判别分类和支持向量机
判别分类方法：用一条分割线或者流形体将各种类型分割开。
边界最大的那条线是模型最优解。
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
from scipy import stats
# 用Seaborn画图
import seaborn as sns; sns.set()
from sklearn.datasets import make_blobs
X, y = make_blobs(n_samples=50, centers=2, random_state=0, cluster_std=0.60)
plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn');
from sklearn.svm import SVC
model = SVC(kernel='linear', C=1e10)
model.fit(X,y)
def plot_svc_decision_function(model, ax=None, plot_support=True):
"""Plot the decision function for a 2D SVC"""
if ax is None:
ax = plt.gca()
xlim = ax.get_xlim()
ylim = ax.get_ylim()
# create grid to evaluate model
x = np.linspace(xlim[0], xlim[1], 30)
y = np.linspace(ylim[0], ylim[1], 30)
Y, X = np.meshgrid(y, x)
xy = np.vstack([X.ravel(), Y.ravel()]).T
P = model.decision_function(xy).reshape(X.shape)
# plot decision boundary and margins
ax.contour(X, Y, P, colors='k',
levels=[-1, 0, 1], alpha=0.5,
linestyles=['--', '-', '--'])
# plot support vectors
if plot_support:
ax.scatter(model.support_vectors_[:, 0],
model.support_vectors_[:, 1],
s=300, linewidth=1, facecolors='none');
ax.set_xlim(xlim)
ax.set_ylim(ylim)
plt.scatter(X[:,0], X[:,1], c=y, s=50,cmap='autumn')
plot_svc_decision_function(model);
print(model.support_vectors_)
fb02c0cb76ec4eaa80619f61472714ee.png
间隔最大的分割线。正好在分割线上的点是拟合的关键点，称为支持向量。
将SVM模型与核函数组合使用，功能会非常强大。
应用核函数化的SVM模型将线性核转变为RBF（径向基函数）核，设置kernel模型超参数即可找到一条合适的非线性决策边界。
from sklearn.datasets import make_circles
X, y = make_circles(100, factor=.1, noise=.1)
clf = SVC(kernel='rbf',C=1e6)
clf.fit(X,y)
plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn')
plot_svc_decision_function(clf)
plt.scatter(clf.support_vectors_[:,0],clf.support_vectors_[:,1],
s=300,lw=1,facecolors='none');
超参数C可以控制边界线的“硬度”。
人脸识别案例
使用主成分分析和支持向量机分类器处理数据集里的人脸图像。
使用网格搜索寻找最优参数组合。
from sklearn.datasets import fetch_lfw_people
faces = fetch_lfw_people(min_faces_per_person=60)
print(faces.target_names)
print(faces.images.shape)
fig, ax = plt.subplots(3, 5)
for i, axi in enumerate(ax.flat):
axi.imshow(faces.images[i], cmap='bone')
axi.set(xticks=[], yticks=[],
xlabel=faces.target_names[faces.target[i]])
from sklearn.svm import SVC
from sklearn.decomposition import PCA
from sklearn.pipeline import make_pipeline
pca = PCA(n_components=150, svd_solver='randomized', whiten=True, random_state=42)
svc = SVC(kernel='rbf', class_weight='balanced')
model = make_pipeline(pca, svc)
from sklearn.model_selection import train_test_split
Xtrain, Xtest, ytrain, ytest = train_test_split(faces.data, faces.target, random_state=42)
from sklearn.model_selection import GridSearchCV
param_grid = {'svc__C': [1, 5, 10, 50],
'svc__gamma': [0.0001, 0.0005, 0.001, 0.005]}
grid = GridSearchCV(model, param_grid)
%time grid.fit(Xtrain, ytrain)
print(grid.best_params_)
model = grid.best_estimator_
yfit=model.predict(Xtest)
fig, ax = plt.subplots(4, 6)
for i, axi in enumerate(ax.flat):
axi.imshow(Xtest[i].reshape(62, 47), cmap='bone')
axi.set(xticks=[], yticks=[])
axi.set_ylabel(faces.target_names[yfit[i]].split()[-1],
color='black' if yfit[i] == ytest[i] else 'red')
fig.suptitle('Predicted Names; Incorrect Labels in Red', size=14)
fb3bc8da8f6f47adad14266dddd7464e.png
可以画出混淆矩阵：
from sklearn.metrics import classification_report
print(classification_report(ytest, yfit,
target_names=faces.target_names))
from sklearn.metrics import confusion_matrix
mat = confusion_matrix(ytest, yfit)
sns.heatmap(mat.T, square=True, annot=True, fmt='d', cbar=False,
xticklabels=faces.target_names,
yticklabels=faces.target_names)
plt.xlabel('true label')
plt.ylabel('predicted label');
总结
- 对高维数据的学习效果比较好。
- 与和函数方法的配合具有通用性。
- 通常只会在其他简单、快速、调优难度小的方法不能满足需求时，才会选择支持向量机。
