数据分析项目-房价预测

import pandas as pd import math import numpy as np from sklearn.model_selection import train_test_split from sklearn.preprocessing import MinMaxScaler import matplotlib.pyplot as plt data = pd.read_csv('bj_housing.csv') Y_true = data[['Value']] X = data.drop('Value', axis = 1) minimum_price = np.min(Y_true) maximum_price = np.max(Y_true) scaler = MinMaxScaler() X=scaler.fit_transform(X) Y_true=scaler.fit_transform(Y_true) np.random.seed(12) np.random.shuffle(X) np.random.seed(12) np.random.shuffle(Y_true) X_train, X_test, Y_train, Y_test = train_test_split(X, Y_true, test_size=0.20, random_state=0) #Z1=x*w1/Z2=A1*w2 def re_Z(w,x,b): Z=np.dot(x,w)+b return Z def active(z): row=z.shape[0] col=z.shape[1] A = np.ones(shape=(row, col), dtype='float') for i in range(row): for j in range(col): A[i,j]=1/(1+math.exp(-z[i,j])) return A def grad_active(z): row = z.shape[0] col = z.shape[1] grad_z = np.ones(shape=(row, col), dtype='float') for i in range(row): for j in range(col): grad_z[i,j]=math.exp(-z[i,j])/((1+math.exp(-z[i,j]))*(1+math.exp(-z[i,j]))) return grad_z #Loss function def Loss(w1,w2,b1,b2,x,y_true): N=x.shape[0] Z1=re_Z(w1,x,b1) A1=active(Z1) Z2=re_Z(w2,A1,b2) A2=active(Z2) L=y_true-A2 return (1/N)*np.dot(L.T,L) #using gradient descent to update w and b def gradient_w2(w1,w2,b1,b2,x,y_true,a=0.1): N=x.shape[0] L_total=0 for i in range(N): n=x[i,:] Z1 = re_Z(w1, n.reshape((1,x.shape[1])),b1) A1 = active(Z1) Z2 = re_Z(w2, A1,b2) A2 = active(Z2) L_total = L_total + grad_active((A2-y_true[i,0]))*(A1.T) w2=w2-(2*a/N)*L_total return w2 def gradient_w1(w1,w2,b1,b2,x,y_true,a=0.1): N=x.shape[0] L2_total=0 for i in range(N): n = x[i, :] Z1 = re_Z(w1, n.reshape((1,x.shape[1])),b1) A1 = active(Z1) Z2 = re_Z(w2, A1,b2) A2 = active(Z2) L2_total = L2_total + (n.reshape((1,x.shape[1]))).T*(grad_active(grad_active((A2-y_true[i,0]))*w2.T)) w1=w1-(2*a/N)*L2_total return w1 def gradient_b1(w1,w2,b1,b2,x,y_true,a=0.1): N=x.shape[0] L_total=0 for i in range(N): n=x[i,:] Z1 = re_Z(w1, n.reshape((1,x.shape[1])),b1) A1 = active(Z1) Z2 = re_Z(w2, A1,b2) A2 = active(Z2) L_total = L_total + (grad_active(grad_active((A2-y_true[i,0]))*w2.T)) b1 = b1 - (2 * a / N) * L_total return b1 def gradient_b2(w1,w2,b1,b2,x,y_true,a=0.1): N=x.shape[0] L_total=0 for i in range(N): n=x[i,:] Z1 = re_Z(w1, n.reshape((1,x.shape[1])),b1) A1 = active(Z1) Z2 = re_Z(w2, A1,b2) A2 = active(Z2) L_total = L_total + grad_active((A2-y_true[i,0])) b2=b2-(2*a/N)*L_total return b2 # find the optimal w and b def gradient_descent(x,y_true,ER=1e-15, MAX_LOOP=150): N_feature=x.shape[1] w1=np.random.randn(N_feature,10) w2 = np.random.randn(10, 1) b1 = np.random.randn(1, 10) b2 = np.random.randn(1, 1) i = 0 error = 1 train_loss=[] test_loss=[] while error > ER and i < MAX_LOOP: y_now=Loss(w1,w2,b1,b2,x,y_true) w1_old = w1 w2_old = w2 b1_old = b1 b2_old = b2 w1 = gradient_w1(w1_old, w2_old, b1_old, b2_old, x, y_true, a=0.1) w2 = gradient_w2(w1_old, w2_old, b1_old, b2_old, x, y_true, a=0.1) b1 = gradient_b1(w1_old, w2_old, b1_old, b2_old, x, y_true, a=0.1) b2 = gradient_b2(w1_old, w2_old, b1_old, b2_old, x, y_true, a=0.1) y_next=Loss(w1,w2,b1,b2,x,y_true) er = abs(y_next-y_now) Loss_train = Loss(w1, w2, b1, b2, X_train, Y_train) Loss_test = Loss(w1, w2, b1, b2, X_test, Y_test) train_loss.append(Loss_train[0,0]) test_loss.append(Loss_test[0,0]) error=er[0,0] i+= 1 return w1,w2,b1,b2,train_loss,test_loss # use training set to get optimal w and b a=gradient_descent(X_train,Y_train) w1=a[0] w2=a[1] b1=a[2] b2=a[3] train_loss =a[4] test_loss = a[5] print('the optimal w1 is\n',w1,'\n the optimal w2 is\n',w2,'\nthe optimal b1 is\n',b1,'\n the optimal b2 is\n',b2) # use the test set to test model's error Loss_test=Loss(w1,w2,b1,b2,X_test,Y_test) print('\n\nthe Loss of the test set is\n ',Loss_test) x=list(range(len(train_loss))) plt.plot(x,train_loss,'r-',label="train") plt.plot(x,test_loss,'b-',label="test") plt.legend() plt.xlabel("i") plt.ylabel('Loss') plt.show()