"""
.. module:: CKernelLinear
:synopsis: Linear kernel
.. moduleauthor:: Battista Biggio <battista.biggio@unica.it>
.. moduleauthor:: Marco Melis <marco.melis@unica.it>
"""
from sklearn import metrics
from secml.array import CArray
from secml.ml.kernels import CKernel
[docs]class CKernelLinear(CKernel):
"""Linear kernel.
Given matrices X and RV, this is computed by::
K(x, rv) = x * rv^T
for each pair of rows in X and in RV.
Attributes
----------
class_type : 'linear'
Examples
--------
>>> from secml.array import CArray
>>> from secml.ml.kernels.c_kernel_linear import CKernelLinear
>>> print(CKernelLinear().k(CArray([[1,2],[3,4]]), CArray([[10,20],[30,40]])))
CArray([[ 50. 110.]
[110. 250.]])
>>> print(CKernelLinear().k(CArray([[1,2],[3,4]])))
CArray([[ 5. 11.]
[11. 25.]])
"""
__class_type = 'linear'
def _forward(self, x):
"""Compute the linear kernel between x and cached rv.
Parameters
----------
x : CArray or array_like
Array of shape (n_x, n_features).
Returns
-------
kernel : CArray
Kernel between x and cached rv. Array of shape (n_x, n_rv).
"""
return CArray(metrics.pairwise.linear_kernel(
CArray(x).get_data(), CArray(self._rv).get_data()))
def _backward(self, w=None):
"""Calculate Linear kernel gradient wrt cached vector 'x'.
The gradient of Linear kernel is given by::
dK(rv,x)/dx = rv
Parameters
----------
w : CArray of shape (1, n_rv) or None
if CArray, it is pre-multiplied to the gradient
of the module, as in standard reverse-mode autodiff.
Returns
-------
kernel_gradient : CArray
Kernel gradient of rv with respect to vector x,
shape (n_rv, n_features) if n_rv > 1 and w is None,
else (1, n_features).
"""
# Checking if cached x is a vector
if not self._cached_x.is_vector_like:
raise ValueError(
"kernel gradient can be computed only wrt vector-like arrays.")
if self._rv is None:
raise ValueError("Please run forward with caching=True or set"
"`rv` first.")
# Format of output array should be the same as rv
grad = self._rv.deepcopy()
grad = grad.tosparse() if self._cached_x.issparse else grad.todense()
return grad if w is None else w.dot(grad)