7 支持向量机SMO算法（python代码）

原理参考：https://zhuanlan.zhihu.com/p/77750026
SMO算法python代码
公式参考统计学习方法第7章

import numpy as np
import pandas as pd
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
import math

def create_data():
    iris = load_iris()
    df=pd.DataFrame(iris.data,columns=iris.feature_names)
    df['label']=iris.target
    df.columns=['sepal length', 'sepal width', 'petal length', 'petal width', 'label']
    data=np.array(df.iloc[:100,[0,1,-1]])
    for i in range(len(data)):
        if data[i,-1]==0:
            data[i,-1]=-1
    return data[:,:2], data[:,-1]

X,y=create_data()
X_train,X_test,y_train,y_test=train_test_split(X,y,test_size=0.2)

# SMO算法
class SVM:
#     定义最大迭代次数，核函数
    def __init__(self, max_iter, kernel='linear'):
        self.max_iter = max_iter
        self._kernel = kernel
#     m样本量，n维度，X样本， Y样本类别，b,alpha拉格朗日乘子,E,C
    def init_args(self, features, labels):
        self.m, self.n = features.shape
        self.X = features
        self.Y = labels
        self.b = 0.0
        self.alpha = np.ones(self.m)
        
        # Ei是g(x)预测值-实际值,保存至列表
        self.E = [self._E(i) for i in range(self.m)]
        # 惩罚参数
        self.C=1.0 
 
    # 核函数
    def kernel(self,x1,x2):
        if self._kernel=='linear': #线性分类器 k(x,y)=x*y
            return sum([x1[k]*x2[k] for k in range(self.n)])  
        elif self._kernel=='poly':
            return (sum([x1[k]*x2[k] for k in range(self.n)])+1)**2  #d阶多项式分类器 k(x,y)={(x*y)+1}d
        return 0

    def _KKT(self, i):  #p147   7.111~7.113
        y_g = self._g(i)*self.Y[i]
        if self.alpha[i]==0:
            return y_g >=1
        elif 0<self.alpha[i]<self.C:
            return y_g ==1
        else:
            return y_g<=1
    
    # g(x)预测值，输入（X[i]）
    def _g(self,i):
        r = self.b
        for j in range(self.m):
            r += self.alpha[j]*self.Y[j]*self.kernel(self.X[i], self.X[j])   # p145 公式7.105   7.117
        return r
    
    # E（x）为g(x)对输入x的预测值和实际值y的差
    def _E(self, i):
        return self._g(i)-self.Y[i]    
    
    
    def _init_alpha(self):
         #外层循环首先遍历所有满足0<a<C的样本点，检验是否满足KKT  P147
        index_list=[i for i in range(self.m) if 0<self.alpha[i]<1]
        # 否则遍历整个训练集
        non_satisfy_list = [i for i in range(self.m) if i not in index_list]
        index_list.extend(non_satisfy_list)
        
        for i in index_list:
            if self._KKT(i):
                continue
            E1=self.E[i]
            # 如果E1是+，选择最小的；如果E1是负的，选择最大的
            if E1 >= 0:
                j = min(range(self.m), key=lambda x: self.E[x])
            else:
                j = max(range(self.m), key=lambda x: self.E[x])
            return i, j
    
    def _compare(self,_alpha, L, H):  #7.108
        if _alpha > H:
            return H
        elif _alpha<L:
            return L
        else:
            return _alpha
        
    def fit(self, features, labels):
        self.init_args(features, labels)   
        for t in range(self.max_iter):    # 迭代
            # train   变量的选择 i1 i2
            i1,i2 = self._init_alpha()
            # 边界  p144~145
            if self.Y[i1]==self.Y[i2]:
                L = max(0, self.alpha[i1] + self.alpha[i2] - self.C)
                H = min(self.C, self.alpha[i1] + self.alpha[i2])
            else:
                L = max(0, self.alpha[i2] - self.alpha[i1])
                H = min(self.C, self.C + self.alpha[i2] - self.alpha[i1])
            
            E1=self.E[i1]
            E2=self.E[i2]
            # eta = k11+k22-2k12  公式7.107
            eta=self.kernel(self.X[i1],self.X[i1])+self.kernel(self.X[i2],self.X[i2])-2*self.kernel(self.X[i1],self.X[i2])
            if eta<=0:
                continue
           
            alpha2_new_unc=self.alpha[i2]+self.Y[i2]*(E1-E2)/eta   #7.106
            alpha2_new = self._compare(alpha2_new_unc, L, H)    #7.108
            alpha1_new = self.alpha[i1] + self.Y[i1] * self.Y[i2] * (self.alpha[i2] - alpha2_new)  #7.109
            
            # 7.115
            b1_new = -E1 - self.Y[i1] * self.kernel(self.X[i1], self.X[i1]) * (
                alpha1_new - self.alpha[i1]) - self.Y[i2] * self.kernel(
                    self.X[i2],self.X[i1]) * (alpha2_new - self.alpha[i2]) + self.b
            
            # 7.116
            b2_new = -E2 - self.Y[i1] * self.kernel(self.X[i1], self.X[i2]) * (
                alpha1_new - self.alpha[i1]) - self.Y[i2] * self.kernel(
                    self.X[i2],self.X[i2]) * (alpha2_new - self.alpha[i2]) + self.b
            
            # p148
            if 0 < alpha1_new < self.C:
                b_new = b1_new
            elif 0 < alpha2_new < self.C:
                b_new = b2_new
            else:
                # 选择中点
                b_new = (b1_new + b2_new) / 2

            # 更新参数
            self.alpha[i1] = alpha1_new
            self.alpha[i2] = alpha2_new
            self.b = b_new

            self.E[i1] = self._E(i1)
            self.E[i2] = self._E(i2)
        return 'train done!'
    
    def predict(self, data):
        # g(xi)
        r = self.b
        for i in range(self.m):
            r += self.alpha[i] * self.Y[i] * self.kernel(data, self.X[i])
        return 1 if r > 0 else -1

    def score(self, X_test, y_test):
        right_count = 0
        for i in range(len(X_test)):
            result = self.predict(X_test[i])
            if result == y_test[i]:
                right_count += 1
        return right_count / len(X_test)

svm = SVM(max_iter=200,kernel='poly')
svm.fit(X_train, y_train)
svm.score(X_test, y_test)

直接调用sklearn函数
from sklearn.svm import SVC
clf = SVC()
clf.fit(X_train, y_train)
clf.score(X_test, y_test)