不调包，用numpy实现svm，对鸢尾花进行二分类（smo算法）
import random
import matplotlib.pyplot as plt
import numpy as np
from sklearn.datasets import load_iris
class Supper_Vector_Machine:
def __init__(self, dataset, target, C, toler, Iter_max):
self.dataset = dataset
self.target = target
self.N, self.M = len(self.dataset), len(dataset[0])
self.C = C
self.toler = toler
self.b = 0
self.Alpha = np.zeros(self.N)
'''最多遍历iter次，若都符合KKT条件，则说明基本符合alpha基本都符合'''
self.iter_max = Iter_max
self.w = np.zeros(self.M)
def Fx(self, i):
fxi = 0
for k in range(self.N):
fxi += self.Alpha[k] * self.target[k] * np.matmul(self.dataset[i], self.dataset[k].T)
fxi += self.b
return fxi
def Kernel(self, i, j):
result = np.matmul(self.dataset[i], self.dataset[j].T)
return result
def random_j(self, i):
while True:
j = random.choice(range(self.N))
if j != i:
return j
def get_L_H(self, i, j):
L, H = 0, 0
if self.target[i] != self.target[j]:
L = max([0, self.Alpha[j] - self.Alpha[i]])
H = min([self.C, self.C + self.Alpha[j] - self.Alpha[i]])
else:
L = max([0, self.Alpha[j] + self.Alpha[i] - self.C])
H = min([self.C, self.Alpha[i] + self.Alpha[j]])
return L, H
def filter(self, L, H, alpha_j):
if alpha_j < L:
alpha_j = L
if alpha_j > H:
alpha_j = H
return alpha_j
def SMO(self):
iter = 0
while iter < self.iter_max:
change_num = 0
for i in range(self.N):
Fx_i = self.Fx(i)
Ex_i = Fx_i - self.target[i]
'''确定是否符合KKT条件，不符合就进行更新'''
if self.target[i] * Ex_i < -self.toler and self.Alpha[i] < self.C or self.target[
i] * Ex_i > self.toler and self.Alpha[i] > 0:
j = self.random_j(i)
print('i:{},j:{}'.format(i, j))
Fx_j = self.Fx(j)
Ex_j = Fx_j - self.target[j]
alpha_i = self.Alpha[i]
alpha_j = self.Alpha[j]
L, H = self.get_L_H(i, j)
if L == H:
print('L == H')
continue
eta = self.Kernel(i, i) + self.Kernel(j, j) - 2 * self.Kernel(i, j)
if eta <= 0:
print('eta <= 0')
continue
''''更新a_j'''
self.Alpha[j] += self.target[j] * (Ex_i - Ex_j) / eta
self.Alpha[j] = self.filter(L, H, self.Alpha[j])
if abs(self.Alpha[j] - alpha_j) < 0.00001:
print('alpha够精确了')
continue
'''更新alpha[i]'''
self.Alpha[i] += self.target[i] * self.target[j] * (alpha_j - self.Alpha[j])
'''更新b'''
b1 = self.b - Ex_i - self.target[i] * self.Kernel(i, i) * (self.Alpha[i] - alpha_i) - self.target[
j] * self.Kernel(i, j) * (self.Alpha[j] - alpha_j)
b2 = self.b - Ex_j - self.target[i] * self.Kernel(i, j) * (self.Alpha[i] - alpha_i) - self.target[
j] * self.Kernel(j, j) * (self.Alpha[j] - alpha_j)
if 0 < self.Alpha[i] < self.C:
self.b = b1
elif 0 < self.Alpha[j] < self.C:
self.b = b2
else:
self.b = (b1 + b2) / 2.0
print(self.Alpha[i], self.Alpha[j])
change_num += 1
if change_num == 0:
iter += 1
else:
iter = 0
for i in range(self.N):
self.w += self.target[i] * self.Alpha[i] * self.dataset[i]
def display(self):
svm_point = []
for i in range(100):
if self.Alpha[i] > 0:
print('第{}个是支持向量'.format(i), self.dataset[i], self.target[i])
svm_point.append(i)
x_point = np.array([i[0] for i in dataset])
y_point = np.array([i[1] for i in dataset])
x = np.linspace(4, 6, 5)
y = -(self.w[0] * x + self.b) / self.w[1]
plt.scatter(x_point[:50], y_point[:50], color='red')
plt.scatter(x_point[-50:], y_point[-50:], color='blue')
support_vector = np.array([dataset[i] for i in svm_point])
plt.scatter(support_vector[:, 0], support_vector[:, 1], color='black')
plt.plot(x, y)
plt.show()
if __name__ == '__main__':
dataset, target = load_iris()['data'][:100, :2], load_iris()['target'][:100]
target = np.array([1 if i == 1 else -1 for i in target])
model = Supper_Vector_Machine(dataset, target, 100, 0.01, 40)
model.SMO()
print(model.w)
print(model.b)
model.display()
快速理解SMO算法_哔哩哔哩_bilibili
b站这位老师讲的SMO非常详细，推荐大家看一下，不过i和j的选择并没有参考该视频中的启发式方法（用kkt条件选择的话，我这边敲了几天都比较失败），i和j的选择我打算使用全部遍历的方法虽然耗时比较长，但效果总体还行
这是效果图，看上去效果还行的