def kernel_evaluation(K):
kernel_results_dict = {}
K = kernel_normalization(K) # normalize the kernel K (useless in the case of HPK computed on normalized data)
kernel_results_dict['score_margin'] = margin(K,
Ytr) # the distance between the positive and negative classes in the kernel space
kernel_results_dict['score_radius'] = radius(
K) # the radius of the Einimum Enclosing Ball containing data in the kernel space
kernel_results_dict['score_ratio'] = ratio(K,
Ytr) # the radius/margin ratio defined as (radius**2/margin**2)/n_examples
kernel_results_dict['score_froben'] = frobenius(K) # the Frobenius norm of a kernel matrix
kernel_results_dict['score_trace'] = trace(K) # the trace of the kernel matrix
return kernel_results_dict
def _arrange_kernel(self):
print "WARNING: probably not working"
Y = [1 if y == self.classes_[1] else -1 for y in self.Y]
n = len(self.Y)
YY = spdiag(Y)
actual_weights = np.ones(self.n_kernels) / (1.0 * self.n_kernels
) #current
obj = None
#weights = np.ones(self.n_kernels) / (1.0 *self.n_kernels) #current
print actual_weights
self.objs = []
cstep = self.step
self.margin = []
for i in xrange(self.max_iter):
Kc = summation(self.KL, actual_weights)
#ottimizzo su alpha (posso prenderlo dallo step precedente....)
clf = SVC(C=self.C, kernel='precomputed').fit(Kc, Y)
alpha = np.zeros(n)
alpha[clf.support_] = clf.dual_coef_
alpha = matrix(alpha)
#dati gli alpha ottimizzo sui pesi
J = (-0.5 * alpha.T * YY * matrix(Kc) * YY *
alpha)[0] + np.sum(alpha)
grad = [(-0.5 * alpha.T * YY * matrix(_K) * YY * alpha)[0]
for _K in self.KL]
mu = np.argmax(actual_weights) #all'inizio sono tutti uguali
idx = np.where(actual_weights == max(actual_weights))
mu = np.argmax(np.array(grad)[idx])
D = [ 0 if actual_weights[j]==0 and grad[j] - grad[mu] > 0 else \
-grad[j] + grad[mu] if actual_weights[j]>0 and j!=mu else \
np.sum([grad[v]-grad[mu] for v in range(self.n_kernels) if grad[v]>0]) if j==mu else\
0
for j in range(self.n_kernels)]
print 'd', D
#aggiorno i pesi dato il gradiente
weights = actual_weights + cstep * np.array(
D) #originalmente era un +
weights = weights.clip(0.0)
if weights.sum() == 0.0:
print i, 'zero', weights
cstep /= 2.0
continue
weights = weights / weights.sum()
#riottimizzo sugli alfa
Kc = summation(self.KL, weights)
clf = SVC(C=self.C, kernel='precomputed').fit(Kc, Y)
alpha = np.zeros(n)
alpha[clf.support_] = clf.dual_coef_
alpha = matrix(alpha)
new_obj = (-0.5 * alpha.T * YY * matrix(Kc) * YY *
alpha)[0] + np.sum(alpha)
if obj and abs(new_obj - obj) / n < self.tol:
#completato
#print i,'tol'
self.objs.append(new_obj)
actual_weights = weights
print 'terminato', new_obj, obj
break
elif new_obj <= obj or not obj:
#tutto in regola
#print i,'new step',new_ratio
ma = margin(Kc, Y)
if len(self.margin) > 0 and self.margin[-1] > ma:
continue
self.margin.append(ma)
obj = new_obj
actual_weights = weights
print actual_weights, obj
self.objs.append(obj)
else:
#supero il minimo
weights = actual_weights
cstep /= 2.0
print i, 'overflow', cstep
continue
self._steps = i + 1
self.weights = np.array(actual_weights)
self.ker_matrix = summation(self.KL, self.weights)
return self.ker_matrix
def _arrange_kernel(self):
Y = [1 if y==self.classes_[1] else -1 for y in self.Y]
n = len(self.Y)
R = np.array([radius(K) for K in self.KL])
YY = matrix(np.diag(self.Y))
actual_weights = np.ones(self.n_kernels) / (1.0 *self.n_kernels) #current
actual_ratio = None
#weights = np.ones(self.n_kernels) / (1.0 *self.n_kernels) #current
self.ratios = []
cstep = self.step
for i in xrange(self.max_iter):
ru2 = np.dot(actual_weights,R**2)
C = self.C / ru2
Kc = matrix(summation(self.KL,actual_weights))
clf = SVC(C=C, kernel='precomputed').fit(Kc,Y)
alpha = np.zeros(n)
alpha[clf.support_] = clf.dual_coef_
alpha = matrix(alpha)
Q = Kc + spdiag( [ru2/self.C] * n )
J = (-0.5 * alpha.T * YY * Q * YY * alpha)[0] + np.sum(alpha)
grad = [(-0.5 * alpha.T * YY *(Kc+ spdiag([_r**2/self.C]*n)) * YY * alpha)[0] for _r in R]
weights = actual_weights + cstep * np.array(grad) #originalmente era un +
weights = weights.clip(0.0)
if weights.sum() == 0.0:
#print i,'zero'
cstep /= -2.0
continue
weights = weights/weights.sum()
Kc = summation(self.KL,weights)
new_ratio = radius(Kc)**2 / margin(Kc,Y)**2
if actual_ratio and abs(new_ratio - actual_ratio)/n < self.tol:
#completato
#print i,'tol'
