机器学习之二分类画出决策边界

二分类画出决策边界

// 二分类决策边界
import numpy as np
import matplotlib.pyplot as plt

data = np.loadtxt('ex2data2.txt', delimiter=',')
x, y = np.hsplit(data, [-1, ])
X = np.insert(x, 0, 1, axis=1)


def Map(x1, x2):
    degrees = 6
    out = np.ones((x1.shape[0], 1))
    for i in range(1, degrees + 1):
        for j in range(0, i + 1):
            a1 = x1 ** (i - j)
            a2 = x2 ** (j)
            term = (a1 * a2).reshape(a1.shape[0], 1)
            out = np.hstack((out, term))
    return out


onex = Map(X[:, 1], X[:, 2])

#前向传播
def model(X, theta):
    z = X.dot(theta)
    h = 1 / (1 + np.exp(-z))
    return h

#损失函数
def Cost(theta, X, y, lamda):
    m = len(y)
    h = model(X, theta)
    cost = -np.mean(y * np.log(h) + (1 - y) * np.log(1 - h))
    reg = lamda / (2 * m) * np.sum(theta[1:] * theta[1:])
    return cost + reg

#梯度下降
def Grad(theta, X, y, lamda):
    h = model(X, theta)
    grad = (1 / m) * X.T.dot(h - y)
    reg = theta[1:]
    reg = np.insert(reg, 0, 0, axis=0)
    thetareg = lamda / m * reg
    return thetareg + grad

#训练模型
def train(theta, X, y, lamda, iters=1000, alpha=1):
    Jlist = []
    for i in range(iters):
        h = model(X, theta)
        cost = Cost(theta, X, y, lamda)
        grad = Grad(theta, X, y, lamda)
        theta = theta - alpha * grad
        if i % 200 == 0:
            print('第{}次，代价{}'.format(i, cost))
            Jlist.append(cost)
    return theta, Jlist


def comput(theta):
    h = model(onex, theta)
    tiao = np.where(h >= 0.5, 1, 0)
    jisuan = np.mean(np.equal(tiao, y))
    return jisuan


def plot_show(theta, lamda):
    size = 100
    x1 = np.linspace(-1, 1.5, size)
    x2 = np.linspace(-1, 1.5, size)
    z = np.zeros((len(x1), len(x2)))
    for i in range(len(x1)):
        for j in range(len(x2)):
            new = Map(np.array([x1[i]]), np.array([x2[j]]))
            z[i][j] = new.dot(theta)
    z = z.transpose()
    mycontour = plt.contour(x1, x2, z, [0])
    plt.clabel(mycontour, inline=1, fontsize=10, fmt='lamda%d' % lamda)


if __name__ == '__main__':
    lamda = 10
    m, n = onex.shape
    theta = np.zeros((n, 1))
    theta, cost = train(theta, onex, y, lamda)
    print(lamda, comput(theta))

    plt.scatter(X[:, 1], X[:, 2], c=y.ravel(), s=18)
    plot_show(theta, lamda)
    plt.show()

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