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在 XOR 数据集上展示高斯过程分类 (GPC)#

此示例展示了在 XOR 数据集上应用 GPC。比较了一个平稳的各向同性核 (RBF) 和一个非平稳核 (DotProduct)。在这个特定的数据集上，DotProduct 核获得了显著更好的结果，因为类边界是线性的，并且与坐标轴重合。通常情况下，平稳核往往能获得更好的结果。

302**2 * RBF(length_scale=1.55) Log-Marginal-Likelihood:-24.237, 316**2 * DotProduct(sigma_0=0.0104) ** 2 Log-Marginal-Likelihood:-9.284

/app/scikit-learn-main-origin/sklearn/gaussian_process/kernels.py:431: ConvergenceWarning:

The optimal value found for dimension 0 of parameter k1__constant_value is close to the specified upper bound 100000.0. Increasing the bound and calling fit again may find a better value.

# 作者：scikit-learn 开发者
# SPDX-License-Identifier: BSD-3-Clause

import matplotlib.pyplot as plt
import numpy as np

from sklearn.gaussian_process import GaussianProcessClassifier
from sklearn.gaussian_process.kernels import RBF, DotProduct

xx, yy = np.meshgrid(np.linspace(-3, 3, 50), np.linspace(-3, 3, 50))
rng = np.random.RandomState(0)
X = rng.randn(200, 2)
Y = np.logical_xor(X[:, 0] > 0, X[:, 1] > 0)

# 拟合模型
plt.figure(figsize=(10, 5))
kernels = [1.0 * RBF(length_scale=1.15), 1.0 * DotProduct(sigma_0=1.0) ** 2]
for i, kernel in enumerate(kernels):
    clf = GaussianProcessClassifier(kernel=kernel, warm_start=True).fit(X, Y)

    # 为网格上的每个数据点绘制决策函数
    Z = clf.predict_proba(np.vstack((xx.ravel(), yy.ravel())).T)[:, 1]
    Z = Z.reshape(xx.shape)

    plt.subplot(1, 2, i + 1)
    image = plt.imshow(
        Z,
        interpolation="nearest",
        extent=(xx.min(), xx.max(), yy.min(), yy.max()),
        aspect="auto",
        origin="lower",
        cmap=plt.cm.PuOr_r,
    )
    contours = plt.contour(xx, yy, Z, levels=[0.5], linewidths=2, colors=["k"])
    plt.scatter(X[:, 0], X[:, 1], s=30, c=Y, cmap=plt.cm.Paired, edgecolors=(0, 0, 0))
    plt.xticks(())
    plt.yticks(())
    plt.axis([-3, 3, -3, 3])
    plt.colorbar(image)
    plt.title(
        "%s\n Log-Marginal-Likelihood:%.3f"
        % (clf.kernel_, clf.log_marginal_likelihood(clf.kernel_.theta)),
        fontsize=12,
    )

plt.tight_layout()
plt.show()