python实现梯度下降并可视化

python实现梯度下降并可视化

import numpy as np
import matplotlib.pyplot as plt


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]
        totalError += (y - (w * x + b)) ** 2
    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]
        b_gradient += -(2 / N) * (y - ((w_current * x) + b_current))
        w_gradient += -(2 / N) * x * (y - ((w_current * x) + b_current))
    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
    m = starting_w
    for i in range(num_iterations):
        b, m = step_gradient(b, m, np.array(points), learning_rate)
    return b, m


def run():
    points = np.genfromtxt("E:\GithubProject\Deep-Learning-with-PyTorch-Tutorials\lesson04-简单回归案例实战\data.csv",
                           delimiter=",")
    learning_rate = 0.0001
    initial_b = 0
    initial_w = 0
    num_iterations = 10000
    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)))

    p=np.array(points)
    plt.figure()
    plt.plot(p[:,0],p[:,1],'ro')
    plt.xlabel('x')
    plt.ylabel('y')
    plt.title('data')


    print("Running...")
    b, w = gradient_descent_runner(points, initial_b, initial_w, learning_rate, num_iterations)
    print("After {0} iterations b={1},m={2},error={3}".format(num_iterations, b, w,
                                                              compute_error_for_line_given_points(b, w, points)))

    x=np.linspace(0,100,100)
    y=w*x+b
    plt.plot(x,y,'orange')
    plt.show()


if __name__ == "__main__":
    run()

下面是可视化图以及拟合的曲线

数据就不给了，就是一堆点集，读者可以随机来生成