Source code for

.. module:: CKernelLinear
   :synopsis: Linear kernel

.. moduleauthor:: Battista Biggio <>
.. moduleauthor:: Marco Melis <>

from sklearn import metrics

from secml.array import CArray
from 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 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