人工智能—Python实现线性回归

from sklearn import linear_model from sklearn.linear_model import LinearRegression import matplotlib.pyplot as plt#用于作图 from pylab import * mpl.rcParams['font.sans-serif'] = ['SimHei'] mpl.rcParams['axes.unicode_minus'] = False import numpy as np#用于创建向量     reg=linear_model.LinearRegression(fit_intercept=True,normalize=False) x=[[32.50235],[53.4268],[61.53036],[47.47564],[59.81321],[55.14219],[52.14219],[39.29957],  [48.10504],[52.55001],[45.41873],[54.35163],[44.16405],[58.16847],[56.72721]] y=[31.70701,68.7776,62.56238,71.54663,87.23093,78.21152,79.64197,59.17149,75.33124,71.30088,55.16568,82.47885,62.00892 ,75.39287,81.43619] reg.fit(x,y) k=reg.coef_#获取斜率w1,w2,w3,...,wn b=reg.intercept_#获取截距w0 x0=np.arange(30,60,0.2) y0=k*x0+b print("k={0},b={1}".format(k,b)) plt.scatter(x,y) plt.plot(x0,y0,label='LinearRegression') plt.xlabel('X') plt.ylabel('Y') plt.legend() plt.show()

k=[1.36695374],b=0.13079331831460195

#方法1 import numpy as np import matplotlib.pyplot as plt from pylab import * mpl.rcParams['font.sans-serif'] = ['SimHei'] mpl.rcParams['axes.unicode_minus'] = False #数据生成 data = [] for i in range(100):     x = np.random.uniform(3., 12.)     # mean=0, std=1     eps = np.random.normal(0., 1)     y = 1.677 * x + 0.039 + eps     data.append([x, y])   data = np.array(data)   #统计误差 # y = wx + b def compute_error_for_line_given_points(b, w, points):     totalError = 0     for i in range(0, len(points)):         x = points[i, 0]         y = points[i, 1]         # computer mean-squared-error         totalError += (y - (w * x + b)) ** 2     # average loss for each point     return totalError / float(len(points))     #计算梯度 def step_gradient(b_current, w_current, points, learningRate):     b_gradient = 0     w_gradient = 0     N = float(len(points))     for i in range(0, len(points)):         x = points[i, 0]         y = points[i, 1]         # grad_b = 2(wx+b-y)         b_gradient += (2/N) * ((w_current * x + b_current) - y)         # grad_w = 2(wx+b-y)*x         w_gradient += (2/N) * x * ((w_current * x + b_current) - y)     # update w'     new_b = b_current - (learningRate * b_gradient)     new_w = w_current - (learningRate * w_gradient)     return [new_b, new_w]   #迭代更新 def gradient_descent_runner(points, starting_b, starting_w, learning_rate, num_iterations):     b = starting_b     w = starting_w     # update for several times     for i in range(num_iterations):         b, w = step_gradient(b, w, np.array(points), learning_rate)     return [b, w]     def main():       learning_rate = 0.0001     initial_b = 0  # initial y-intercept guess     initial_w = 0  # initial slope guess     num_iterations = 1000     print("迭代前 b = {0}, w = {1}, error = {2}"           .format(initial_b, initial_w,                   compute_error_for_line_given_points(initial_b, initial_w, data))           )     print("Running...")     [b, w] = gradient_descent_runner(data, initial_b, initial_w, learning_rate, num_iterations)     print("第 {0} 次迭代结果 b = {1}, w = {2}, error = {3}".           format(num_iterations, b, w,                  compute_error_for_line_given_points(b, w, data))           )     plt.plot(data[:,0],data[:,1], color='b', marker='+', linestyle='--',label='true')     plt.plot(data[:,0],w*data[:,0]+b,color='r',label='predict')     plt.xlabel('X')     plt.ylabel('Y')     plt.legend()     plt.show()     if __name__ == '__main__':     main()    

#方法2   import numpy as np import pandas as pd import matplotlib.pyplot as plt import matplotlib as mpl mpl.rcParams["font.sans-serif"]=["SimHei"] mpl.rcParams["axes.unicode_minus"]=False     # y = wx + b #Import data file=pd.read_csv("data.csv")   def compute_error_for_line_given(b, w):     totalError = np.sum((file['y']-(w*file['x']+b))**2)     return np.mean(totalError)   def step_gradient(b_current, w_current,  learningRate):     b_gradient = 0     w_gradient = 0     N = float(len(file['x']))     for i in range (0,len(file['x'])):         # grad_b = 2(wx+b-y)         b_gradient += (2 / N) * ((w_current * file['x'] + b_current) - file['y'])         # grad_w = 2(wx+b-y)*x         w_gradient += (2 / N) * file['x'] * ((w_current * file['x'] + b_current) - file['x'])     # update w'     new_b = b_current - (learningRate * b_gradient)     new_w = w_current - (learningRate * w_gradient)     return [new_b, new_w]     def gradient_descent_runner( starting_b, starting_w, learning_rate, num_iterations):     b = starting_b     w = starting_w     # update for several times     for i in range(num_iterations):         b, w = step_gradient(b, w,  learning_rate)     return [b, w]     def main():     learning_rate = 0.0001     initial_b = 0  # initial y-intercept guess     initial_w = 0  # initial slope guess     num_iterations = 100     print("Starting gradient descent at b = {0}, w = {1}, error = {2}"           .format(initial_b, initial_w,                   compute_error_for_line_given(initial_b, initial_w))           )     print("Running...")     [b, w] = gradient_descent_runner(initial_b, initial_w, learning_rate, num_iterations)     print("After {0} iterations b = {1}, w = {2}, error = {3}".           format(num_iterations, b, w,                  compute_error_for_line_given(b, w))           )     plt.plot(file['x'],file['y'],'ro',label='线性回归')     plt.xlabel('X')     plt.ylabel('Y')     plt.legend()     plt.show()         if __name__ == '__main__':     main()

