1, support vector machine SVM is a very important and extensive machine learning algorithms, it's algorithm to find the best possible starting point is the decision boundary, making the generalization ability of the model as good as possible, so SVM prediction of future data but also more accurate.
2, SVM can only solve classification problems, but also solve regression problems, the overall principle is similar, but slightly different.
Implementation is shown below in the code sklearn chapter calls SVM algorithm:
# (A) sklearn utilizing SVM classification algorithm to solve the problem
import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets
d=datasets.load_iris()
x=d.data
y=d.target
x=x[y<2,:2]
y=y[y<2]
print(x)
print(y)
plt.figure()
plt.scatter(x[y==0,0],x[y==0,1],color="r")
plt.scatter(x[y==1,0],x[y==1,1],color="g")
plt.show()
#进行数据据标准化处理（线性方式）
from sklearn.preprocessing import StandardScaler
s1=StandardScaler()
s1.fit(x)
x_standard=s1.transform(x)
print(np.hstack([x,x_standard]))
#导入sklearn中SVM的线性分类算法LinearSVC
from sklearn.svm import LinearSVC
s11=LinearSVC(C=1e9) #多分类问题的实现需要提交参数penalty=l1/l2（正则化方式）以及multi_class=ovo/ovr（采用何种方式多分类训练）
s11.fit(x_standard,y)
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_pre=model.predict(x_new)
zz=y_pre.reshape(x0.shape)
from matplotlib.colors import ListedColormap
cus=ListedColormap(["#EF9A9A","#FFF59D","#90CAF9"])
plt.contourf(x0,x1,zz,cmap=cus)
plot_decision_boundary(s11,axis=([-3,3,-3,3]))
plt.scatter(x_standard[y==0,0],x_standard[y==0,1],color="r")
plt.scatter(x_standard[y==1,0],x_standard[y==1,1],color="g")
plt.show()
print(s11.coef_)
print(s11.intercept_)
#输出svc函数的决策边界
def plot_svc_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_pre=model.predict(x_new)
zz=y_pre.reshape(x0.shape)
from matplotlib.colors import ListedColormap
cus=ListedColormap(["#EF9A9A","#FFF59D","#90CAF9"])
plt.contourf(x0,x1,zz,cmap=cus)
w=model.coef_[0]
b=model.intercept_[0]
x1=np.linspace(axis[0],axis[1],200)
upy=-w[0]*x1/w[1]-b/w[1]+1/w[1]
downy=-w[0]*x1/w[1]-b/w[1]-1/w[1]
upindex=((upy>axis[2])&(upy<axis[3]))
downindex = ((downy > axis[2]) & (downy < axis[3]))
plt.plot(x1[upindex],upy[upindex],"r")
plt.plot(x1[downindex],downy[downindex],"g")
plot_svc_decision_boundary(s11,axis=([-3,3,-3,3]))
plt.scatter(x_standard[y==0,0],x_standard[y==0,1],color="r")
plt.scatter(x_standard[y==1,0],x_standard[y==1,1],color="g")
plt.show()
#sklearn中对于非线性数据的svm应用（多项式应用方式）
#1利用管道pipeline来进行多项式核函数的SVM算法
import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets
x,y=datasets.make_moons(noise=0.05,random_state=666) #生成数据默认为100个数据样本
print(x.shape)
print(y.shape)
plt.figure()
plt.scatter(x[y==0,0],x[y==0,1],color="r")
plt.scatter(x[y==1,0],x[y==1,1],color="g")
plt.show()
from sklearn.preprocessing import PolynomialFeatures
from sklearn.preprocessing import StandardScaler
from sklearn.svm import LinearSVC
from sklearn.pipeline import Pipeline
def polyniomailSVC(degree,C=1.0):
return Pipeline([("poly",PolynomialFeatures(degree=degree)),
("std_scaler",StandardScaler()),
("LinearSVC",LinearSVC(C=C))
])
p=polyniomailSVC(degree=3)
p.fit(x,y)
plot_decision_boundary(p,axis=([-1,2.5,-1,1.5]))
plt.scatter(x[y==0,0],x[y==0,1],color="r")
plt.scatter(x[y==1,0],x[y==1,1],color="g")
plt.show()
#2直接利用sklearn中自带的多项式核函数SVM算法，主要的参数kernel="poly"
from sklearn.svm import SVC
def polynomialkernelSVC(degree,C=1.0):
return Pipeline(
[
("std_canler",StandardScaler()),
("kernelsvc",SVC(kernel="poly",degree=degree,C=C))
]
)
p1=polynomialkernelSVC(degree=3)
