矩陣運算

多元線性回歸

梯度下降法-多元線性回歸

import numpy as np from numpy import genfromtxt import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D # 讀入數據 data = genfromtxt(r"Delivery.csv",delimiter=',') print(data)

# 切分數據 x_data = data[:,:-1] y_data = data[:,-1] print(x_data) print(y_data)

# 學習率learning rate lr = 0.0001 # 參數 theta0 = 0 theta1 = 0 theta2 = 0 # 最大迭代次數 epochs = 1000# 最小二乘法 def compute_error(theta0, theta1, theta2, x_data, y_data):totalError = 0for i in range(0, len(x_data)):totalError += (y_data[i] - (theta1 * x_data[i,0] + theta2*x_data[i,1] + theta0)) ** 2return totalError / float(len(x_data))def gradient_descent_runner(x_data, y_data, theta0, theta1, theta2, lr, epochs):# 計算總數據量m = float(len(x_data))# 循環epochs次for i in range(epochs):theta0_grad = 0theta1_grad = 0theta2_grad = 0# 計算梯度的總和再求平均for j in range(0, len(x_data)):theta0_grad += (1/m) * ((theta1 * x_data[j,0] + theta2*x_data[j,1] + theta0) - y_data[j])theta1_grad += (1/m) * x_data[j,0] * ((theta1 * x_data[j,0] + theta2*x_data[j,1] + theta0) - y_data[j])theta2_grad += (1/m) * x_data[j,1] * ((theta1 * x_data[j,0] + theta2*x_data[j,1] + theta0) - y_data[j])# 更新b和ktheta0 = theta0 - (lr*theta0_grad)theta1 = theta1 - (lr*theta1_grad)theta2 = theta2 - (lr*theta2_grad)return theta0, theta1, theta2 print("Starting theta0 = {0}, theta1 = {1}, theta2 = {2}, error = {3}".format(theta0, theta1, theta2, compute_error(theta0, theta1, theta2, x_data, y_data))) print("Running...") theta0, theta1, theta2 = gradient_descent_runner(x_data, y_data, theta0, theta1, theta2, lr, epochs) print("After {0} iterations theta0 = {1}, theta1 = {2}, theta2 = {3}, error = {4}".format(epochs, theta0, theta1, theta2, compute_error(theta0, theta1, theta2, x_data, y_data)))

ax = plt.figure().add_subplot(111, projection = '3d') ax.scatter(x_data[:,0], x_data[:,1], y_data, c = 'r', marker = 'o', s = 100) #點為紅色三角形 x0 = x_data[:,0] x1 = x_data[:,1] # 生成網格矩陣 x0, x1 = np.meshgrid(x0, x1) z = theta0 + x0*theta1 + x1*theta2 # 畫3D圖 ax.plot_surface(x0, x1, z) #設置坐標軸 ax.set_xlabel('Miles') ax.set_ylabel('Num of Deliveries') ax.set_zlabel('Time') #顯示圖像 plt.show()

sklearn-多元線性回歸

import numpy as np from numpy import genfromtxt from sklearn import linear_model import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D # 讀入數據 data = genfromtxt(r"Delivery.csv",delimiter=',') print(data)

# 切分數據 x_data = data[:,:-1] y_data = data[:,-1] print(x_data) print(y_data)

# 創建模型 model = linear_model.LinearRegression() model.fit(x_data, y_data) # 系數 print("coefficients:",model.coef_)# 截距 print("intercept:",model.intercept_)# 測試 x_test = [[102,4]] predict = model.predict(x_test) print("predict:",predict)

ax = plt.figure().add_subplot(111, projection = '3d') ax.scatter(x_data[:,0], x_data[:,1], y_data, c = 'r', marker = 'o', s = 100) #點為紅色三角形 x0 = x_data[:,0] x1 = x_data[:,1] # 生成網格矩陣 x0, x1 = np.meshgrid(x0, x1) z = model.intercept_ + x0*model.coef_[0] + x1*model.coef_[1] # 畫3D圖 ax.plot_surface(x0, x1, z) #設置坐標軸 ax.set_xlabel('Miles') ax.set_ylabel('Num of Deliveries') ax.set_zlabel('Time') #顯示圖像 plt.show()

總結

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