import numpy as np
from . perceptron import Perceptron
[docs]class SecondOrderPerceptron(Perceptron):
"""Second Order Perceptron model.
Cesa-Bianchi, N.; Conconi, A. & Gentile, C.
A Second-Order perceptron algorithm
SIAM Journal on Computing, 105, 34, 640-668
Attributes:
a (:obj:`float`, optional): Trade-off parameter. a is in the range
`[0,1]`. Defaults to 1.
num_iterations (:obj:`int`, optional): Number of iterations
to run the training for. Defaults to 1.
random_state (:obj:`int`, optional): The random seed to use
with the pseudo-random generator. Defaults to `None`.
positive_label (:obj:`int`, optional): The number in the output
field that represents the positive label. The value passed
should be different than -1. Defaults to 1.
class_weight (:obj:`dict`, optional): Represents the relative
weight of the labels in the data. Useful for imbalanced
classification tasks.
Raises:
AssertionError: if `positive_label` is equal to -1.
"""
def __init__(
self,
a=1,
num_iterations=1,
random_state=None,
positive_label=1,
class_weight=None
):
super().__init__(
num_iterations=num_iterations,
random_state=random_state,
positive_label=positive_label,
class_weight=class_weight
)
self._a = a
def _setup(self, X: np.ndarray):
"""Initializes the values for the model' parameters.
Based on the data in argument, this method initializes
the covariance matrix `sigma`.
Args:
X (:obj:`numpy.ndarray`): Input data with n rows and
m columns
Returns:
None
"""
self._sigma = self._a * np.identity(X.shape[1])
def _update(self, x: np.ndarray, y: int):
"""Updates the weight vector in case a mistake occured.
When presented with a data point, this method evaluates
the error and based on the result, updates or not the
weights vector.
Args:
x (:obj:`np.ndarray` or `list`): An array representing
one single data point. Array needs to be 2D.
y (`int`): Output value for the data point. Takes value
between 1 and -1.
Returns:
None
Raises:
IndexError: if the value x is not 2D.
"""
x_ = np.expand_dims(x, axis=0)
s_t = x_ @ self._sigma.T
v_t = x @ s_t.T
beta_t = 1/(v_t + 1)
sigma_t = self._sigma - beta_t * (s_t.T @ s_t)
f_t = self.weights @ sigma_t @ x_.T
if np.sign(f_t) != y:
self.weights = self.weights + y * x * self.class_weight_[y]
self._sigma = sigma_t
[docs] def get_params(self, deep=True):
"""Get parameters for this estimator.
This function is for use with hyper-parameter tuning utilities
such as `GridSearchCV`_.
Args:
deep(:obj:`bool`, optional): If True, will return the parameters
for this estimator and contained sub-objects that are
estimators. Defaults to True.
.. _GridSearchCV:
https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html
"""
params = super().get_params()
params['a'] = self._a
return params