绘制scikit-learn（sklearn）SVM决策边界/表面

Question

我目前正在使用python的scikit库使用线性内核执行多类SVM。 样本训练数据和测试数据如下：

模型数据：

x = [[20,32,45,33,32,44,0],[23,32,45,12,32,66,11],[16,32,45,12,32,44,23],[120,2,55,62,82,14,81],[30,222,115,12,42,64,91],[220,12,55,222,82,14,181],[30,222,315,12,222,64,111]]
y = [0,0,0,1,1,2,2]

我想绘制决策边界并可视化数据集。有人可以帮忙绘制此类数据吗？

上面给出的数据只是模拟数据，因此可以随时更改值。 至少如果您可以建议要执行的步骤，这将很有帮助。 预先感谢

Answer 1

您只需选择2个功能即可。原因是您无法绘制7D图。选择2个特征后，仅将其用于决策表面的可视化。

现在，您要问的下一个问题是How can I choose these 2 features?。好吧，有很多方法。您可以执行univariate F-value (feature ranking) test并查看哪些功能/变量最重要。然后，您可以将这些用于绘图。另外，我们可以使用PCA将尺寸从7减少到2。

---

2个特征的2D绘图并使用虹膜数据集

from sklearn.svm import SVC
import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm, datasets

iris = datasets.load_iris()
# Select 2 features / variable for the 2D plot that we are going to create.
X = iris.data[:, :2]  # we only take the first two features.
y = iris.target

def make_meshgrid(x, y, h=.02):
    x_min, x_max = x.min() - 1, x.max() + 1
    y_min, y_max = y.min() - 1, y.max() + 1
    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
    return xx, yy

def plot_contours(ax, clf, xx, yy, **params):
    Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
    Z = Z.reshape(xx.shape)
    out = ax.contourf(xx, yy, Z, **params)
    return out

model = svm.SVC(kernel='linear')
clf = model.fit(X, y)

fig, ax = plt.subplots()
# title for the plots
title = ('Decision surface of linear SVC ')
# Set-up grid for plotting.
X0, X1 = X[:, 0], X[:, 1]
xx, yy = make_meshgrid(X0, X1)

plot_contours(ax, clf, xx, yy, cmap=plt.cm.coolwarm, alpha=0.8)
ax.scatter(X0, X1, c=y, cmap=plt.cm.coolwarm, s=20, edgecolors='k')
ax.set_ylabel('y label here')
ax.set_xlabel('x label here')
ax.set_xticks(())
ax.set_yticks(())
ax.set_title(title)
ax.legend()
plt.show()

---

编辑：应用PCA减少尺寸。

from sklearn.svm import SVC
import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm, datasets
from sklearn.decomposition import PCA

iris = datasets.load_iris()

X = iris.data  
y = iris.target

pca = PCA(n_components=2)
Xreduced = pca.fit_transform(X)

def make_meshgrid(x, y, h=.02):
    x_min, x_max = x.min() - 1, x.max() + 1
    y_min, y_max = y.min() - 1, y.max() + 1
    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
    return xx, yy

def plot_contours(ax, clf, xx, yy, **params):
    Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
    Z = Z.reshape(xx.shape)
    out = ax.contourf(xx, yy, Z, **params)
    return out

model = svm.SVC(kernel='linear')
clf = model.fit(Xreduced, y)

fig, ax = plt.subplots()
# title for the plots
title = ('Decision surface of linear SVC ')
# Set-up grid for plotting.
X0, X1 = Xreduced[:, 0], Xreduced[:, 1]
xx, yy = make_meshgrid(X0, X1)

plot_contours(ax, clf, xx, yy, cmap=plt.cm.coolwarm, alpha=0.8)
ax.scatter(X0, X1, c=y, cmap=plt.cm.coolwarm, s=20, edgecolors='k')
ax.set_ylabel('PC2')
ax.set_xlabel('PC1')
ax.set_xticks(())
ax.set_yticks(())
ax.set_title('Decison surface using the PCA transformed/projected features')
ax.legend()
plt.show()

Answer 2

您还可以使用软件包seaborn，在其中您可以选择进行特征到特征的散点图，如here所示。

Answer 3

您可以使用mlxtend。很干净。

首先执行pip install mlxtend，然后：

from sklearn.svm import SVC
import matplotlib.pyplot as plt
from mlxtend.plotting import plot_decision_regions

svm = SVC(C=0.5, kernel='linear')
svm.fit(X, y)
plot_decision_regions(X, y, clf=svm, legend=2)
plt.show()

其中 X 是二维数据矩阵，而 y 是训练标签的关联向量。