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:
numpy : 產生陣列數值
matplotlib.pyplot : 用來繪製影像
sklearn.svm : SVM 支持向量機之演算法物件
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)
將 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()
EX 1:Non_linear_SVM.md
機器學習資料集 Datasets