"""
.. module:: CKernelHistIntersect
:synopsis: Histogram Intersection kernel
.. moduleauthor:: Battista Biggio <battista.biggio@unica.it>
.. moduleauthor:: Marco Melis <marco.melis@unica.it>
"""
import numpy as np
from secml.array import CArray
from secml.ml.kernels import CKernel
[docs]class CKernelHistIntersect(CKernel):
"""Histogram Intersection Kernel.
Given matrices X and RV, this is computed by::
K(x, rv) = sum_i ( min(x[i], rv[i]) )
for each pair of rows in X and in RV.
Attributes
----------
class_type : 'hist-intersect'
Examples
--------
>>> from secml.array import CArray
>>> from secml.ml.kernels.c_kernel_histintersect import CKernelHistIntersect
>>> print(CKernelHistIntersect().k(CArray([[1,2],[3,4]]), CArray([[10,20],[30,40]])))
CArray([[3. 3.]
[7. 7.]])
>>> print(CKernelHistIntersect().k(CArray([[1,2],[3,4]])))
CArray([[3. 3.]
[3. 7.]])
"""
__class_type = 'hist-intersect'
def _forward(self, x):
"""Compute the histogram intersection 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).
"""
k = CArray.zeros(shape=(x.shape[0], self._rv.shape[0]))
x_nd, rv_nd = x.tondarray(), self._rv.tondarray()
if x.shape[0] <= self._rv.shape[0]: # loop on the matrix with less samples
# loop over samples in x, and compute x_i vs rv
for i in range(k.shape[0]):
k[i, :] = CArray(np.minimum(x_nd[i, :], rv_nd).sum(axis=1))
else:
# loop over samples in rv, and compute rv_j vs x
for j in range(k.shape[1]):
k[:, j] = CArray(np.minimum(x_nd, rv_nd[j, :]).sum(axis=1)).T
return k
def _backward(self, w=None):
"""Calculate Histogram Intersection kernel gradient wrt
cached vector 'x'.
The kernel is computed between each row of rv
(denoted with rk) and x, as::
sum_i ( min(rk[i], x[i]) )
The gradient computed w.r.t. x is thus
1 if x[i] < rk[i], and 0 elsewhere.
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:
# Broadcasting not supported for sparse arrays
x_broadcast = self._cached_x.repmat(self._rv.shape[0], 1)
else: # Broadcasting is supported by design for dense arrays
x_broadcast = self._cached_x
grad = CArray.zeros(shape=self._rv.shape,
sparse=self._cached_x.issparse)
grad[x_broadcast < self._rv] = 1 # TODO support from CArray still missing
return grad if w is None else w.dot(grad)