EX 4: SVM_with _custom _kernel.md

Last updated 18 days ago

https://scikit-learn.org/stable/auto_examples/svm/plot_custom_kernel.html#sphx-glr-auto-examples-svm-plot-custom-kernel-py

在範例七中介紹了SVM 不同內建 Kernel 的比較,此範例用來展示,如何自行設計 SVM 的 Kernel

(一)引入函式庫

引入函式如下:

  1. numpy : 產生陣列數值

  2. matplotlib.pyplot : 用來繪製影像

  3. sklearn.svm : SVM 支持向量機之演算法物件

  4. sklearn.datasets : 匯入內建資料庫

import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm, datasets
# import some data to play with
iris = datasets.load_iris()
X = iris.data[:, :2] # we only take the first two features. We could
# avoid this ugly slicing by using a two-dim dataset
Y = iris.target

iris = datasets.load_iris() : 匯入內建資料庫鳶尾花的資料,將資料存入變數iris中

(二)SVM Model

def my_kernel(X, Y):
"""
We create a custom kernel:
(2 0)
k(X, Y) = X ( ) Y.T
(0 1)
"""
M = np.array([[2, 0], [0, 1.0]])
return np.dot(np.dot(X, M), Y.T)

自行定義函式來設計出自己想要的 Kernel 型式

h = .02 # step size in the mesh
# we create an instance of SVM and fit out data.
clf = svm.SVC(kernel=my_kernel)
clf.fit(X, Y)

svm.SVC 的 Kernel 設成自訂的 Kernel 型式

# 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].
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))
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])

np.meshgrid : 生成網格採樣點

# Put the result into a color plot
Z = Z.reshape(xx.shape)
plt.pcolormesh(xx, yy, Z, cmap=plt.cm.Paired)
# Plot also the training points
plt.scatter(X[:, 0], X[:, 1], c=Y, cmap=plt.cm.Paired, edgecolors='k')
plt.title('3-Class classification using Support Vector Machine with custom'
' kernel')
plt.axis('tight')
plt.show()

最後利用以上指令將結果圖顯示出來,plt.pcolormesh會根據clf.predict的結果繪製分類圖。

plt.pcolormesh : 能夠利用色塊的方式直觀表現出分類邊界

以下為結果圖 :

(三)完整程式碼

Python source code: plot_custom_kernel.py

https://scikit-learn.org/stable/_downloads/plot_custom_kernel.py

iPython source code: plot_custom_kernel.ipynb

https://scikit-learn.org/stable/_downloads/plot_custom_kernel.ipynb

"""
======================
SVM with custom kernel
======================
Simple usage of Support Vector Machines to classify a sample. It will
plot the decision surface and the support vectors.
"""
print(__doc__)
import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm, datasets
# import some data to play with
iris = datasets.load_iris()
X = iris.data[:, :2] # we only take the first two features. We could
# avoid this ugly slicing by using a two-dim dataset
Y = iris.target
def my_kernel(X, Y):
"""
We create a custom kernel:
(2 0)
k(X, Y) = X ( ) Y.T
(0 1)
"""
M = np.array([[2, 0], [0, 1.0]])
return np.dot(np.dot(X, M), Y.T)
h = .02 # step size in the mesh
# we create an instance of SVM and fit out data.
clf = svm.SVC(kernel=my_kernel)
clf.fit(X, Y)
# 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].
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))
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
# Put the result into a color plot
Z = Z.reshape(xx.shape)
plt.pcolormesh(xx, yy, Z, cmap=plt.cm.Paired)
# Plot also the training points
plt.scatter(X[:, 0], X[:, 1], c=Y, cmap=plt.cm.Paired, edgecolors='k')
plt.title('3-Class classification using Support Vector Machine with custom'
' kernel')
plt.axis('tight')
plt.show()