python 实现 svm算法
svm算法,说到底就是二次优化问题。
带有约束的二次优化问题。
1、线性优化问题,课件Leture5-QP
(1)使用pulp
参考 https://www.coin-or.org/PuLP/CaseStudies/a_blending_problem.html
python代码:
# problem
def qp_test1():
prob = LpProblem("qp_test1", LpMinimize)
x1 = LpVariable("x1", 0, None, LpInteger)
x2 = LpVariable("x2", 0, None, LpInteger)
prob += 50*x1+36*x2, "Cost"
prob += x1>=0, "x1"
prob += x2>=0, "x2"
prob += 5*x1+3*x2>=45, "cond1"
prob.solve()
print("Status:", LpStatus[prob.status])
for v in prob.variables():
print(v.name, "=", v.varValue)
(2)使用cvxopt
在cvxopt中,matrix是按照列优先。
m=matrix([[2,2, 1],[3, 3,4]])
m是3行2列,每一个[]表示一个列。
http://www.seas.ucla.edu/~vandenbe/publications/mlbook.pdf
c=[40, 36]
[-5 -3] -45
[-1 0] 0
[0 -1] 0
G = [[-5, -1, 0], [-3, 0, -1]]
h = [-45, 0 ,0]
代码:(注意数字必须加小数点,否则报错)
c = matrix([-2.0, -5.0])
A = matrix( [[2.0, 1.0, -1.0], [-1.0, 2.0, 1.0]] )
b = matrix([4.0, 9.0, 3.0])
sol = solvers.lp(c,A,b)
print(sol['x'])
2.二次优化问题
标准公式