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class SVM(object):
def __init__(self,n_in,c0=1,c1=1,loss = RAMP_LOSS,gamma = 0.5):
self.dim = n_in
self.w = np.zeros(n_in)
self.b = np.zeros(1)
self.c0 = c0
self.c1 = c1
self.gamma = gamma
self.x = None
self.y = None
def train(self,x,y):
#setup
self.x = x
self.y = y
x_2 = np.zeros(len(y))
for i in range(self.dim):
x_2 += x[:,i]**2
x_2 = np.tile(x_2,(len(y),1))
yy = np.tile(y,(len(y),1))
yy = yy * yy.T
K = np.exp(-self.gamma*(x_2 + x_2.T - 2*x.dot(x.T))) * yy
'''
conpute a^t by solving the following convex problem
max(a - 1/2*a^T*K*a)
subject to y*a = 0, -b^(t-1)<=a<=C-b^(t-1)
'''
self.w = np.ones(len(x))
s = -1
c = np.array([self.c0 if y_i == 1 else self.c1 for y_i in y])
b_old = np.zeros(len(y))
b_new = np.zeros(len(y))
def f(x_l):
return (y*np.asarray(alpha)).dot(np.exp((-self.gamma*(self.x-x_l)**2).sum(1)))+self.b
while True:
#set variables and constraint -b^(t-1)<=a<=C-b^(t-1)
m = gurobi.Model("qp")
a = {}
for i in range(len(y)):
a[i] = m.addVar(lb=-b_old[i],ub=c[i]-b_old[i])
m.update()
#set objective
Ka = {}
aKa = gurobi.QuadExpr()
for i in range(len(y)):
Ka[i] = gurobi.LinExpr()
for j in range(len(y)):
Ka[i].add(a[i],K[i,j])
for i in range(len(y)):
aKa.add(a[i] * Ka[i])
objective = gurobi.quicksum(a) - 1.0/2*aKa
m.setObjective(objective,gurobi.GRB.MAXIMIZE)
m.update()
#add constraints
ya = gurobi.LinExpr()
for i in range(len(y)):
ya += a[i]*y[i]
m.addConstr(ya == 0,"c0")
m.update()
#m.params.logToConsole = 0
m.optimize()
alpha = {}
i = 0
for v in m.getVars():
alpha[i] = v.x
i += 1
alpha = alpha.values()
#compute b
new_b = 0.
count = 0
for i in range(len(alpha)):
if (0 < alpha[i]) & (alpha[i] < c[i]):
new_b += y[i]-(f(x[i])-self.b)
count += 1
self.b = new_b/count
print self.b
#compute beta
b_new = np.array([c[i] if y[i]*f(x[i]) < s else 0 for i in range(len(y))])
if (b_old == b_new).all():
break
b_old = b_new
self.w = y*np.array(alpha)#np.array(-np.asarray([1 if y[i]*f(x[i]) <= 0 else 0 for i in range(len(y))])*c*y)
#print self.w,self.b
def predict(self,x):
return self.w.dot(np.exp((-self.gamma*(self.x-x)**2).sum(1)))+self.b
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