numpy實現簡單的任意層數的BP神經網路設計

阿新 • • 發佈：2020-12-19

技術標籤：造輪子

手寫了一個簡單的BP神經網路：其原理不再贅述了，傳遞函式只有sigmoid,tansig或者是Weak_relu,使用了一個3輸入2輸出的運算元為例，損失函式為平方誤差：

# -*- coding: utf-8 -*-
"""
Created on Wed Dec 16 19:03:01 2020

@author: SUE
"""


import numpy as np
import matplotlib.pyplot as plt
import math
def sigmoid(x):
    y=np.zeros((len(x),1))
    for i in range(len(x)):
        y[i]= 1/(1+math.exp(-x[i]))
    return y
def Weak_Relu(x):
    alpha=0.05
    y=np.zeros((len(x),1))
    for i in range(len(x)):
        if(x[i]>0):
            y[i]=x[i]
        else:
            y[i]=alpha*x[i]
    return y
def tansig(x):
    y=np.zeros((len(x),1))
    for i in range(len(x)):
        y[i]= (math.exp(x[i])-math.exp(-x[i]))/(math.exp(x[i])+math.exp(-x[i]))
    return y
def diff_sigmoid(x):
    y=np.zeros((len(x),1))
    for i in range(len(x)):
        y[i]= math.exp(-x[i])/(1+math.exp(-x[i]))/(1+math.exp(-x[i]))
    return y
def diff_weak_Relu(x):
    alpha=0.05
    y=np.zeros((len(x),1))
    for i in range(len(x)):
        if(x[i]>0):
            y[i]=1
        else:
            y[i]=alpha
    return y
def diff_tansig(x):
    y=np.zeros((len(x),1))
    for i in range(len(x)):
        y[i]= 1-(math.exp(x[i])-math.exp(-x[i]))/(math.exp(x[i])+math.exp(-x[i]))*(math.exp(x[i])-math.exp(-x[i]))/(math.exp(x[i])+math.exp(-x[i]))
    return y
def process(W,b,x,stimulate_fun):
    return stimulate_fun(np.dot(W,x)+b)
def qua_Err(x,OUTPUT):
    DE=[]
    for i in range(len(x)):
        DE.append(2*(x[i]-OUTPUT[i]))
    return DE
def set_up_BP(NeuNumList):
        W=[]#連線陣
        b=[]#偏置
        for i in range(len(NeuNumList)):
            if(i<len(NeuNumList)-1):
                W.append(np.random.rand(NeuNumList[i+1],NeuNumList[i])*1-0.5)
                b.append(np.random.rand(NeuNumList[i+1],1))
        return W,b
def get_first_x(W,b,Act,INPUT):#輸入引數Act是啟用函式指標
    x=[]
    x.append(INPUT)
    for i in range(len(b)):
        x.append(process(W[i],b[i],x[len(x)-1],Act[i]))
    return x
def get_diff_list(W,b,Act,x,OUTPUT,ERRFUN):#最後一列是損失函式型別
    #返回的是最終誤差對於每個引數的偏導數
    ERR=ERRFUN(x[len(x)-1],OUTPUT)            
    DW=[]
    Db=[]
    for i in range(len(b)):
         TW=[]
         Tb=[]
         D=[]
         if(Act[len(b)-1-i]==sigmoid):
                D=process(W[len(b)-1-i],b[len(b)-1-i],x[len(b)-1-i],diff_sigmoid)
         elif(Act[len(b)-1-i]==Weak_Relu):
                D=process(W[len(b)-1-i],b[len(b)-1-i],x[len(b)-1-i],diff_weak_Relu)
         elif(Act[len(b)-1-i]==tansig):
                D=process(W[len(b)-1-i],b[len(b)-1-i],x[len(b)-1-i],diff_tansig)
         Tb=ERR*D
         TW=np.dot(Tb,x[len(b)-1-i].T)
         ERR=[]
         ERR=np.dot(W[len(b)-1-i].T,Tb)
         DW.append(TW)
         Db.append(Tb)
    return DW,Db
def Drill(W,b,Act,INPUT,OUTPUT,ERRFUN,epoch,step):#最後兩個元素是訓練代數和步長
    for i in range(epoch):
        s=0
        Db=[]
        DW=[]
        for j in range(len(INPUT)):
          x=[]
          x=get_first_x(W,b,Act,np.array(INPUT[j],ndmin=2).T)
          OP=np.array(OUTPUT[j],ndmin=2).T
          s=s+sum((abs(x[len(x)-1]-OP)))
          TW=[]
          Tb=[]
          TW,Tb=get_diff_list(W,b,Act,x,OP,qua_Err)
          if(DW==[]):
              DW=TW
              Db=Tb
          else:
              for k in range(len(DW)):
                  DW[k]=DW[k]+TW[k]
                  Db[k]=Db[k]+Tb[k]
        for j in range(len(b)):
            W[j]=W[j]-step*DW[len(b)-1-j]
            b[j]=b[j]-step*Db[len(b)-1-j]
        print('第 %d 次迭代的誤差之和(一範數)是: '%(i+1),end='')
        print("%f" %s)
    return W,b
def predict(W,b,Act,INPUT):
    x=np.array(INPUT,ndmin=2).T
    for i in range(len(b)):
        x=process(W[i],b[i],x,Act[i])
    return x

