Source code for

.. module:: CKernelChebyshevDistance
   :synopsis: Chebyshev distance kernel

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

from sklearn import metrics

from secml.array import CArray
from import CKernel

[docs]class CKernelChebyshevDistance(CKernel): """Chebyshev distance kernel. Given matrices X and RV, this is computed as:: K(x, rv) = max(|x - rv|) for each pair of rows in X and in RV. Attributes ---------- class_type : 'chebyshev-dist' Examples -------- >>> from secml.array import CArray >>> from import CKernelChebyshevDistance >>> x = CArray([[1,2],[3,4]]) >>> v = CArray([[5,6],[7,8]]) >>> print(CKernelChebyshevDistance().k(x,v)) CArray([[-4. -6.] [-2. -4.]]) >>> print(CKernelChebyshevDistance().k(x)) CArray([[-0. -2.] [-2. -0.]]) """ __class_type = 'chebyshev-dist' def _forward(self, x): """Compute (negative) Chebyshev distances 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, shape (n_x, n_rv). """ if x.issparse is True or self._rv.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(), self._rv.get_data(), metric='chebyshev')) def _backward(self, w=None): """Calculate gradients of Chebyshev kernel wrt cached vector 'x'. The gradient of the negative Chebyshev distance is given by:: dK(rv,x)/dx = - sign(rv - x) 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.") if self._cached_x.issparse is True or self._rv.issparse is True: raise TypeError( "Chebyshev Kernel not available for sparse data." "See `sklearn.metrics.pairwise_distances`.") diff = self._rv - self._cached_x m = abs(diff).max(axis=1) # extract m from each row grad = CArray.zeros(shape=diff.shape) grad[diff >= m] = 1 # this correctly broadcasts per-row comparisons grad[diff <= -m] = -1 return grad if w is None else