"""
.. module:: CLossHinge
:synopsis: Hinge Loss Functions
.. moduleauthor:: Marco Melis <marco.melis@unica.it>
"""
from secml.ml.classifiers.loss import CLossClassification
from secml.ml.classifiers.loss.c_loss import _check_binary_score
from secml.ml.classifiers.clf_utils import convert_binary_labels
from secml.array import CArray
[docs]class CLossHinge(CLossClassification):
"""Hinge Loss Function.
The function computes the average distance between the model and
the data using hinge loss, a one-sided metric that considers only
prediction errors.
Hinge loss is used in maximal margin classifiers such as
support vector machines.
After converting the labels to {-1, +1},
then the hinge loss is defined as:
.. math::
L_\\text{Hinge}(y, s) = \\max \\left\\{ 1 - sy, 0 \\right\\}
Attributes
----------
class_type : 'hinge'
suitable_for : 'classification'
"""
__class_type = 'hinge'
[docs] def loss(self, y_true, score, pos_label=1):
"""Computes the value of the hinge loss function.
Parameters
----------
y_true : CArray
Ground truth (correct), targets. Vector-like array.
score : CArray
Outputs (predicted), targets.
2-D array of shape (n_samples, n_classes) or 1-D flat array
of shape (n_samples,). If 1-D array, the probabilities
provided are assumed to be that of the positive class.
pos_label : {0, 1}, optional
The class wrt compute the loss function. Default 1.
If `score` is a 1-D flat array, this parameter is ignored.
Returns
-------
CArray
Loss function. Vector-like array.
"""
if pos_label not in (0, 1):
raise ValueError("only {0, 1} are accepted for `pos_label`")
y_true = convert_binary_labels(y_true).ravel() # Convert to {-1, 1}
score = _check_binary_score(score, pos_label)
# max(0, 1 - y*s)
h = 1.0 - y_true * score
h[h < 0] = 0.0
return h
[docs] def dloss(self, y_true, score, pos_label=1):
"""Computes the derivative of the hinge loss function with respect to `score`.
Parameters
----------
y_true : CArray
Ground truth (correct), targets. Vector-like array.
score : CArray
Outputs (predicted), targets.
2-D array of shape (n_samples, n_classes) or 1-D flat array
of shape (n_samples,). If 1-D array, the probabilities
provided are assumed to be that of the positive class.
pos_label : {0, 1}, optional
The class wrt compute the loss function derivative. Default 1.
If `score` is a 1-D flat array, this parameter is ignored.
Returns
-------
CArray
Derivative of the loss function. Vector-like array.
"""
if pos_label not in (0, 1):
raise ValueError("only {0, 1} are accepted for `pos_label`")
y_true = convert_binary_labels(y_true).ravel() # Convert to {-1, 1}
score = _check_binary_score(score, pos_label)
# 0 if (1 - y*s) < 0 else -y_true
d = -y_true.astype(float) # labels are generally int
h = 1.0 - y_true * score
d[h < 0] = 0.0
return d
[docs]class CLossHingeSquared(CLossClassification):
"""Squared Hinge Loss Function.
The function computes the average distance between the model and
the data using hinge loss, a one-sided metric that considers only
prediction errors.
After converting the labels to {-1, +1}, then the hinge loss is defined as:
.. math::
L^2_\\text{Hinge} (y, s) =
{\\left( \\max \\left\\{ 1 - sy, 0 \\right\\} \\right)}^2
Attributes
----------
class_type : 'hinge-squared'
suitable_for : 'classification'
"""
__class_type = 'hinge-squared'
[docs] def loss(self, y_true, score, pos_label=1):
"""Computes the value of the squared hinge loss function.
Parameters
----------
y_true : CArray
Ground truth (correct), targets. Vector-like array.
score : CArray
Outputs (predicted), targets.
2-D array of shape (n_samples, n_classes) or 1-D flat array
of shape (n_samples,). If 1-D array, the probabilities
provided are assumed to be that of the positive class.
pos_label : {0, 1}, optional
The class wrt compute the loss function. Default 1.
If `score` is a 1-D flat array, this parameter is ignored.
Returns
-------
CArray
Loss function. Vector-like array.
"""
if pos_label not in (0, 1):
raise ValueError("only {0, 1} are accepted for `pos_label`")
y_true = convert_binary_labels(y_true).ravel() # Convert to {-1, 1}
score = _check_binary_score(score, pos_label)
# (max(0, 1 - y*s))^2
h = 1.0 - y_true * score
h[h < 0] = 0.0
return h ** 2
[docs] def dloss(self, y_true, score, pos_label=1):
"""Computes the derivative of the squared hinge loss function with respect to `score`.
Parameters
----------
y_true : CArray
Ground truth (correct), targets. Vector-like array.
score : CArray
Outputs (predicted), targets.
2-D array of shape (n_samples, n_classes) or 1-D flat array
of shape (n_samples,). If 1-D array, the probabilities
provided are assumed to be that of the positive class.
pos_label : {0, 1}, optional
The class wrt compute the loss function derivative. Default 1.
If `score` is a 1-D flat array, this parameter is ignored.
Returns
-------
CArray
Derivative of the loss function. Vector-like array.
"""
if pos_label not in (0, 1):
raise ValueError("only {0, 1} are accepted for `pos_label`")
y_true = convert_binary_labels(y_true).ravel() # Convert to {-1, 1}
score = _check_binary_score(score, pos_label)
# 0 if (1 - y * s) < 0 else -2 * y * (1 - y * s)
h = 1.0 - y_true * score
d = -2.0 * y_true * h
d[h < 0] = 0.0
return d