绘制 SVC 拉普拉斯核的决策边界时出错

Posted 2023-03-12

【中文标题】绘制 SVC 拉普拉斯核的决策边界时出错

【英文标题】：Error in plotting the decision boundary for SVC Laplace kernel

【发布时间】：2021-12-19 06:55:39

【问题描述】：

我正在尝试在此scikit-learn post 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)，就像在帖子中提到的那样，将训练点作为X 和y。我能够使用训练点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

【参考方案1】：

问题是在应用拉普拉斯算子之前，将您的网格网格设为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 放入 2 列中：

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，你可以看到它并没有很好地解决 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

【讨论】：

谢谢解答，可以根据颜色改变形状吗？例如，在上面的答案图中，是否可以将蓝色点的形状更改为三角形，将红色点的形状更改为正方形以便清晰识别？

你需要遍历你的标签，并分别绘制它们，见***.com/questions/30313882/…

谢谢它的工作。