def HPK_kernel(X, T=None, degree=2):
"""performs the HPK kernel between the samples matricex *X* and *T*.
The HPK kernel is defines as:
.. math:: k(x,z) = \langle x,z \rangle^d
Parameters
----------
X : (n,m) array_like,
the train samples matrix.
T : (l,m) array_like,
the test samples matrix. If it is not defined, then the kernel is calculated
between *X* and *X*.
Returns
-------
K : (l,n) ndarray,
the HPK kernel matrix.
"""
if degree < 1:
raise ValueError('degree must be greather than 0')
if degree != floor(degree):
raise ValueError('degree must be int')
X, T = check_X_T(X, T)
return np.dot(X, T.T)**degree
def monotone_dnf_kernel(X,T=None,d=2,c=2):
X, T = check_X_T(X, T)
n = X.shape[1]
n_c = binom(n,c)
XX = np.dot(X.sum(axis=1).reshape(X.shape[0],1), np.ones((1,T.shape[0])))
TT = np.dot(T.sum(axis=1).reshape(T.shape[0],1), np.ones((1,X.shape[0])))
XXc = binom(XX,c)
TTc = binom(TT,c)
return binom(n_c,d) - binom(n_c - XXc, d) - binom(n_c - TTc.T, d) + binom(my_mdk(X,T,c),d)
def monotone_dnf_kernel(X, T=None, d=2, c=2):
X, T = check_X_T(X, T)
n = X.shape[1]
n_c = binom(n, c)
XX = np.dot(X.sum(axis=1).reshape(X.shape[0], 1), np.ones((1, T.shape[0])))
TT = np.dot(T.sum(axis=1).reshape(T.shape[0], 1), np.ones((1, X.shape[0])))
XXc = binom(XX, c)
TTc = binom(TT, c)
return binom(n_c, d) - binom(n_c - XXc, d) - binom(n_c - TTc.T, d) + binom(
my_mdk(X, T, c), d)
def monotone_disjunctive_kernel(X, T=None, d=2):
X, T = check_X_T(X, T)
L = np.dot(X, T.T)
n = X.shape[1]
XX = np.dot(X.sum(axis=1).reshape(X.shape[0], 1), np.ones((1, T.shape[0])))
TT = np.dot(T.sum(axis=1).reshape(T.shape[0], 1), np.ones((1, X.shape[0])))
N_x = n - XX
N_t = n - TT
N_xz = N_x - TT.T + L
N_d = binom(n, d)
N_x = binom(N_x, d)
N_t = binom(N_t, d)
N_xz = binom(N_xz, d)
return (N_d - N_x - N_t.T + N_xz)
def monotone_disjunctive_kernel(X,T=None,d=2):
X, T = check_X_T(X, T)
L = np.dot(X,T.T)
n = X.shape[1]
XX = np.dot(X.sum(axis=1).reshape(X.shape[0],1), np.ones((1,T.shape[0])))
TT = np.dot(T.sum(axis=1).reshape(T.shape[0],1), np.ones((1,X.shape[0])))
N_x = n - XX
N_t = n - TT
N_xz = N_x - TT.T + L
N_d = binom(n, d)
N_x = binom(N_x,d)
N_t = binom(N_t,d)
N_xz = binom(N_xz,d)
return (N_d - N_x - N_t.T + N_xz)
def homogeneous_polynomial_kernel(X, T=None, degree=2):
"""performs the HPK kernel between the samples matricex *X* and *T*.
The HPK kernel is defines as:
.. math:: k(x,z) = \langle x,z \rangle^d
Parameters
----------
X : (n,m) array_like,
the train samples matrix.
T : (l,m) array_like,
the test samples matrix. If it is not defined, then the kernel is calculated
between *X* and *X*.
Returns
-------
K : (l,n) ndarray,
the HPK kernel matrix.
"""
X, T = check_X_T(X, T)
return np.dot(X, T.T)**degree
def homogeneous_polynomial_kernel(X, T=None, degree=2):
"""performs the HPK kernel between the samples matricex *X* and *T*.
The HPK kernel is defines as:
.. math:: k(x,z) = \langle x,z \rangle^d
Parameters
----------
X : (n,m) array_like,
the train samples matrix.
T : (l,m) array_like,
the test samples matrix. If it is not defined, then the kernel is calculated
between *X* and *X*.
Returns
-------
K : (l,n) ndarray,
the HPK kernel matrix.
"""
X, T = check_X_T(X, T)
return np.dot(X,T.T)**degree
def d_kernel(X, k=2):
X, _ = check_X_T(X, None)
R = co.matrix((X.T > 0) * 1.0)
n = R.size[0]
m = R.size[1]
x_choose_k = [0] * (n + 1)
x_choose_k[0] = 0
for i in range(1, n + 1):
x_choose_k[i] = binom(i, k)
nCk = x_choose_k[n]
X = R.T * R
K = co.matrix(0.0, (X.size[0], X.size[1]))
for i in range(m):
for j in range(i, m):
n_niCk = x_choose_k[n - int(X[i, i])]
n_njCk = x_choose_k[n - int(X[j, j])]
n_ni_nj_nijCk = x_choose_k[n - int(X[i, i]) - int(X[j, j]) +
int(X[i, j])]
K[i, j] = K[j, i] = nCk - n_niCk - n_njCk + n_ni_nj_nijCk
return np.array(K)
def monotone_conjunctive_kernel(X, T=None, c=2):
X, T = check_X_T(X, T)
L = np.dot(X, T.T)
return binom(L, c)
def monotone_conjunctive_kernel(X,T=None,c=2):
X, T = check_X_T(X, T)
L = np.dot(X,T.T)
return binom(L,c)
def all_subsequences_kernel(X, T=None, binary=False):
X, T = check_X_T(X, T)
EX = all_subsequences_embedding(X, binary=binary)
ET = all_subsequences_embedding(T, binary=binary)
return dictionary_dot(EX, ET)
def fixed_length_subsequences_kernel(X, T=None, p=2, binary=False):
X, T = check_X_T(X, T)
EX = fixed_length_subsequences_embedding(X, p=p, binary=binary)
ET = fixed_length_subsequences_embedding(T, p=p, binary=binary)
return dictionary_dot(EX, ET)
def spectrum_kernel(X, T=None, p=2, binary=False):
X, T = check_X_T(X, T)
EX = spectrum_embedding(X, p=p, binary=binary)
ET = spectrum_embedding(T, p=p, binary=binary)
return dictionary_dot(EX, ET)