Starting gradient descent at b = 0, w = 0, error = 75104.71822821398 Running... After 100 iterations b = 0     0.014845 1     0.325621 2     0.036883 3     0.502265 4     0.564917 5     0.479366 6     0.568968 7     0.422619 8     0.565073 9     0.393907 10    0.216854 11    0.580750 12    0.379350 13    0.361574 14    0.511651 dtype: float64, w = 0     0.999520 1     0.994006 2     0.999405 3     0.989645 4     0.990683 5     0.991444 6     0.989282 7     0.989573 8     0.988498 9     0.992633 10    0.995329 11    0.989490 12    0.991617 13    0.993872 14    0.991116 dtype: float64, error = 6451.5510231710905

#方法3   import numpy as np   points = np.genfromtxt("data.csv", delimiter=",") #从数据读入到返回需要两个迭代循环，第一个迭代将文件中每一行转化为一个字符串序列， #第二个循环迭代对每个字符串序列指定合适的数据类型: # y = wx + b def compute_error_for_line_given_points(b, w, points):     totalError = 0     for i in range(0, len(points)):         x = points[i, 0]         y = points[i, 1]         # computer mean-squared-error         totalError += (y - (w * x + b)) ** 2     # average loss for each point     return totalError / float(len(points))     def step_gradient(b_current, w_current, points, learningRate):     b_gradient = 0     w_gradient = 0     N = float(len(points))     for i in range(0, len(points)):         x = points[i, 0]         y = points[i, 1]         # grad_b = 2(wx+b-y)         b_gradient += (2 / N) * ((w_current * x + b_current) - y)         # grad_w = 2(wx+b-y)*x         w_gradient += (2 / N) * x * ((w_current * x + b_current) - y)     # update w'     new_b = b_current - (learningRate * b_gradient)     new_w = w_current - (learningRate * w_gradient)     return [new_b, new_w]     def gradient_descent_runner(points, starting_b, starting_w, learning_rate, num_iterations):     b = starting_b     w = starting_w     # update for several times     for i in range(num_iterations):         b, w = step_gradient(b, w, np.array(points), learning_rate)     return [b, w]     def main():     learning_rate = 0.0001     initial_b = 0  # initial y-intercept guess     initial_w = 0  # initial slope guess     num_iterations = 1000     print("Starting gradient descent at b = {0}, w = {1}, error = {2}"           .format(initial_b, initial_w,                   compute_error_for_line_given_points(initial_b, initial_w, points))           )     print("Running...")     [b, w] = gradient_descent_runner(points, initial_b, initial_w, learning_rate, num_iterations)     print("After {0} iterations b = {1}, w = {2}, error = {3}".           format(num_iterations, b, w,                  compute_error_for_line_given_points(b, w, points))           )     if __name__ == '__main__':     main()

#1.导入包 import matplotlib.pyplot as plt import numpy as np import pandas as pd from sklearn import linear_model   #2.加载训练数据，建立回归方程 # 取数据集(1) datasets_X = []     #存放房屋面积 datasets_Y = []     #存放交易价格 fr = open('房价与房屋尺寸.csv','r')    #读取文件，r: 以只读方式打开文件，w: 打开一个文件只用于写入。 lines = fr.readlines()              #一次读取整个文件。 for line in lines:                  #逐行进行操作，循环遍历所有数据     items = line.strip().split(',')    #去除数据文件中的逗号,strip()用于移除字符串头尾指定的字符（默认为空格或换行符）或字符序列。                                        #split（‘ '）: 通过指定分隔符对字符串进行切片，如果参数 num 有指定值，则分隔 num+1 个子字符串。     datasets_X.append(int(items[0]))   #将读取的数据转换为int型，并分别写入     datasets_Y.append(int(items[1]))   length = len(datasets_X)              #求得datasets_X的长度，即为数据的总数 datasets_X = np.array(datasets_X).reshape([length,1])   #将datasets_X转化为数组，并变为1维，以符合线性回归拟合函数输入参数要求 datasets_Y = np.array(datasets_Y)                    #将datasets_Y转化为数组   #取数据集(2) '''fr = pd.read_csv('房价与房屋尺寸.csv',encoding='utf-8') datasets_X=fr['房屋面积'] datasets_Y=fr['交易价格']'''   minX = min(datasets_X) maxX = max(datasets_X) X = np.arange(minX,maxX).reshape([-1,1])        #以数据datasets_X的最大值和最小值为范围，建立等差数列，方便后续画图。                                                 #reshape([-1,1]），转换成１列，reshape([２,－1]）：转换成两行 linear = linear_model.LinearRegression()      #调用线性回归模块，建立回归方程，拟合数据 linear.fit(datasets_X, datasets_Y)   #3.斜率及截距 print('Coefficients:', linear.coef_)      #查看回归方程系数(k) print('intercept:', linear.intercept_)    ##查看回归方程截距(b) print('y={0}x+{1}'.format(linear.coef_,linear.intercept_)) #拟合线   # 4.图像中显示 plt.scatter(datasets_X, datasets_Y, color = 'red') plt.plot(X, linear.predict(X), color = 'blue') plt.xlabel('Area') plt.ylabel('Price') plt.show()

Coefficients: [0.14198749] intercept: 53.43633899175563 y=[0.14198749]x+53.43633899175563