# -*- coding: utf-8 -*-
# Author: Joris Jensen <jjensen@techfak.uni-bielefeld.de>
#
# License: BSD 3 clause
from __future__ import division
import numpy as np
from scipy.optimize import minimize
from .glvq import GlvqModel, _squared_euclidean
from sklearn.utils import validation
[docs]class GrlvqModel(GlvqModel):
"""Generalized Relevance Learning Vector Quantization
Parameters
----------
prototypes_per_class : int or list of int, optional (default=1)
Number of prototypes per class. Use list to specify different
numbers per class.
initial_prototypes : array-like, shape = [n_prototypes, n_features + 1],
optional
Prototypes to start with. If not given initialization near the class
means. Class label must be placed as last entry of each prototype.
initial_relevances : array-like, shape = [n_prototypes], optional
Relevances to start with. If not given all relevances are equal.
regularization : float, optional (default=0.0)
Value between 0 and 1. Regularization is done by the log determinant
of the relevance matrix. Without regularization relevances may
degenerate to zero.
max_iter : int, optional (default=2500)
The maximum number of iterations.
gtol : float, optional (default=1e-5)
Gradient norm must be less than gtol before successful termination
of l-bfgs-b.
beta : int, optional (default=2)
Used inside phi.
1 / (1 + np.math.exp(-beta * x))
C : array-like, shape = [2,3] ,optional
Weights for wrong classification of form (y_real,y_pred,weight)
Per default all weights are one, meaning you only need to specify
the weights not equal one.
display : boolean, optional (default=False)
Print information about the bfgs steps.
random_state : int, RandomState instance or None, optional
If int, random_state is the seed used by the random number generator;
If RandomState instance, random_state is the random number generator;
If None, the random number generator is the RandomState instance used
by `np.random`.
Attributes
----------
w_ : array-like, shape = [n_prototypes, n_features]
Prototype vector, where n_prototypes in the number of prototypes and
n_features is the number of features
c_w_ : array-like, shape = [n_prototypes]
Prototype classes
classes_ : array-like, shape = [n_classes]
Array containing labels.
lambda_ : array-like, shape = [n_prototypes]
Relevances
See also
--------
GlvqModel, GmlvqModel, LgmlvqModel
"""
[docs] def __init__(self, prototypes_per_class=1, initial_prototypes=None,
initial_relevances=None, regularization=0.0,
max_iter=2500, gtol=1e-5, beta=2, C=None, display=False,
random_state=None):
super(GrlvqModel, self).__init__(prototypes_per_class,
initial_prototypes, max_iter,
gtol, beta, C, display, random_state)
self.regularization = regularization
self.initial_relevances = initial_relevances
def _optgrad(self, variables, training_data, label_equals_prototype,
random_state, lr_relevances=0, lr_prototypes=1):
n_data, n_dim = training_data.shape
nb_prototypes = self.c_w_.shape[0]
prototypes = variables.reshape(variables.size // n_dim, n_dim)[
:nb_prototypes]
lambd = variables[prototypes.size:]
lambd[lambd < 0] = 0.0000001 # dirty fix if all values are smaller 0
dist = _squared_euclidean(lambd * training_data,
lambd * prototypes)
d_wrong = dist.copy()
d_wrong[label_equals_prototype] = np.inf
distwrong = d_wrong.min(1)
pidxwrong = d_wrong.argmin(1)
d_correct = dist
d_correct[np.invert(label_equals_prototype)] = np.inf
distcorrect = d_correct.min(1)
pidxcorrect = d_correct.argmin(1)
distcorrectpluswrong = distcorrect + distwrong
distcorectminuswrong = distcorrect - distwrong
mu = distcorectminuswrong / distcorrectpluswrong
mu = np.vectorize(self.phi_prime)(mu)
g = np.zeros(prototypes.shape)
distcorrectpluswrong = 4 / distcorrectpluswrong ** 2
gw = np.zeros(lambd.size)
for i in range(nb_prototypes):
idxc = i == pidxcorrect
idxw = i == pidxwrong
dcd = mu[idxw] * distcorrect[idxw] * distcorrectpluswrong[idxw]
dwd = mu[idxc] * distwrong[idxc] * distcorrectpluswrong[idxc]
if lr_relevances > 0:
difc = training_data[idxc] - prototypes[i]
difw = training_data[idxw] - prototypes[i]
gw -= dcd.dot(difw ** 2) - dwd.dot(difc ** 2)
if lr_prototypes > 0:
g[i] = dcd.dot(difw) - dwd.dot(difc)
elif lr_prototypes > 0:
g[i] = dcd.dot(training_data[idxw]) - \
dwd.dot(training_data[idxc]) + \
