二分类BP算法代码及注释
import numpy as np import matplotlib.pyplot as plt # 中文、负号 plt.rcParams['font.sans-serif'] = ['SimHei'] plt.rcParams['axes.unicode_minus'] = False #数据集 x1 = [0.697,0.774,0.634,0.608,0.556,0.403,0.481,0.437,0.666,0.243,0.245,0.343,0.639,0.657,0.360,0.593,0.719] x2 = [0.460,0.376,0.264,0.318,0.215,0.237,0.149,0.211,0.091,0.267,0.057,0.099,0.161,0.198,0.370,0.042,0.103] y = [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] #数据提取 x = np.c_[x1,x2] # 数据预处理 def preProcess(x,y): # 特征缩放(标准化) x -= np.mean(x,0) x /= np.std(x,0,ddof=1) # 数据初始化 x = np.c_[np.ones(len(x)),x] y = np.c_[y] return x,y #调用预处理函数 x,y = preProcess(x,y) # 洗牌 np.random.seed(7) order = np.random.permutation(len(x)) x = x[order] y = y[order] #数据集切分(train/test) train_x,test_x = np.split(x,[int(0.7*len(x))]) train_y,test_y = np.split(y,[int(0.7*len(x))]) # 正向传播算法 # 激活函数(逻辑函数) def g(z,deriv=False): if deriv: return z*(1-z) return 1/(1+np.exp(-z)) # 定义模型 def model(x,theta1,theta2,theta3): z2 = np.dot(x,theta1) a2 = g(z2) z3 = np.dot(a2, theta2) a3 = g(z3) z4 = np.dot(a3, theta3) a4 = g(z4) return a2,a3,a4 # 代价函数 def costFunc(h,y): j = (-1/len(y))*np.sum(y*np.log(h) + (1-y)*np.log(1-h)) return j # 向后传播(BP算法) def BP(a1,a2,a3,a4,theta1,theta2,theta3,alpha,y): # 求delta值 delta4 = a4 - y delta3 = np.dot(delta4,theta3.T)*g(a3,True) delta2 = np.dot(delta3,theta2.T)*g(a2,True) # 求deltaTheta deltatheta3 = (1/len(y))*np.dot(a3.T,delta4) deltatheta2 = (1/len(y))*np.dot(a2.T,delta3) deltatheta1 = (1/len(y))*np.dot(a1.T,delta2) # 更新theta theta1 -= alpha*deltatheta1 theta2 -= alpha*deltatheta2 theta3 -= alpha*deltatheta3 return theta1,theta2,theta3 # 梯度下降函数 def gradDesc(x,y,alpha=0.7,max_iter=10000,hidden_layer_size=(17,8)): m,n = x.shape k = y.shape[1] # 初始化theta theta1 = 2 * np.random.rand(n,hidden_layer_size[0]) - 1 theta2 = 2 * np.random.rand(hidden_layer_size[0],hidden_layer_size[1]) - 1 theta3 = 2 * np.random.rand(hidden_layer_size[1],k) - 1 # 初始化代价 j_history = np.zeros(max_iter) for i in range(max_iter): # 求预测值 a2, a3, a4 = model(x,theta1,theta2,theta3) # 记录代价 j_history[i] = costFunc(a4,y) # 反向传播，更新参数 theta1, theta2, theta3 = BP(x, a2, a3, a4, theta1, theta2, theta3, alpha, y) return j_history,theta1, theta2, theta3 #调用梯度下降函数 j_history,theta1, theta2, theta3 = gradDesc(train_x,train_y) #训练集预测值 train_a2,train_a3,train_h = model(train_x,theta1, theta2, theta3) #预测结果标签 test_a2,test_a3,test_h = model(test_x,theta1, theta2, theta3) #定义准确率 def score(h,y): count = 0 for i in range(len(y)): if np.where(h[i] >= 0.5,1,0) == y[i]: count += 1 return count/len(y) print('训练集准确率:',score(train_h,train_y)) print('测试集准确率:',score(test_h,test_y)) # 画图 plt.title('代价函数图像') plt.plot(j_history) plt.show()
