def _cvxmod_minimize(self, lb, ub, **kwargs):
""" solve quadratic problem using CVXMOD interface
Keyword arguments:
lb, ub -- vectors of lower and upper bounds (potentially modified by
added tolerance)
Modified member variables:
status, solution, obj_value
Returns: nothing
"""
# shorter names
v = self.cvxmodV
A = self.cvxmodMatrix
minus_w = cvxmod.matrix(self.obj.f) # negative wildtype solution
lb = cvxmod.matrix(lb)
ub = cvxmod.matrix(ub)
if self.weights is not None:
weights = cvxmod.matrix(diag(sqrt(self.weights)))
if self.Aineq is not None:
Aineq = cvxmod.matrix(array(self.Aineq))
bineq = cvxmod.matrix(self.bineq)
if self.weights is None:
p = cvxmod.problem(cvxmod.minimize(
cvxmod.norm2(v + minus_w)), [
cvxmod.abs(A * v) < self.matrix_tol,
Aineq * v <= bineq + self.matrix_tol, v >= lb, v <= ub
])
else:
p = cvxmod.problem(
cvxmod.minimize(cvxmod.norm2(weights * (v + minus_w))), [
cvxmod.abs(A * v) < self.matrix_tol,
Aineq * v <= bineq + self.matrix_tol, v >= lb, v <= ub
])
else:
if self.weights is None:
p = cvxmod.problem(
cvxmod.minimize(cvxmod.norm2(v + minus_w)),
[cvxmod.abs(A * v) < self.matrix_tol, v >= lb, v <= ub])
else:
p = cvxmod.problem(
cvxmod.minimize(cvxmod.norm2(weights * (v + minus_w))),
[cvxmod.abs(A * v) < self.matrix_tol, v >= lb, v <= ub])
self.status = cvxToSolverStatus(p.solve())
if not v.value:
self.solution = []
else:
self.solution = array(list(v.value))
try:
self.obj_value = p.value
except cvxmod.OptvarValueError:
self.obj_value = inf
def _compute(self): start = datetime.datetime.now() gamma = self.gamma (N,d) = self.data.shape X = self.data Xcmf = ( (X.reshape(N,1,d) > transpose(X.reshape(N,1,d),[1,0,2])).prod(2).sum(1,dtype=float) / N ).reshape([N,1]) sigma = .75 / sqrt(N) K = self._K( X.reshape(N,1,d), transpose(X.reshape(N,1,d), [1,0,2]), gamma ).reshape([N,N]) #NOTE: this integral depends on K being the gaussian kernel Kint = ( (1.0/gamma)*scipy.special.ndtr( (X-X.T)/gamma ) ) alpha = cvxmod.optvar( 'alpha',N,1) alpha.pos = True pK = cvxmod.param( 'K',N,N ) pK.psd = True pK.value = cvxopt.matrix(K,(N,N) ) pKint = cvxmod.param( 'Kint',N,N ) pKint.value = cvxopt.matrix(Kint,(N,N)) #pKint.pos = True pXcmf = cvxmod.param( 'Xcmf',N,1) pXcmf.value = cvxopt.matrix(Xcmf, (N,1)) #pXcmf.pos = True objective = cvxmod.minimize( cvxmod.atoms.quadform(alpha, pK) ) eq1 = cvxmod.abs( pXcmf - ( pKint * alpha ) ) <= sigma eq2 = cvxmod.sum( alpha ) == 1.0 # Solve! p = cvxmod.problem( objective = objective, constr = [eq1, eq2] ) start = datetime.datetime.now() p.solve() duration = datetime.datetime.now() - start print "optimized in %ss" % (float(duration.microseconds)/1000000) beta = ma.masked_less( alpha.value, 1e-7 ) mask = ma.getmask( beta ) data = ma.array(X,mask=mask) self.Fl = Xcmf self.beta = beta.compressed().reshape([ 1, len(beta.compressed()) ]) self.SV = data.compressed().reshape([len(beta.compressed()),1]) print "%s SV's found" % len(self.SV)
def _compute(self):
C = self.C
gamma = self.gamma
(N, d) = self.data.shape
X = self.data
Xcmf = (
(X.reshape(N, 1, d) > transpose(X.reshape(N, 1, d), [1, 0, 2])).prod(2).sum(1, dtype=float) / N
).reshape([N, 1])
sigma = 0.75 / sqrt(N)
K = self._K(X.reshape(N, 1, d), transpose(X.reshape(N, 1, d), [1, 0, 2]), gamma).reshape([N, N])
# NOTE: this integral depends on K being the gaussian kernel
Kint = (1.0 / gamma) * scipy.special.ndtr((X - X.T) / gamma)
alpha = cvxmod.optvar("alpha", N, 1)
alpha.pos = True
xi = cvxmod.optvar("xi", N, 1)
xi.pos = True
pXcmf = cvxmod.param("Xcmf", N, 1)
pXcmf.pos = True
pXcmf.value = cvxopt.matrix(Xcmf, (N, 1))
pKint = cvxmod.param("Kint", N, N)
pKint.value = cvxopt.matrix(Kint, (N, N))
objective = cvxmod.minimize(cvxmod.sum(cvxmod.atoms.power(alpha, 2)) + (C * cvxmod.sum(xi)))
eq1 = cvxmod.abs((pKint * alpha) - pXcmf) <= sigma + xi
eq2 = cvxmod.sum(alpha) == 1.0
# Solve!
p = cvxmod.problem(objective=objective, constr=[eq1, eq2])
p.solve()
beta = ma.masked_less(alpha.value, 1e-7)
mask = ma.getmask(beta)
data = ma.array(X, mask=mask)
self.beta = beta.compressed().reshape([1, len(beta.compressed())])
self.SV = data.compressed().reshape([len(beta.compressed()), 1])
print "%s SV's found" % len(self.SV)
