ハード制限機能を備えたフォワード多層ニューラルネットワーク

import numpy as np
from matplotlib import pyplot as plt
import random
plt.rcParams['font.sans-serif'] = ['SimHei']  # 显示中文标签
plt.rcParams['axes.unicode_minus'] = False


def yxf(x):
    if x >= 0:
        return 1
    else:
        return 0


def juzheng(a, b):
    sum = 0
    for i in range(len(a)):
        sum = sum + a[i]*b[i]
    return sum


x0_r = []
x1_r = []
x0_r1 = []
x1_r1 = []
x0_r2 = []
x1_r2 = []
label1 = []
label2 = []
label3 = []
for i in range(800):
    x0 = 2*random.random()
    x1 = 4*random.random()-1
    x0_r.append(x0)
    x1_r.append(x1)
    if 1.5*x0 - x1 - 1 <= 0:
        label1.append(1)
    elif 1.5*x0 - x1 - 1 > 0:
        label1.append(0)
for i in range(800):
    x0 = x0_r[i]
    x1 = x1_r[i]
    if (-1)*x0 - x1 + 4 >= 0:
        label2.append(1)
    elif (-1)*x0 - x1 + 4 < 0:
        label2.append(0)
for i in range(800):
    x0 = x0_r[i]
    x1 = x1_r[i]
    if 4*x0 - x1 - 1 >= 0:
        label3.append(1)
    elif 4*x0 - x1 - 1 < 0:
        label3.append(0)

err = 1
k = 0

w1 = [1+random.random() for i in range(3)]
w2 = [1+random.random() for i in range(3)]
w3 = [1+random.random() for i in range(3)]
w0 = [0.1, 0.1, 0.1]
label0 = []

for i in range(len(label3)):
    if label1[i] == 1 and label2[i] == 1 and label3[i] == 1:
        label0.append(1)
    else:
        label0.append(0)
for i in range(len(label1)):
    if label0[i] == 1:
        plt.plot(x0_r[i], x1_r[i], 'k*')
    else:
        plt.plot(x0_r[i], x1_r[i], 'bs')
plt.show()
while err > 0:
    tj = []
    for i in range(len(label1)):
        X1 = [x0_r[i], x1_r[i], 1]
        # 第一层第一个神经元 
        I1 = juzheng(X1, w1)
        y1 = yxf(I1)
        dui1 = label1[i] - y1
        w1[0] = w1[0] + 0.005 * dui1 * X1[0]
        w1[1] = w1[1] + 0.1 * dui1 * X1[1]
        w1[2] = w1[2] + 0.1 * dui1 * X1[2]
        # 第一层第二个神经元
        I2 = juzheng(X1, w2)
        y2 = yxf(I2)
        dui2 = label2[i] - y2
        w2[0] = w2[0] + 0.005 * dui2 * X1[0]
        w2[1] = w2[1] + 0.1 * dui2 * X1[1]
        w2[2] = w2[2] + 0.1 * dui2 * X1[2]
        # 第一层第三个神经元
        I3 = juzheng(X1, w3)
        y3 = yxf(I3)
        dui3 = label3[i] - y3
        w3[0] = w3[0] + 0.005 * dui3 * X1[0]
        w3[1] = w3[1] + 0.1 * dui3 * X1[1]
        w3[2] = w3[2] + 0.1 * dui3 * X1[2]
        # 第二层
        Y0 = [y1, y2, y3]
        I0 = juzheng(Y0, w0)
        y0 = yxf(I0-2.9999)
        dui0 = label0[i] - y0
        w0[0] = w0[0] + 0.05 * dui0 * Y0[0]
        w0[1] = w0[1] + 0.05 * dui0 * Y0[1]
        w0[2] = w0[2] + 0.05 * dui0 * Y0[2]
        tj.append(abs(dui0))
    err = sum(tj)
    k = k+1
    print('第{}次迭代不满足条件的点有{}个'.format(k, err))


xx = np.linspace(-1, 4, 100)
yab = -w1[2] / w1[1] - w1[0] / w1[1] * xx
yac = -w2[2] / w2[1] - w2[0] / w2[1] * xx
ybc = -w3[2] / w3[1] - w3[0] / w3[1] * xx
print('w1:', w1)
print('w3:', w2)
print('w3:', w3)
print('w0:', w0)
plt.figure()
plt.plot(xx, yab, label='AB')
plt.plot(xx, yac, label='BC')
plt.plot(xx, ybc, label='AC')
plt.legend()
plt.xlim([0, 2])
plt.ylim([-2, 4])
y0_r = []
y1_r = []
y2_r = []
y3_r = []
for i in range(2000):
    x0 = 2*random.random()
    x1 = 4*random.random()-1
    X1 = [x0, x1, 1]
    y1 = yxf(juzheng(X1, w1))
    y2 = yxf(juzheng(X1, w2))
    y3 = yxf(juzheng(X1, w3))
    Y = [y1, y2, y3]
    y0 = yxf(juzheng(Y, w0)-2.9999)
    if y0:
        plt.plot(x0, x1, 'k*')
    else:
        plt.plot(x0, x1, 'gs')
    y0_r.append(y0)
    y1_r.append(y1)
    y2_r.append(y2)
    y3_r.append(y3)
plt.show()

トレーニングデータセット

試験結果

ニューラルネットワークの重み