p1.fit(x,y)
plot_decision_boundary(p1,axis=([-1,2.5,-1,1.5]))
plt.scatter(x[y==0,0],x[y==0,1],color="r")
plt.scatter(x[y==1,0],x[y==1,1],color="g")
plt.show()
#直观理解高斯核函数
import numpy as np
import matplotlib.pyplot as plt
x=np.arange(-4,5,1)
y=np.array((x>=-2)&(x<=2),dtype="int")
print(x)
print(y)
plt.figure()
plt.scatter(x[y==0],[0]*len(x[y==0]),color="r")
plt.scatter(x[y==1],[0]*len(x[y==1]),color="g")
plt.show()
def gauss(x,y):
gamma=1
return np.exp(-gamma*(x-y)**2)
l1,l2=-1,1
x_new=np.empty((len(x),2))
for i ,data in enumerate(x):
x_new[i,0]=gauss(data,l1)
x_new[i,1]=gauss(data,l2)
plt.scatter(x_new[y==0,0],x_new[y==0,1],color="r")
plt.scatter(x_new[y==1,0],x_new[y==1,1],color="g")
plt.show()
#调用sklearn中的高斯核函数RBF核（超参数主要是gamma）
import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets
x,y=datasets.make_moons(noise=0.1,random_state=666) #生成数据默认为100个数据样本
print(x.shape)
print(y.shape)
plt.figure()
plt.scatter(x[y==0,0],x[y==0,1],color="r")
plt.scatter(x[y==1,0],x[y==1,1],color="g")
plt.show()
from sklearn.model_selection import train_test_split
x_train,x_test,y_train,y_test=train_test_split(x,y,random_state=666)
from sklearn.preprocessing import StandardScaler
from sklearn.svm import SVC
from sklearn.pipeline import Pipeline
def RBFkernelSVC(gamma):
return Pipeline([
("std",StandardScaler()),
("svc",SVC(kernel="rbf",gamma=gamma))
])
sv=RBFkernelSVC(gamma=1)
sv.fit(x_train,y_train)
plot_decision_boundary(sv,axis=([-1.5,2.5,-1,1.5]))
plt.scatter(x[y==0,0],x[y==0,1],color="r")
plt.scatter(x[y==1,0],x[y==1,1],color="g")
plt.show()
print(sv.score(x_test,y_test))
from sklearn import datasets
d=datasets.load_iris()
x=d.data
y=d.target
from sklearn.model_selection import train_test_split
x_train,x_test,y_train,y_test=train_test_split(x,y,random_state=666)
sv=RBFkernelSVC(gamma=10)
sv.fit(x_train,y_train)
print(sv.score(x_test,y_test))
#（二）sklearn中利用SVM算法解决回归问题（epsilon为重要的超参数）
from sklearn import datasets
d=datasets.load_boston()
x=d.data
y=d.target
from sklearn.preprocessing import StandardScaler
s1=StandardScaler()
s1.fit(x)
x=s1.transform(x)
from sklearn.model_selection import train_test_split
x_train,x_test,y_train,y_test=train_test_split(x,y,random_state=666)
from sklearn.svm import LinearSVR
from sklearn.svm import SVR
from sklearn.preprocessing import StandardScaler
def StandardLinearSVR(epsilon):
return Pipeline([
("std",StandardScaler()),
("svr",LinearSVR(epsilon=epsilon))
])
sv=LinearSVR()
param_grid=[{
"epsilon":[i for i in np.arange(0,10,0.001)]
}]
from sklearn.model_selection import GridSearchCV
grid_search=GridSearchCV(sv,param_grid,n_jobs=-1,verbose=0)
grid_search.fit(x_train,y_train)
print(grid_search.best_params_)
print(grid_search.best_score_)
def polyniomailSVR(degree,C,epsilon):
return Pipeline([("poly",PolynomialFeatures(degree=degree)),
("std_scaler",StandardScaler()),
("LinearSVC",LinearSVR(C=C,epsilon=epsilon))
])
p1=polyniomailSVR(degree=2,C=1,epsilon=0.5)
p1.fit(x_train,y_train)
print(p1.score(x_test,y_test))
def polynomialkernelSVR(degree,coefo,epsilon):
return Pipeline(
[
("std_canler",StandardScaler()),
("kernelsvc",SVR(kernel="poly",degree=degree,coef0=coefo,epsilon=epsilon))
]
)
p1=polynomialkernelSVR(degree=3,C=1,epsilon=0.1)
p1.fit(x_train,y_train)
print(p1.score(x_test,y_test))
def RBFkernelSVR(gamma,epsilon):
return Pipeline([
("std",StandardScaler()),
("svc",SVR(kernel="rbf",gamma=gamma,epsilon=epsilon))
])
p2=RBFkernelSVR(gamma=0.05,epsilon=0.1)
p2.fit(x_train,y_train)
print(p2.score(x_test,y_test))
运行结果如下所示：
