# python 单变量线性回归

## 单变量线性回归(Linear Regression with One Variable)¶

In [54]:
#初始化工作
import random
import numpy as np
import matplotlib.pyplot as plt

# This is a bit of magic to make matplotlib figures appear inline in the notebook
# rather than in a new window.
%matplotlib inline
plt.rcParams['figure.figsize'] = (10.0, 8.0) # set default size of plots
plt.rcParams['image.interpolation'] = 'nearest'
plt.rcParams['image.cmap'] = 'gray'

# Some more magic so that the notebook will reload external python modules;
%autoreload 2

### 1、加载数据与可视化¶

In [55]:
print('Plotting Data ...')

data = []
with open(filename, 'r') as f:
line = line.split(',')
current = [float(item) for item in line]
#5.5277,9.1302
data.append(current)
return data

data = np.array(data)
print(data.shape)

x = data[:, 0]; y = data[:,1]
m = data.shape[0]
#number of training examples
plt.plot(x,y,'rx')
plt.ylabel('Profit in $10,000s'); plt.xlabel('Population of City in 10,000s'); plt.title("Training data")  Plotting Data ... (97, 2)  Out[55]: <matplotlib.text.Text at 0x2e663d888d0> ## 2、通过梯度下降求解theta¶ In [56]: x = x.reshape(-1,1) # 添加一列1 X = np.hstack([x,np.ones((x.shape[0], 1))]) theta = np.zeros((2, 1)) y = y.reshape(-1,1) #计算损失 def computeCost(X, y, theta): m = y.shape[0] J = (np.sum((X.dot(theta) - y)**2)) / (2*m) #X (m,2) theta (2,1) = m*1 return J #梯度下降 def gradientDescent(X, y, theta, alpha, num_iters): m = y.shape[0] # 存储历史误差 J_history = np.zeros((num_iters, 1)) for iter in range(num_iters): # 对J求导，得到 alpha/m * (WX - Y)*x(i)， theta = theta - ( alpha/m) * X.T.dot(X.dot(theta) - y) J_history[iter] = computeCost(X, y, theta) return J_history,theta iterations = 1500 #迭代次数 alpha = 0.01 #学习率 j = computeCost(X,y,theta) J_history,theta = gradientDescent(X, y, theta, alpha, iterations) print('Theta found by gradient descent: %f %f'%(theta[0][0],theta[1][0])) plt.plot(J_history) plt.ylabel('lost'); plt.xlabel('iter count')  Theta found by gradient descent: 1.166362 -3.630291  Out[56]: <matplotlib.text.Text at 0x2e661194ac8> ### 3、训练结果可视化¶ In [57]: #number of training examples plt.plot(data[:,0],data[:,1],'rx') plt.plot(X[:,0], X.dot(theta), '-') plt.ylabel('Profit in$10,000s');
plt.xlabel('Population of City in 10,000s');
plt.title("Training data")

Out[57]:
<matplotlib.text.Text at 0x2e662155198>

### 4、可视化 J(theta_0, theta_1)¶

In [75]:
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter

theta0_vals = np.linspace(-10, 10, 100)
theta1_vals = np.linspace(-10, 10, 100)

J_vals = np.zeros((theta0_vals.shape[0], theta1_vals.shape[0]));

# 填充J_vals
for i in range(theta0_vals.shape[0]):
for j in range(theta1_vals.shape[0]):
t = [theta0_vals[i],theta1_vals[j]]
J_vals[i,j] = computeCost(X, y, t)

fig = plt.figure()
ax = fig.gca(projection='3d')

theta0_vals, theta1_vals = np.meshgrid(theta0_vals, theta1_vals)
# Plot the surface.
surf = ax.plot_surface(theta0_vals, theta1_vals, J_vals, cmap=cm.coolwarm,
linewidth=0, antialiased=False)

# 定制Z轴.
ax.zaxis.set_major_locator(LinearLocator(10))
ax.zaxis.set_major_formatter(FormatStrFormatter('%d'))

# Add a color bar which maps values to colors.
fig.colorbar(surf, shrink=0.5, aspect=5)

plt.show()


In [ ]:

posted @ 2017-02-16 16:46  JadePeng  阅读(938)  评论(0编辑  收藏  举报