辅助函数绘制的子图出现意外偏移

Question

我正在尝试将两个图合并为一个：

1. http://scikit-learn.org/stable/auto_examples/linear_model/plot_sgd_iris.html
2. http://scikit-learn.org/stable/auto_examples/ensemble/plot_voting_decision_regions.html#sphx-glr-auto-examples-ensemble-plot-voting-decision-regions-py

在左图中，我想显示决策边界与对应于 OVA 分类器的超平面，在右图中，我想显示决策概率。

这是目前为止的代码：

import numpy as np
import matplotlib.pyplot as plt
import seaborn as sn

from sklearn import datasets
from sklearn import preprocessing
from sklearn.neighbors import KNeighborsClassifier
from sklearn.tree import DecisionTreeClassifier
from sklearn.linear_model import SGDClassifier
from sklearn.svm import SVC

def plot_hyperplane(c, color, fitted_model):
    """
    Plot the one-against-all classifiers for the given model.

    Parameters
    --------------

    c : index of the hyperplane to be plot
    color : color to be used when drawing the line
    fitted_model : the fitted model
    """
    xmin, xmax = plt.xlim()
    ymin, ymax = plt.ylim()

    try:
        coef = fitted_model.coef_
        intercept = fitted_model.intercept_
    except:
        return

    def line(x0):
        return (-(x0 * coef[c, 0]) - intercept[c]) / coef[c, 1]

    plt.plot([xmin, xmax], [line(xmin), line(xmax)], ls="--", color=color, zorder=3)


def plot_decision_boundary(X, y, fitted_model, features, targets):
    """
    This function plots a model decision boundary as well as it tries to plot 
    the decision probabilities, if available.
    Requires a model fitted with two features only.

    Parameters
    --------------

    X : the data to learn
    y : the classification labels
    fitted_model : the fitted model
    """
    cmap = plt.get_cmap('Set3')
    prob = cmap
    colors = [cmap(i) for i in np.linspace(0, 1, len(fitted_model.classes_))]

    plt.figure(figsize=(9.5, 5))
    for i, plot_type in enumerate(['Decision Boundary', 'Decision Probabilities']):
        plt.subplot(1, 2, i+1)

        mesh_step_size = 0.01  # step size in the mesh
        x_min, x_max = X[:, 0].min() - .1, X[:, 0].max() + .1
        y_min, y_max = X[:, 1].min() - .1, X[:, 1].max() + .1
        xx, yy = np.meshgrid(np.arange(x_min, x_max, mesh_step_size), np.arange(y_min, y_max, mesh_step_size))
        # First plot, predicted results using the given model
        if i == 0:
            Z = fitted_model.predict(np.c_[xx.ravel(), yy.ravel()])
            for h, color in zip(fitted_model.classes_, colors):
                plot_hyperplane(h, color, fitted_model) 
        # Second plot, predicted probabilities using the given model
        else:
            prob = 'RdYlBu_r'
            try:
                Z = fitted_model.predict_proba(np.c_[xx.ravel(), yy.ravel()])[:, 1]
            except:
                plt.text(0.4, 0.5, 'Probabilities Unavailable', horizontalalignment='center', 
                         verticalalignment='center', transform=plt.gca().transAxes, fontsize=12)
                plt.axis('off')
                break
        Z = Z.reshape(xx.shape)
        # Display Z
        plt.imshow(Z, interpolation='nearest', cmap=prob, alpha=0.5, 
                   extent=(x_min, x_max, y_min, y_max), origin='lower', zorder=1)
        # Plot the data points
        for i, color in zip(fitted_model.classes_, colors):
            idx = np.where(y == i)
            plt.scatter(X[idx, 0], X[idx, 1], facecolor=color, edgecolor='k', lw=1,
                        label=iris.target_names[i], cmap=cmap, alpha=0.8, zorder=2)
        plt.title(plot_type + '\n' + 
                  str(fitted_model).split('(')[0]+ ' Test Accuracy: ' + str(np.round(fitted_model.score(X, y), 5)))
        plt.xlabel(features[0])
        plt.ylabel(features[1])
        plt.gca().set_aspect('equal')   
    plt.legend(loc='center left', bbox_to_anchor=(1, 0.5))    
    plt.tight_layout()
    plt.subplots_adjust(top=0.9, bottom=0.08, wspace=0.02)
    plt.show()


if __name__ == '__main__': 
    iris = datasets.load_iris()
    X = iris.data[:, [0, 2]]
    y = iris.target

    scaler = preprocessing.StandardScaler().fit_transform(X)

    clf1 = DecisionTreeClassifier(max_depth=4)
    clf2 = KNeighborsClassifier(n_neighbors=7)
    clf3 = SVC(kernel='rbf', probability=True)
    clf4 = SGDClassifier(alpha=0.001, n_iter=100).fit(X, y)

    clf1.fit(X, y)
    clf2.fit(X, y)
    clf3.fit(X, y)
    clf4.fit(X, y)

    plot_decision_boundary(X, y, clf1, iris.feature_names, iris.target_names[[0, 2]])
    plot_decision_boundary(X, y, clf2, iris.feature_names, iris.target_names[[0, 2]])
    plot_decision_boundary(X, y, clf3, iris.feature_names, iris.target_names[[0, 2]])
    plot_decision_boundary(X, y, clf4, iris.feature_names, iris.target_names[[0, 2]])

结果：

可以看出，对于最后一个示例（给定代码中的clf4），到目前为止，我无法将超平面绘制在错误的位置。我想知道如何纠正这个问题。应将它们转换为适合模型所用特征的正确范围。

谢谢。

Answer 1

显然，问题在于表示超平面的虚线末端与最终和预期的xlim 和ylim 不一致。这种情况的一个好处是您已经定义了x_min, x_max, y_min, y_max。所以使用它并通过在绘制超平面之前应用以下 3 行来修复 xlim 和 ylim（具体来说，在您的注释行前面添加 # First plot, predicted results using the given model）。

        ax = plt.gca()
        ax.set_xlim((x_min, x_max), auto=False)
        ax.set_ylim((y_min, y_max), auto=False)