机器学习之代价函数

# -*- coding:utf8 -*-

"""
@author: [email protected]

@date: Tue, May 23 2017

@time: 19:05:20 GMT+8
"""
import matplotlib.pyplot as plt
import numpy as np

# 都转换成列向量
X = np.array([[0, 1, 2, 4]]).T
Y = np.array([[0, 1, 2, 4]]).T

# 三个不同的theta_1值
theta1 = np.array([[0, 0]]).T
theta2 = np.array([[0, 0.5]]).T
theta3 = np.array([[0, 1]]).T

# 矩阵X的行列(m,n)
X_size = X.shape

# 创建一个(4,1)的单位矩阵
X_0 = np.ones((X_size[0], 1))

# 形成点的坐标
X_with_x0 = np.concatenate((X_0, X), axis=1)

# 两个数组点积
h1 = np.dot(X_with_x0, theta1)
h2 = np.dot(X_with_x0, theta2)
h3 = np.dot(X_with_x0, theta3)

# r:red x: x marker
plt.plot(X, Y, 'rx', label='y')
plt.title("Cost Function Example")
plt.grid(True)
plt.plot(X, h1, color='b', label='h1, theta_1=0')
plt.plot(X, h2, color='m', label='h2, theta_1=0.5')
plt.plot(X, h3, color='g', label='h3, theta_1=1')

# 坐标轴名称
plt.xlabel('X')
plt.ylabel('y/h')

# 坐标轴范围
plt.axis([-0.1, 4.5, -0.1, 4.5])
# plt.legend(loc='upper left')
plt.legend(loc='best')
plt.savefig('liner_gression_error.png', dpi=200)
plt.show()

# -*- coding:utf8 -*-

"""
@author: [email protected]

@date: Tue, May 23 2017

@time: 19:05:20 GMT+8
"""

import matplotlib.pyplot as plt
import numpy as np

def calcu_cost(theta, X, Y):
    """ 计算代价函数的值

    :param theta: 斜率
    :param X: x值
    :param Y: y值
    :return: J值
    """
    m = X.shape[0]
    h = np.dot(X, theta)
    return np.dot((h - Y).T, (h - Y)) / (2 * m)


X = np.array([[0, 1, 2, 4]]).T
Y = np.array([[0, 1, 2, 4]]).T

# 从-2到4之间返回均匀间隔的数字,共101个
# theta是101*1的矩阵
theta = np.array([np.linspace(-2, 4, 101)]).T

J_list = []
for i in range(101):
    current_theta = theta[i:(i + 1)].T
    cost = calcu_cost(current_theta, X, Y)
    J_list.append(cost[0, 0])

plt.plot(theta, J_list)

plt.xlabel('theta_1')
plt.ylabel('J(theta)')
plt.title('Cost Function Example1')
plt.grid(True)
plt.savefig('cost_theta.png', dpi=200)
plt.show()

# -*- coding:utf8 -*-

"""
@author: [email protected]

@date: Tue, May 23 2017

@time: 19:05:20 GMT+8

matplotlib version: 2.0.2
"""

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.axes3d import Axes3D
import numpy as np


def calcu_cost(theta_0, theta_1, X, Y):
    """ 计算代价函数的值

    :param theta_0: y轴上的值
    :param theta_1: 斜率
    :param X: x值
    :param Y: y值
    :return: J值
    """
    m = X.shape[0]
    h = np.dot(X, theta_1) + theta_0
    return np.dot((h - Y).T, (h - Y)) / (2 * m)


X = np.array([[0, 1, 2, 4]]).T
Y = np.array([[0, 1, 2, 4]]).T

# 预估的点数
points_num = 41
# 点数最小值
min_point = -2
# 点数最大值
max_point = 2

# 从-2到4之间返回均匀间隔的数字,共101个
origin_theta_0 = np.array([np.linspace(min_point, max_point, points_num)]).T
origin_theta_1 = np.array([np.linspace(min_point, max_point, points_num)]).T

theta_0_list = []
theta_1_list = []

J_list = []
for i in range(points_num):
    current_theta_0 = origin_theta_0[i:(i + 1)].T
    for j in range(points_num):
        theta_0_list.append(current_theta_0[0, 0])
        current_theta_1 = origin_theta_1[j:(j + 1)].T
        theta_1_list.append(current_theta_1[0, 0])
        cost = calcu_cost(current_theta_0, current_theta_1, X, Y)
        J_list.append(cost[0, 0])

fig = plt.figure()
ax = Axes3D(fig)
ax.scatter(theta_0_list, theta_1_list, J_list, color='c')

for j in range(len(theta_0_list)):
    if J_list[j] == min(J_list):
        label_txt = 'Min J_theta(%s, %s)= %s' % (str(theta_0_list[j]), str(theta_1_list[j]), str(J_list[j]))
        ax.scatter(theta_0_list[j], theta_1_list[j], J_list[j], color='k', label=label_txt)
ax.set_xlabel('theta_0')
ax.set_ylabel('theta_1')
ax.set_zlabel('J_theta')
ax.legend(loc='upper right')
ax.view_init(30, 35)
plt.show()