python - 绘制 SVC 拉普拉斯核的决策边界时出错

Question

我正在尝试在此scikit-learn 帖子的类似行上使用预先计算的拉普拉斯内核（下面的代码）绘制 SVM 分类器的决策边界。我将测试点作为网格值(xx, yy)，就像帖子中提到的那样，训练点X 和y. 我能够使用训练点来拟合预先计算的内核。

import numpy as np
#from sklearn.model_selection import train_test_split
import matplotlib.pyplot as plt
from sklearn.datasets import load_iris
from sklearn.svm import SVC
from sklearn.metrics.pairwise import laplacian_kernel

#Load the iris data
iris_data = load_iris()

#Split the data and target
X = iris_data.data[:, :2]
y = iris_data.target

#Step size in mesh plot
h = 0.02

#Convert X and y to a numpy array
X = np.array(X)
y = np.array(y)

#Using Laplacian kernel - https://scikit-learn.org/stable/modules/metrics.html#laplacian-kernel
K = np.array(laplacian_kernel(X, gamma=.5))
svm = SVC(kernel='precomputed').fit(K, np.ravel(y))

# create a mesh to plot in
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, h),
                     np.arange(y_min, y_max, h))

# Plot the decision boundary. For that, we will assign a color to each
# point in the mesh [x_min, x_max]x[y_min, y_max].
#plt.subplot(2, 2, i + 1)
#plt.subplots_adjust(wspace=0.4, hspace=0.4)

# Calculate the gram matrix for test points. Here is where the error is coming. xx- test, X-train.
K_test = np.array(laplacian_kernel(xx, X,  gamma=.5)) 

#Predict using the gram matrix for test
Z = svm.predict(np.c_[K_test])

# Put the result into a color plot
Z = Z.reshape(xx.shape)
plt.contourf(xx, yy, Z, cmap=plt.cm.coolwarm, alpha=0.8)

# Plot also the training points
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.coolwarm)
plt.xlabel('Sepal length')
plt.ylabel('Sepal width')
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())
plt.xticks(())
plt.yticks(())
plt.title('SVC with Laplace kernel')

plt.show()

但是，当我尝试在图表上为网格点绘制决策边界时，出现以下错误。

Traceback (most recent call last):
  File "/home/user/Src/laplce.py", line 37, in <module>
    K_test = np.array(laplacian_kernel(xx, X,  gamma=.5)) 
  File "/home/user/.local/lib/python3.9/site-packages/sklearn/metrics/pairwise.py", line 1136, in laplacian_kernel
    X, Y = check_pairwise_arrays(X, Y)
  File "/home/user/.local/lib/python3.9/site-packages/sklearn/utils/validation.py", line 63, in inner_f
    return f(*args, **kwargs)
  File "/home/user/.local/lib/python3.9/site-packages/sklearn/metrics/pairwise.py", line 160, in check_pairwise_arrays
    raise ValueError("Incompatible dimension for X and Y matrices: "
ValueError: Incompatible dimension for X and Y matrices: X.shape[1] == 280 while Y.shape[1] == 2

那么，如何解决错误并绘制虹膜数据的决策边界？提前致谢

标签： pythonmatplotlibscikit-learnsvmcontour

Answer 1

问题是在应用拉普拉斯算子之前让您的网格网格进入与训练矩阵相同的维度。所以如果我们运行下面的代码来适应 svm ：

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import load_iris
from sklearn.svm import SVC
from sklearn.metrics.pairwise import laplacian_kernel

iris_data = load_iris()

X = iris_data.data[:, :2]
y = iris_data.target
h = 0.02

K = laplacian_kernel(X,gamma=.5)
svm = SVC(kernel='precomputed').fit(K, y)

像你一样创建网格：

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

xx,yy = np.meshgrid(np.arange(x_min, x_max, h),np.arange(y_min, y_max, h))

您对拉普拉斯算子的原始输入是 (150,2)，因此您基本上需要将您的xx,yy输入分为 2 列：

x_test = np.vstack([xx.ravel(),yy.ravel()]).T

K_test = laplacian_kernel(x_test, X,  gamma=.5)
Z = svm.predict(K_test)
Z = Z.reshape(xx.shape)

然后绘制：

plt.contourf(xx, yy, Z, cmap=plt.cm.coolwarm, alpha=0.8)
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.coolwarm)
plt.xlabel('Sepal length')
plt.ylabel('Sepal width')
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())

这些点或多或少是正确的，您可以看到它不能很好地解决 1,2：

pd.crosstab(y,svm.predict(K))

col_0   0   1   2
row_0           
0   49  1   0
1   0   35  15
2   0   11  39