1、支撑向量机SVM是一种非常重要和广泛的机器学习算法，它的算法出发点是尽可能找到最优的决策边界，使得模型的泛化能力尽可能地好，因此SVM对未来数据的预测也是更加准确的。

2、SVM既可以解决分类问题，又可以解决回归问题，原理整体相似，不过也稍有不同。

 

在sklearn章调用SVM算法的代码实现如下所示：

#（一）sklearn中利用SVM算法解决分类问题

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[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：