探索核函数的优势和缺陷

from sklearn.datasets import load_breast_cancer
from sklearn.model_selection import train_test_split
from sklearn.svm import SVC
import matplotlib.pyplot as plt
import numpy as np
from time import time
import datetime

cancer = load_breast_cancer()
x = cancer.data
y = cancer.target

plt.scatter(x[:, 0], x[:, 1], c=y)
plt.show()

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from sklearn.decomposition import PCA

x_dr = PCA(n_components=2).fit_transform(x)
plt.scatter(x_dr[:, 0], x_dr[:, 1], c=y)
plt.show()

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from mpl_toolkits import mplot3d

r = np.exp(-(x**2).sum(1))  # r.shape(300,)
rlim = np.linspace(min(r), max(r), 500)


# 定义一个绘制三维图像的函数
# elev表示上下旋转的角度
# azim表示平行旋转的角度
def plot_3D(elev=45, azim=30, x=x, y=y) -> None:
    ax = plt.subplot(projection="3d")
    ax.scatter3D(x[:, 0], x[:, 1], r, c=y, s=50, cmap="rainbow")
    ax.view_init(elev=elev, azim=azim)
    ax.set_xlabel("x")
    ax.set_ylabel("y")
    ax.set_zlabel("r")
    plt.show()


plot_3D()

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x_train, x_test, y_train, y_test = train_test_split(
    x, y, test_size=0.3, random_state=420
)

kernel = ["linear", "poly", "rbf", "sigmoid"]
time0 = time()
for i in kernel:
    clf = SVC(kernel=i, gamma="auto", degree=1, cache_size=5000).fit(x_train, y_train)
    print("The accuracy under kernel %s is %f" % (i, clf.score(x_test, y_test)))
    print(datetime.datetime.fromtimestamp(time() - time0).strftime("%M:%S:%f"))

The accuracy under kernel linear is 0.929825
00:00:278035
The accuracy under kernel poly is 0.923977
00:00:311496
The accuracy under kernel rbf is 0.596491
00:00:329552
The accuracy under kernel sigmoid is 0.596491
00:00:336953

import pandas as pd

data = pd.DataFrame(x)
data.describe([0.1, 0.15, 0.25, 0.50, 0.75, 0.90, 0.99]).T
# 量纲不统一，需要标准化

from sklearn.preprocessing import StandardScaler

x = StandardScaler().fit_transform(x)

x_train, x_test, y_train, y_test = train_test_split(
    x, y, test_size=0.3, random_state=420
)

kernel = ["linear", "poly", "rbf", "sigmoid"]
time0 = time()
for i in kernel:
    clf = SVC(kernel=i, gamma="auto", degree=1, cache_size=5000).fit(x_train, y_train)
    print("The accuracy under kernel %s is %f" % (i, clf.score(x_test, y_test)))
    print(datetime.datetime.fromtimestamp(time() - time0).strftime("%M:%S:%f"))

The accuracy under kernel linear is 0.976608
00:00:003820
The accuracy under kernel poly is 0.964912
00:00:007333
The accuracy under kernel rbf is 0.970760
00:00:013197
The accuracy under kernel sigmoid is 0.953216
00:00:019282

gamma_range = np.logspace(-10, 1, 50)
score = []
for i in gamma_range:
    clf = SVC(kernel="rbf", gamma=i, degree=1, cache_size=5000).fit(x_train, y_train)
    score.append(clf.score(x_test, y_test))
print(max(score), gamma_range[score.index(max(score))])
plt.plot(gamma_range, score)
plt.show()

0.9766081871345029 0.012067926406393264

from sklearn.model_selection import StratifiedShuffleSplit
from sklearn.model_selection import GridSearchCV

gamma_range = np.logspace(-10, 1, 20)
coef0_range = np.linspace(0, 5, 10)

param = dict(gamma=gamma_range, coef0=coef0_range)

cv = StratifiedShuffleSplit(n_splits=5, test_size=0.3, random_state=420)

grid = GridSearchCV(
    SVC(kernel="poly", cache_size=5000, degree=1), param_grid=param, cv=cv
)

grid.fit(x, y)

print(
    "The best parameters are %s with a score of %0.5f"
    % (grid.best_params_, grid.best_score_)
)
print(datetime.datetime.fromtimestamp(time() - time0).strftime("%M:%S:%f"))

The best parameters are {'coef0': 0.0, 'gamma': 0.18329807108324375} with a score of 0.96959
41:01:513573

重要参数 C

# (0.01,30,50)
C_range = np.linspace(0.01, 30, 50)
score = []
for c in C_range:
    clf = SVC(kernel="linear", C=c, cache_size=5000).fit(x_train, y_train)
    score.append(clf.score(x_test, y_test))
print(max(score), C_range[score.index(max(score))])
plt.plot(C_range, score)
plt.show()

0.9766081871345029 1.2340816326530613

# (0.01,30,50)
C_range = np.linspace(0.01, 30, 50)
score = []
for c in C_range:
    clf = SVC(kernel="rbf", C=c, cache_size=5000).fit(x_train, y_train)
    score.append(clf.score(x_test, y_test))
print(max(score), C_range[score.index(max(score))])
plt.plot(C_range, score)
plt.show()

0.9883040935672515 25.103673469387758

# 进一步细化
C_range = np.linspace(0.01, 30, 50)
score = []
for c in C_range:
    clf = SVC(kernel="rbf", C=c, cache_size=5000).fit(x_train, y_train)
    score.append(clf.score(x_test, y_test))
print(max(score), C_range[score.index(max(score))])
plt.plot(C_range, score)
plt.show()
print(datetime.datetime.fromtimestamp(time() - time0).strftime("%M:%S:%f"))

0.9883040935672515 25.026315789473685

10:56:038874

# 进行交叉验证
from sklearn.model_selection import cross_val_score

C_range = np.linspace(3, 4, 50)
score = []
for c in C_range:
    clf = SVC(kernel="rbf", C=c, cache_size=5000)
    score.append(cross_val_score(clf, x, y, cv=10).mean())
print(max(score), C_range[score.index(max(score))])
plt.plot(C_range, score)
plt.show()
print(datetime.datetime.fromtimestamp(time() - time0).strftime("%M:%S:%f"))

0.982456140350877 3.0

24:23:139221

clf = SVC(kernel="rbf", C=3, gamma="auto", cache_size=5000).fit(x_train, y_train)
clf.score(x_test, y_test)
clf.get_params()

{'C': 3,
 'break_ties': False,
 'cache_size': 5000,
 'class_weight': None,
 'coef0': 0.0,
 'decision_function_shape': 'ovr',
 'degree': 3,
 'gamma': 'auto',
 'kernel': 'rbf',
 'max_iter': -1,
 'probability': False,
 'random_state': None,
 'shrinking': True,
 'tol': 0.001,
 'verbose': False}