# -*- coding:utf-8 -*-
import numpy as np
[docs]class fourier:
"""
random feature maps
``Psi(X; W,b) = cos[X * Wt + b] * alpha``
where
- X: input, N-by-d matrix
- W: weight, l-by-d matrix
- Wt: transpose of W
- b: bias, 1-by-l matrix
- alpha: coefficient
and
- N: number of data
- d: dimension of input
- l: number of basis
Attributes
==========
params: Tuple
W, b, alpha
nbasis: int
number of basis
References
==========
A. Rahimi and B. Recht, "Random features for large-scale kernel machines,"
in "Advances in neural information processing systems," 2007, pp. 1177-1184.
"""
def __init__(self, params):
"""
Parameters
----------
params: Tuple
W, b, alpha
"""
self._check_params(params)
self._check_len_params(params)
self.params = params
self.nbasis = self.params[1].shape[0]
[docs] def get_basis(self, X, params=None):
"""
compute the value of basis
Parameters
==========
X: numpy.ndarray
input
params: Tuple
W, b, alpha
(default: self.params)
Returns
=======
Psi(X; W,b): numpy.ndarray
N-by-l matrix
``cos[X * Wt + b] * alpha``
where ``Wt`` is the transpose of ``W``.
"""
if params is None:
params = self.params
self._check_params(params)
self._check_len_params(params)
return np.cos(np.dot(X, params[0].transpose()) + params[1]) * params[2]
[docs] def set_params(self, params):
"""
update basis parameters
Parameters
==========
params: tuple
W, b, alpha
"""
self._check_params(params)
self._check_len_params(params)
self.params = params
[docs] def show(self):
"""
print parameters
"""
print("W = ", self.params[0])
print("b = ", self.params[1])
print("alpha = ", self.params[2])
def _check_params(self, params):
"""
Parameters
==========
params: tuple
W, b, alpha
Raises
======
ValueError
if ``params`` is not a 3-dimensional tuple
"""
if not isinstance(params, tuple):
raise ValueError("The variable < params > must be a tuple.")
if len(params) != 3:
raise ValueError("The variable < params > must be 3-dimensional tuple.")
def _check_len_params(self, params):
"""
Parameters
==========
params: tuple
W, b, alpha
Raises
======
ValueError
when dim of W and b are mismatch
or alpha is not a scalar
"""
if params[0].shape[0] != params[1].shape[0]:
raise ValueError(
"The length of 0-axis of W must be same as the length of b."
)
if hasattr(params[2], "__len__"):
if len(params[2]) != 1:
raise ValueError("The third entry of <params> must be a scalar.")
else:
if isinstance(params[2], str):
raise ValueError("The third entry of <params> must be a scalar.")