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 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 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 tanimoto_kernel(X, T=None): #?
X, T = check_X_T(X, T)
L = np.dot(X, T.T)
xx = np.linalg.norm(X, axis=1)
tt = np.linalg.norm(T, axis=1)