 -*-import numpy as npfrom random import random as rdn'''說明：我們構(gòu)造1000條數(shù)據(jù)，每條數(shù)據(jù)有三個(gè)屬性(用a1 , a2 , a3表示)a1 離散型 取值 1 到 10 ， 均勻分布a2 離散型 取值 1 到 10 ， 均勻分布a3 連續(xù)型 取值 1 到 100 ， 且符合正態(tài)分布 各屬性之間獨(dú)立。共2個(gè)分類(0 , 1)，屬性值與類別之間的關(guān)系如下，0 : a1 in [1 , 3] and a2 in [4 , 10] and a3 <= 501 : a1 in [1 , 3] and a2 in [4 , 10] and a3 > 500 : a1 in [1 , 3] and a2 in [1 , 3] and a3 > 301 : a1 in [1 , 3] and a2 in [1 , 3] and a3 <= 300 : a1 in [4 , 10] and a2 in [4 , 10] and a3 <= 501 : a1 in [4 , 10] and a2 in [4 , 10] and a3 > 500 : a1 in [4 , 10] and a2 in [1 , 3] and a3 > 301 : a1 in [4 , 10] and a2 in [1 , 3] and a3 <= 30'''def genData() : #為a3生成符合正態(tài)分布的數(shù)據(jù) a3_data = np.random.randn(1000) * 30 + 50 data = [] for i in range(1000) : #生成a1 a1 = int(rdn()*10) + 1 if a1 > 10 :  a1 = 10 #生成a2 a2 = int(rdn()*10) + 1 if a2 > 10 :  a2 = 10 #取a3 a3 = a3_data[i]  #計(jì)算這條數(shù)據(jù)對(duì)應(yīng)的類別 c_id = 0 if a1 <= 3 and a2 >= 4 and a3 <= 50 :  c_id = 0  elif a1 <= 3 and a2 >= 4 and a3 > 50 :  c_id = 1  elif a1 <= 3 and a2 < 4 and a3 > 30 :  c_id = 0 elif a1 <= 3 and a2 < 4 and a3 <= 30 :  c_id = 1 elif a1 > 3 and a2 >= 4 and a3 <= 50 :  c_id = 0  elif a1 > 3 and a2 >= 4 and a3 > 50 :  c_id = 1  elif a1 > 3 and a2 < 4 and a3 > 30 :  c_id = 0 elif a1 > 3 and a2 < 4 and a3 <= 30 :  c_id = 1 else :  print('error') #拼合成字串 str_line = str(i) + ',' + str(a1) + ',' + str(a2) + ',' + str(a3) + ',' + str(c_id) data.append(str_line) return '/n'.join(data)

激活函數(shù)

# -*- coding: utf-8 -*-"""Created on Sun Dec 2 14:49:31 2018@author: congpeiqing"""import numpy as np#sigmoid函數(shù)的導(dǎo)數(shù)為 f(x)*(1-f(x))def sigmoid(x) : return 1/(1 + np.exp(-x))