40琳拨、高斯過程分類的等概率線(GPC)

import numpy as np

from matplotlib import pyplot as plt

from matplotlib import cm

from sklearn.gaussian_process import GaussianProcessClassifier

from sklearn.gaussian_process.kernels import DotProduct, ConstantKernel as C

plt.rcParams['font.sans-serif'] = ['SimHei']

plt.rcParams['axes.unicode_minus'] = False

# 幾個常數(shù)

lim = 8

def g(x):

? ? """The function to predict (classification will then consist in predicting

? ? whether g(x) <= 0 or not)"""

? ? return 5. - x[:, 1] - .5 * x[:, 0] ** 2.

# 實驗設(shè)計

X = np.array([[-4.61611719, -6.00099547],

? ? ? ? ? ? ? [4.10469096, 5.32782448],

? ? ? ? ? ? ? [0.00000000, -0.50000000],

? ? ? ? ? ? ? [-6.17289014, -4.6984743],

? ? ? ? ? ? ? [1.3109306, -6.93271427],

? ? ? ? ? ? ? [-5.03823144, 3.10584743],

? ? ? ? ? ? ? [-2.87600388, 6.74310541],

? ? ? ? ? ? ? [5.21301203, 4.26386883]])

# 觀察

y = np.array(g(X) > 0, dtype=int)

# 實例化和擬合高斯過程模型

kernel = C(0.1, (1e-5, np.inf)) * DotProduct(sigma_0=0.1) ** 2

gp = GaussianProcessClassifier(kernel=kernel)

gp.fit(X, y)

print("Learned kernel: %s " % gp.kernel_)

# 求實函數(shù)與預(yù)測概率

res = 50

x1, x2 = np.meshgrid(np.linspace(- lim, lim, res),

? ? ? ? ? ? ? ? ? ? np.linspace(- lim, lim, res))

xx = np.vstack([x1.reshape(x1.size), x2.reshape(x2.size)]).T

y_true = g(xx)

y_prob = gp.predict_proba(xx)[:, 1]

y_true = y_true.reshape((res, res))

y_prob = y_prob.reshape((res, res))

#繪制概率分類等值

fig = plt.figure(1)

ax = fig.gca()

ax.axes.set_aspect('equal')

plt.xticks([])

plt.yticks([])

ax.set_xticklabels([])

ax.set_yticklabels([])

plt.xlabel('$x_1$')

plt.ylabel('$x_2$')

cax = plt.imshow(y_prob, cmap=cm.gray_r, alpha=0.8,

? ? ? ? ? ? ? ? extent=(-lim, lim, -lim, lim))

norm = plt.matplotlib.colors.Normalize(vmin=0., vmax=0.9)

cb = plt.colorbar(cax, ticks=[0., 0.2, 0.4, 0.6, 0.8, 1.], norm=norm)

cb.set_label(r'${\rm \mathbb{P}}\left[\widehat{G}(\mathbf{x}) \leq 0\right]$')

plt.clim(0, 1)

plt.plot(X[y <= 0, 0], X[y <= 0, 1], 'r.', markersize=12)

plt.plot(X[y > 0, 0], X[y > 0, 1], 'b.', markersize=12)

plt.contour(x1, x2, y_true, [0.], colors='k', linestyles='dashdot')

cs = plt.contour(x1, x2, y_prob, [0.666], colors='b',

? ? ? ? ? ? ? ? linestyles='solid')

plt.clabel(cs, fontsize=11)

cs = plt.contour(x1, x2, y_prob, [0.5], colors='k',

? ? ? ? ? ? ? ? linestyles='dashed')

plt.clabel(cs, fontsize=11)

cs = plt.contour(x1, x2, y_prob, [0.334], colors='r',

? ? ? ? ? ? ? ? linestyles='solid')

plt.clabel(cs, fontsize=11)

plt.title("高斯過程分類的等概率線(GPC)" , fontsize=12)

plt.show()