"""
.. module:: CKernelChebyshevDistance
:synopsis: Chebyshev distance kernel
.. moduleauthor:: Marco Melis <marco.melis@unica.it>
.. moduleauthor:: Battista Biggio <battista.biggio@unica.it>
"""
from sklearn import metrics
from secml.array import CArray
from secml.ml.kernel import CKernel
[docs]class CKernelChebyshevDistance(CKernel):
"""Chebyshev distance kernel.
Given matrices X and Y, this is computed as::
K(x, y) = max(|x - y|)
for each pair of rows in X and in Y.
Attributes
----------
class_type : 'chebyshev-dist'
Parameters
----------
batch_size : int or None, optional
Size of the batch used for kernel computation. Default None.
.. deprecated:: 0.10
Examples
--------
>>> from secml.array import CArray
>>> from secml.ml.kernel.c_kernel_chebyshev_distance import CKernelChebyshevDistance
>>> print(CKernelChebyshevDistance().k(CArray([[1,2],[3,4]]), CArray([[5,6],[7,8]])))
CArray([[-4. -6.]
[-2. -4.]])
>>> print(CKernelChebyshevDistance().k(CArray([[1,2],[3,4]])))
CArray([[0. -2.]
[-2. 0.]])
"""
__class_type = 'chebyshev-dist'
def __init__(self, batch_size=None):
super(CKernelChebyshevDistance, self).__init__(batch_size=batch_size)
def _k(self, x, y):
"""Compute (negative) Chebyshev distances between x and y.
Parameters
----------
x : CArray or array_like
First array of shape (n_x, n_features).
y : CArray or array_like
Second array of shape (n_y, n_features).
Returns
-------
kernel : CArray
Kernel between x and y, shape (n_x, n_y).
See Also
--------
:meth:`CKernel.k` : Main computation interface for kernels.
"""
if x.issparse is True or y.issparse is True:
raise TypeError(
"Chebyshev Kernel not available for sparse data."
"See `sklearn.metrics.pairwise_distances`.")
return -CArray(metrics.pairwise.pairwise_distances(
x.get_data(), y.get_data(), metric='chebyshev'))
def _gradient(self, u, v):
"""Calculate gradients of Chebyshev kernel wrt vector 'v'.
The gradient of the negative Chebyshev distance is given by::
dK(u,v)/dv = -sign(u-v)
Parameters
----------
u : CArray
First array of shape (nx, n_features).
v : CArray
Second array of shape (1, n_features).
Returns
-------
kernel_gradient : CArray
Kernel gradient of u with respect to vector v,
shape (nx, n_features).
See Also
--------
:meth:`CKernel.gradient` : Gradient computation interface for kernels.
"""
if v.issparse is True:
# Broadcasting not supported for sparse arrays
v_broadcast = v.repmat(u.shape[0], 1)
else: # Broadcasting is supported by design for dense arrays
v_broadcast = v
diff = u - v_broadcast
m = abs(diff).max(axis=1) # extract m from each row
grad = CArray.zeros(shape=diff.shape, sparse=v.issparse)
grad[diff >= m] = 1 # this correctly broadcasts per-row comparisons
grad[diff <= -m] = -1
return grad