def main():
    W,b=set_up_BP([3,10,10,2])
    Act=[tansig,tansig,tansig]
    INPUT=[[-1.0000 ,  -1.0000,   -1.0000],
           [-0.9057,   -0.8800,   -0.9429],
   [-0.7595,   -0.8000,   -0.9429],
   [-0.6717,   -0.7600,   -0.8571],
   [-0.5559,   -0.6400,   -0.6857],
   [-0.5235,   -0.4000,   -0.6000],
   [-0.4805,   -0.3200,   -0.6000],
   [-0.3258,   -0.2000,   -0.3429],
   [-0.2081,   -0.1200,   -0.3429],
   [-0.1248,         0,   -0.2857],
   [-0.0729,    0.2400,   -0.2286],
   [-0.0299,    0.2800,   -0.2286],
   [ 0.0669,    0.3200,   -0.1714],
   [ 0.1996,    0.4000,    0.1429],
   [ 0.3348,    0.5200,    0.3429],
   [ 0.6138,    0.6000,    0.4286],
   [ 0.7555,    0.6800,    0.4286],
   [ 0.8069,    0.8000,    0.6571],
   [ 0.9271,    0.8800,    0.7143],
   [ 1.0000,    1.0000,    1.0000]]
    OUTPUT=[[-1.0000 ,  -1.0000],
   [-0.9431,   -0.9862],
   [-0.8641,   -0.9856],
   [-0.7903,   -0.9842],
   [-0.7217,   -0.9586],
   [-0.6734,   -0.9536],
   [-0.6230,   -0.9419],
   [-0.4457,   -0.7000],
   [-0.3125,   -0.3295],
   [-0.2326,   -0.2513],
   [-0.1706,   -0.0410],
   [-0.2506,   -0.0309],
   [-0.2014,   -0.0969],
   [-0.0885,   -0.0394],
   [ 0.0424,    0.1750],
   [ 0.4773,    0.5097],
   [ 0.6543,    0.6955],
   [ 0.8480,    0.8950],
    [0.9721,    0.9027],
    [1.0000,    1.0000]]
    W,b=Drill(W,b,Act,INPUT,OUTPUT,qua_Err,5000,0.005)
    pre=[]
    for row in INPUT:
        pre.append(predict(W,b,Act,row))
    p=np.zeros((2,20))
    q=np.array(OUTPUT,ndmin=2).T
    for i in range(20):
        p[0][i]=pre[i][0]
        p[1][i]=pre[i][1]
    plt.plot(p[0],p[1],label="Sigmoid",color = "blue")
    plt.plot(q[0],q[1],label="Sigmoid",color = "red")
main()

執行效果: