def test_tracenorm(self):
K = self.X @ self.X.T
trace = metrics.trace(K)
self.assertEqual(trace, 25.75, K)
Kt = preprocessing.tracenorm(K)
self.assertTrue(matNear(Kt * trace / K.shape[0], K))
o_numpy = metrics.trace(K.numpy())
self.assertEqual(trace, o_numpy)
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 tracenorm(K):
"""normalize the trace of a squared kernel matrix
Parameters
----------
K : (n,n) ndarray,
the squared kernel matrix.
Returns
-------
Kt : ndarray,
the trace-normalized version of *K*.
Notes
-----
In trace-normalization, the kernel is divided by the average of the diagonal.
"""
K = check_squared(K)
trn = trace(K) / K.shape[0]
return K / trn
def tracenorm(K):
"""normalize the trace of a squared kernel matrix
Parameters
----------
K : (n,n) ndarray,
the squared kernel matrix.
Returns
-------
Kt : ndarray,
the trace-normalized version of *K*.
Notes
-----
In trace-normalization, the kernel is divided by the average of the diagonal.
"""
K = check_squared(K)
trn = trace(K) / K.shape[0]
return K / trn
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='')
from MKLpy.metrics import spectral_ratio
SR = spectral_ratio(K, norm=True)
print ('%.4f' % SR)
def test_trace(self):
self.assertEqual(metrics.trace(self.K1), 3)
self.assertRaises(SquaredKernelError, metrics.trace, self.X)
def test_tracenorm(self):
K = self.X.dot(self.X.T)
trace = metrics.trace(K)
self.assertEqual(trace, 25, K)
Kt = preprocessing.tracenorm(K)
self.assertTrue(matNear(Kt * trace / K.shape[0], K))
def tracenorm(K):
#return sum([K[i,i] for i in range(k.shape[0])]) / K.shape[0]
trn = trace(K) / K.shape[0]
return K / trn
