import numpy as np
import math
from numpy import linalg as LA
from . __base import OnlineLearningModel
[docs]class ALMA(OnlineLearningModel):
"""A New Approximate Maximal Margin Classification Algorithm.
Gentile, C.
A New Approximate Maximal Margin Classification Algorithm
Journal of Machine Learning Research, 101, 2, 213-242
Attributes:
p (int, optional): ALMA's order with p strictly greater than 0.
Defaults to 2.
C (:obj:`float`, optional): Parameter of ALMA with C strictly greater
than 0. Defaults to 1.
alpha (:obj:`float`, optional): The sensitivity of the model. `alpha`
takes values between 0 (non-inclusive). 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,
alpha=1.0,
p=2,
C=1,
num_iterations=1,
random_state=None,
class_weight=None,
positive_label=1
):
super().__init__(
num_iterations=num_iterations,
random_state=random_state,
positive_label=positive_label,
class_weight=class_weight
)
self._p = p
self._C = C
self._alpha = alpha
self._B = 1
self._k = 0
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.
"""
gamma_k = self._B * math.sqrt(self._p - 1) / math.sqrt(self._k)
if y * self.weights.dot(x) <= (1 - self._alpha) * gamma_k:
eta_k = ((self._C / (math.sqrt(self._p - 1) * math.sqrt(self._k)))
* self.class_weight_[y])
self.weights = self.weights + eta_k * y * x
norm_w = LA.norm(self.weights, ord=self._p)
self.weights = self.weights / (max(1, norm_w))
self._k += 1
def _setup(self, X):
"""Initializes the values for the model' parameters.
Based on the data in argument, this method initializes
the parameters `k` and `B` of the ALMA algorithm.
Args:
X (:obj:`numpy.ndarray`): Input data with n rows and
m columns
Returns:
None
"""
self._k = 1
self._B = 1/self._alpha
[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['p'] = self._p
params['C'] = self._C
params['alpha'] = self._alpha
return params