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多层感知器中的正则化变化#

在合成数据集上比较不同正则化参数 ‘alpha’ 的值。图表显示，不同的 alpha 会产生不同的决策函数。

Alpha 是正则化项（也称为惩罚项）的参数，通过限制权重的大小来对抗过拟合。增加 alpha 可能通过鼓励较小的权重来修正高方差（过拟合的迹象），从而导致决策边界图的曲率较小。同样，减少 alpha 可能通过鼓励较大的权重来修正高偏差（欠拟合的迹象），可能导致更复杂的决策边界。

alpha 0.10, alpha 0.32, alpha 1.00, alpha 3.16, alpha 10.00, alpha 0.10, alpha 0.32, alpha 1.00, alpha 3.16, alpha 10.00, alpha 0.10, alpha 0.32, alpha 1.00, alpha 3.16, alpha 10.00

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

import numpy as np
from matplotlib import pyplot as plt
from matplotlib.colors import ListedColormap

from sklearn.datasets import make_circles, make_classification, make_moons
from sklearn.model_selection import train_test_split
from sklearn.neural_network import MLPClassifier
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import StandardScaler

h = 0.02  # step size in the mesh

alphas = np.logspace(-1, 1, 5)

classifiers = []
names = []
for alpha in alphas:
    classifiers.append(
        make_pipeline(
            StandardScaler(),
            MLPClassifier(
                solver="lbfgs",
                alpha=alpha,
                random_state=1,
                max_iter=2000,
                early_stopping=True,
                hidden_layer_sizes=[10, 10],
            ),
        )
    )
    names.append(f"alpha {alpha:.2f}")

X, y = make_classification(
    n_features=2, n_redundant=0, n_informative=2, random_state=0, n_clusters_per_class=1
)
rng = np.random.RandomState(2)
X += 2 * rng.uniform(size=X.shape)
linearly_separable = (X, y)

datasets = [
    make_moons(noise=0.3, random_state=0),
    make_circles(noise=0.2, factor=0.5, random_state=1),
    linearly_separable,
]

figure = plt.figure(figsize=(17, 9))
i = 1
# 遍历数据集
for X, y in datasets:
    # 划分为训练部分和测试部分
    X_train, X_test, y_train, y_test = train_test_split(
        X, y, test_size=0.4, random_state=42
    )

    x_min, x_max = X[:, 0].min() - 0.5, X[:, 0].max() + 0.5
    y_min, y_max = X[:, 1].min() - 0.5, X[:, 1].max() + 0.5
    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))

    # 先绘制数据集
    cm = plt.cm.RdBu
    cm_bright = ListedColormap(["#FF0000", "#0000FF"])
    ax = plt.subplot(len(datasets), len(classifiers) + 1, i)
    # Plot the training points
    ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright)
    # 和测试点
    ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright, alpha=0.6)
    ax.set_xlim(xx.min(), xx.max())
    ax.set_ylim(yy.min(), yy.max())
    ax.set_xticks(())
    ax.set_yticks(())
    i += 1

    # 遍历分类器
    for name, clf in zip(names, classifiers):
        ax = plt.subplot(len(datasets), len(classifiers) + 1, i)
        clf.fit(X_train, y_train)
        score = clf.score(X_test, y_test)

        # 绘制决策边界。为此，我们将为网格 [x_min, x_max] x [y_min, y_max] 中的每个点分配一个颜色。
        if hasattr(clf, "decision_function"):
            Z = clf.decision_function(np.column_stack([xx.ravel(), yy.ravel()]))
        else:
            Z = clf.predict_proba(np.column_stack([xx.ravel(), yy.ravel()]))[:, 1]

        # 将结果放入彩色图中
        Z = Z.reshape(xx.shape)
        ax.contourf(xx, yy, Z, cmap=cm, alpha=0.8)

        # Plot also the training points
        ax.scatter(
            X_train[:, 0],
            X_train[:, 1],
            c=y_train,
            cmap=cm_bright,
            edgecolors="black",
            s=25,
        )
        # 和测试点
        ax.scatter(
            X_test[:, 0],
            X_test[:, 1],
            c=y_test,
            cmap=cm_bright,
            alpha=0.6,
            edgecolors="black",
            s=25,
        )

        ax.set_xlim(xx.min(), xx.max())
        ax.set_ylim(yy.min(), yy.max())
        ax.set_xticks(())
        ax.set_yticks(())
        ax.set_title(name)
        ax.text(
            xx.max() - 0.3,
            yy.min() + 0.3,
            f"{score:.3f}".lstrip("0"),
            size=15,
            horizontalalignment="right",
        )
        i += 1

figure.subplots_adjust(left=0.02, right=0.98)
plt.show()