self.ratios.append(new_ratio)
actual_weights=weights
#break;
elif new_ratio <= actual_ratio or not actual_ratio:
#tutto in regola
#print i,'new step',new_ratio
actual_ratio = new_ratio
actual_weights = weights
self.ratios.append(actual_ratio)
else:
#supero il minimo
weights = actual_weights
cstep /= -2.0
#print i,'overflow',cstep
continue
self._steps = i+1
self.weights = np.array(actual_weights)
self.ker_matrix = summation(self.KL,self.weights)
return self.ker_matrix
return average(self.KL,weights)
def _arrange_kernel(self):
Y = [1 if y == self.classes_[1] else -1 for y in self.Y]
nn = len(Y)
nk = self.n_kernels
YY = spdiag(Y)
#YY = np.diag(Y)
beta = [0.0] * nk
mu = np.exp(beta)
mu /= mu.sum()
actual_ratio = None
_sol = None
Q = np.array([[
np.dot(self.KL[r].ravel(), self.KL[s].ravel()) for r in range(nk)
] for s in range(nk)])
Q /= np.sum([frobenius(K)**2 for K in self.KL])
#self._H = [ YY * K * YY for K in self.KL]
self.sr, self.margin = [], []
self.obj = []
_beta, _mu = None, None
cstep = self.step
I = np.diag(np.ones(nn))
for i in xrange(self.max_iter):
Kc = summation(self.KL, mu)
#trovo i gamma
#clf = KOMD(kernel='precomputed',lam=self.lam).fit(Kc,Y)
try:
_sol, _margin = margin(Kc, YY, lam=self.lam,
init_sol=None) #_sol)
except:
_sol, _margin = margin(Kc, YY, lam=self.lam, init_sol=None)
gamma = _sol['x']
#gamma = np.matrix(clf.gamma)
#_margin = (gamma.T * YY * Kc * YY * gamma)[0,0]
#grad = np.array([(self.C * np.dot(Q[r],mu) + (gamma.T * self._H[r] * gamma)[0,0]) \
grad = np.array([(self.C * np.dot(Q[r],mu) + (gamma.T * YY * matrix(self.KL[r]) * YY * gamma)[0,0]) \
* mu[r] * (1- mu[r]) \
for r in range(nk)])
_beta = beta + cstep * grad
_mu = np.exp(_beta)
_mu /= _mu.sum()
_obj = _margin + (self.C / 2) * np.dot(_mu, np.dot(_mu, Q))
if (self.obj and _obj < self.obj[-1]
) or _margin < 1.e-5: # nel caso di peggioramento
_mu = mu
_beta = beta
cstep /= 2.0
if cstep < 0.00001: break
else:
self.obj.append(_obj)
self.margin.append(_margin)
mu = _mu
beta = _beta
self._steps = i + 1
#print 'steps', self._steps, 'lam',self.lam,'margin',self.margin[-1]
self.weights = np.array(mu)
self.ker_matrix = summation(self.KL, self.weights)
return self.ker_matrix
#compute homogeneous polynomial kernels with degrees 0,1,2,...,10.
print ('computing Homogeneous Polynomial Kernels...', end='')
from MKLpy.metrics import pairwise
KLtr = [pairwise.homogeneous_polynomial_kernel(Xtr, degree=d) for d in range(11)]
KLte = [pairwise.homogeneous_polynomial_kernel(Xte,Xtr, degree=d) for d in range(11)]
print ('done')
#evaluate kernels in terms of margin, radius etc...
print ('evaluating metrics...', end='')
from MKLpy.metrics import margin, radius, ratio, trace, frobenius
from MKLpy.preprocessing import kernel_normalization
deg = 5
K = KLtr[deg] #the HPK with degree 5
K = kernel_normalization(K) #normalize the kernel K (useless in the case of HPK computed on normalized data)
score_margin = margin(K,Ytr) #the distance between the positive and negative classes in the kernel space
score_radius = radius(K) #the radius of the Einimum Enclosing Ball containing data in the kernel space
score_ratio = ratio (K,Ytr) #the radius/margin ratio defined as (radius**2/margin**2)/n_examples
#the ratio can be also computed as score_radius**2/score_margin**2/len(Ytr)
score_trace = trace (K) #the trace of the kernel matrix
score_froben = frobenius(K) #the Frobenius norm of a kernel matrix
print ('done')
print ('results of the %d-degree HP kernel:' % deg)
print ('margin: %.4f, radius: %.4f, radiu-margin ratio: %.4f,' % (score_margin, score_radius, score_ratio))
print ('trace: %.4f, frobenius norm: %.4f' % (score_trace, score_froben))
#evaluate the empirical complexity of the kernel matrix, i.e. the Spectral Ratio
# Michele Donini, Fabio Aiolli: "Learning deep kernels in the space of dot-product polynomials". Machine Learning (2017)
# Ivano Lauriola, Mirko Polato, Fabio Aiolli: "The Minimum Effort Maximum Output principle applied to Multiple Kernel Learning". ESANN (2018)
print ('computing Spectral Ratio...', end='')
def test_margin(self):
self.assertAlmostEqual(metrics.margin(self.K, self.Y), 2**.5, 5)
self.assertRaises(SquaredKernelError, metrics.margin, self.X, self.Y)
self.assertRaises(BinaryProblemError, metrics.margin, self.K,
[1, 2, 3])
self.assertRaises(ValueError, metrics.margin, self.K, [0, 0, 1, 1, 0])