(dwd.sum(0) - dcd.sum(0)) * prototypes[i]
f3 = 0
if self.regularization:
f3 = np.diag(np.linalg.pinv(np.sqrt(np.diag(lambd))))
if lr_relevances > 0:
gw = 2 / n_data * lr_relevances * \
gw - self.regularization * f3
if lr_prototypes > 0:
g[:nb_prototypes] = 1 / n_data * lr_prototypes * \
g[:nb_prototypes] * lambd
g = np.append(g.ravel(), gw, axis=0)
g = g * (1 + 0.0001 * (random_state.rand(*g.shape) - 0.5))
return g
def _optfun(self, variables, training_data, label_equals_prototype):
n_data, n_dim = training_data.shape
nb_prototypes = self.c_w_.shape[0]
prototypes = variables.reshape(variables.size // n_dim, n_dim)[
:nb_prototypes]
lambd = variables[prototypes.size:]
dist = _squared_euclidean(lambd * training_data,
lambd * prototypes)
d_wrong = dist.copy()
d_wrong[label_equals_prototype] = np.inf
distwrong = d_wrong.min(1)
d_correct = dist
d_correct[np.invert(label_equals_prototype)] = np.inf
distcorrect = d_correct.min(1)
distcorrectpluswrong = distcorrect + distwrong
distcorectminuswrong = distcorrect - distwrong
mu = distcorectminuswrong / distcorrectpluswrong
mu *= self.c_[label_equals_prototype.argmax(1), d_wrong.argmin(1)]
return np.vectorize(self.phi)(mu).sum(0)
def _optimize(self, x, y, random_state):
if not isinstance(self.regularization,
float) or self.regularization < 0:
raise ValueError("regularization must be a positive float")
nb_prototypes, nb_features = self.w_.shape
if self.initial_relevances is None:
self.lambda_ = np.ones([nb_features])
else:
self.lambda_ = validation.column_or_1d(
validation.check_array(self.initial_relevances, dtype='float',
ensure_2d=False))
if self.lambda_.size != nb_features:
raise ValueError("length of initial relevances is wrong"
"features=%d"
"length=%d" % (
nb_features, self.lambda_.size))
self.lambda_ /= np.sum(self.lambda_)
variables = np.append(self.w_.ravel(), self.lambda_, axis=0)
label_equals_prototype = y[np.newaxis].T == self.c_w_
method = 'l-bfgs-b'
res = minimize(
fun=lambda vs: self._optfun(
vs, x, label_equals_prototype=label_equals_prototype),
jac=lambda vs: self._optgrad(
vs, x, label_equals_prototype=label_equals_prototype,
lr_prototypes=1, lr_relevances=0, random_state=random_state),
method=method, x0=variables,
options={'disp': self.display, 'gtol': self.gtol,
'maxiter': self.max_iter})
n_iter = res.nit
res = minimize(
fun=lambda vs: self._optfun(
vs, x, label_equals_prototype=label_equals_prototype),
jac=lambda vs: self._optgrad(
vs, x, label_equals_prototype=label_equals_prototype,
lr_prototypes=0, lr_relevances=1, random_state=random_state),
method=method, x0=res.x,
options={'disp': self.display, 'gtol': self.gtol,
'maxiter': self.max_iter})
n_iter = max(n_iter, res.nit)
res = minimize(
fun=lambda vs: self._optfun(
vs, x, label_equals_prototype=label_equals_prototype),
jac=lambda vs: self._optgrad(
vs, x, label_equals_prototype=label_equals_prototype,
lr_prototypes=1, lr_relevances=1, random_state=random_state),
method=method, x0=res.x,
options={'disp': self.display, 'gtol': self.gtol,
'maxiter': self.max_iter})
n_iter = max(n_iter, res.nit)
self.w_ = res.x.reshape(res.x.size // nb_features, nb_features)[:nb_prototypes]
self.lambda_ = res.x[self.w_.size:]
self.lambda_[self.lambda_ < 0] = 0.0000001
self.lambda_ = self.lambda_ / self.lambda_.sum()
self.n_iter_ = n_iter
def _compute_distance(self, x, w=None, lambda_=None):
if w is None:
w = self.w_
if lambda_ is None:
lambda_ = self.lambda_
nb_samples = x.shape[0]
nb_prototypes = w.shape[0]
distance = np.zeros([nb_prototypes, nb_samples])
for i in range(nb_prototypes):
delta = x - w[i]
distance[i] = np.sum(delta ** 2 * lambda_, 1)
return distance.T
[docs] def project(self, x, dims, print_variance_covered=False):
"""Projects the data input data X using the relevance vector of trained
model to dimension dim
Parameters
----------
x : array-like, shape = [n,n_features]
input data for project
dims : int
dimension to project to
print_variance_covered : boolean
flag to print the covered variance of the projection
Returns
--------
C : array, shape = [n,n_features]
Returns predicted values.
"""
idx = self.lambda_.argsort()[::-1]
if print_variance_covered:
print('variance coverd by projection:',
self.lambda_[idx][:dims].sum() / self.lambda_.sum() * 100)
return x.dot(np.diag(self.lambda_)[idx][:, :dims])