ML - SVM 使用多项式特征

---

SVM中的使用多项式特征

import numpy as np
import matplotlib.pyplot as plt
 
from sklearn import datasets

X, y = datasets.make_moons()
 
X.shape
# (100, 2)
 
y.shape
# (100,)
 
plt.scatter(X[y==0,0], X[y==0,1])
plt.scatter(X[y==1,0], X[y==1,1])
plt.show()

---

X, y = datasets.make_moons(noise=0.15, random_state=666)

plt.scatter(X[y==0,0], X[y==0,1])
plt.scatter(X[y==1,0], X[y==1,1])
plt.show()

---

使用多项式特征的SVM

from sklearn.preprocessing import PolynomialFeatures, StandardScaler
from sklearn.svm import LinearSVC
from sklearn.pipeline import Pipeline

def PolynomialSVC(degree, C=1.0):
    return Pipeline([
        ("poly", PolynomialFeatures(degree=degree)),
        ("std_scaler", StandardScaler()),
        ("linearSVC", LinearSVC(C=C))
    ])

---

poly_svc = PolynomialSVC(degree=3)
poly_svc.fit(X, y)
# Pipeline(steps=[('poly', PolynomialFeatures(degree=3, include_bias=True, interaction_only=False)), ('std_scaler', StandardScaler(copy=True, with_mean=True, with_std=True)), ('linearSVC', LinearSVC(C=1.0, class_weight=None, dual=True, fit_intercept=True, intercept_scaling=1, loss='squared_hinge', max_iter=1000, multi_class='ovr', penalty='l2', random_state=None, tol=0.0001, verbose=0))])

---

def plot_decision_boundary(model, axis):
    
    x0, x1 = np.meshgrid(
        np.linspace(axis[0], axis[1], int((axis[1]-axis[0])*100)).reshape(-1, 1),
        np.linspace(axis[2], axis[3], int((axis[3]-axis[2])*100)).reshape(-1, 1),
    )
    X_new = np.c_[x0.ravel(), x1.ravel()]

    y_predict = model.predict(X_new)
    zz = y_predict.reshape(x0.shape)

    from matplotlib.colors import ListedColormap
    custom_cmap = ListedColormap(['#EF9A9A','#FFF59D','#90CAF9'])
    
    plt.contourf(x0, x1, zz, linewidth=5, cmap=custom_cmap)

plot_decision_boundary(poly_svc, axis=[-1.5, 2.5, -1.0, 1.5])
plt.scatter(X[y==0,0], X[y==0,1])
plt.scatter(X[y==1,0], X[y==1,1])
plt.show()

---

使用多项式核函数的SVM

在 SVM 中，多项式可以不使用 PolynomialFeatures 的方式（先对数据转化为高维的有多项式项的特征，再扔进 LinearSVC）
SVM 算法中 有个方式可以直接使用 多项式的特征，称为 多项式核。计算结果和 PolynomialFeatures 产生的结果不同。

from sklearn.svm import SVC

def PolynomialKernelSVC(degree, C=1.0):
    return Pipeline([
        ("std_scaler", StandardScaler()),
        ("kernelSVC", SVC(kernel="poly", degree=degree, C=C))  # 当 kernel="poly" 的时候，可以同样达到多项式特征的效果。
    ])

poly_kernel_svc = PolynomialKernelSVC(degree=3)
poly_kernel_svc.fit(X, y)
# Pipeline(steps=[('std_scaler', StandardScaler(copy=True, with_mean=True, with_std=True)), ('kernelSVC', SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0, decision_function_shape=None, degree=3, gamma='auto', kernel='poly', max_iter=-1, probability=False, random_state=None, shrinking=True, tol=0.001, verbose=False))])

 
plot_decision_boundary(poly_kernel_svc, axis=[-1.5, 2.5, -1.0, 1.5])
plt.scatter(X[y==0,0], X[y==0,1])
plt.scatter(X[y==1,0], X[y==1,1])
plt.show()

---

---