# -*- 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 scipy.spatial.distance import cdist
from sklearn.base import BaseEstimator, ClassifierMixin
from sklearn.utils import validation
from sklearn.utils.multiclass import unique_labels
from sklearn.utils.validation import check_is_fitted
def _squared_euclidean(a, b=None):
if b is None:
d = np.sum(a ** 2, 1)[np.newaxis].T + np.sum(a ** 2, 1) - 2 * a.dot(
a.T)
else:
d = np.sum(a ** 2, 1)[np.newaxis].T + np.sum(b ** 2, 1) - 2 * a.dot(
b.T)
return np.maximum(d, 0)
[docs]class GlvqModel(BaseEstimator, ClassifierMixin):
"""Generalized 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.
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 bfgs.
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.
See also
--------
GrlvqModel, GmlvqModel, LgmlvqModel
"""
[docs] def __init__(self, prototypes_per_class=1, initial_prototypes=None,
max_iter=2500, gtol=1e-5,
display=False, random_state=None):
self.random_state = random_state
self.initial_prototypes = initial_prototypes
self.prototypes_per_class = prototypes_per_class
self.display = display
self.max_iter = max_iter
self.gtol = gtol
def _optgrad(self, variables, training_data, label_equals_prototype,
random_state):
n_data, n_dim = training_data.shape
nb_prototypes = self.c_w_.size
prototypes = variables.reshape(nb_prototypes, n_dim)
dist = _squared_euclidean(training_data, 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
g = np.zeros(prototypes.shape)
distcorrectpluswrong = 4 / distcorrectpluswrong ** 2
for i in range(nb_prototypes):
idxc = i == pidxcorrect
idxw = i == pidxwrong
dcd = distcorrect[idxw] * distcorrectpluswrong[idxw]
dwd = distwrong[idxc] * distcorrectpluswrong[idxc]
g[i] = dcd.dot(training_data[idxw]) - dwd.dot(
training_data[idxc]) + (dwd.sum(0) -
dcd.sum(0)) * prototypes[i]
g[:nb_prototypes] = 1 / n_data * g[:nb_prototypes]
g = g * (1 + 0.0001 * random_state.rand(*g.shape) - 0.5)
return g.ravel()
def _optfun(self, variables, training_data, label_equals_prototype):
n_data, n_dim = training_data.shape
nb_prototypes = self.c_w_.size
prototypes = variables.reshape(nb_prototypes, n_dim)
dist = _squared_euclidean(training_data, 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
return mu.sum(0)
def _validate_train_parms(self, train_set, train_lab):
random_state = validation.check_random_state(self.random_state)
if not isinstance(self.display, bool):
raise ValueError("display must be a boolean")
if not isinstance(self.max_iter, int) or self.max_iter < 1:
raise ValueError("max_iter must be an positive integer")
if not isinstance(self.gtol, float) or self.gtol <= 0:
raise ValueError("gtol must be a positive float")
train_set, train_lab = validation.check_X_y(train_set, train_lab)
self.classes_ = unique_labels(train_lab)
nb_classes = len(self.classes_)
nb_samples, nb_features = train_set.shape # nb_samples unused
# set prototypes per class
if isinstance(self.prototypes_per_class, int):
if self.prototypes_per_class < 0 or not isinstance(
self.prototypes_per_class, int):
raise ValueError("prototypes_per_class must be a positive int")
nb_ppc = np.ones([nb_classes],
dtype='int') * self.prototypes_per_class
else:
nb_ppc = validation.column_or_1d(
validation.check_array(self.prototypes_per_class,
ensure_2d=False, dtype='int'))
if nb_ppc.min() <= 0:
raise ValueError(
"values in prototypes_per_class must be positive")
if nb_ppc.size != nb_classes:
raise ValueError(
"length of prototypes per class"
" does not fit the number of classes"
"classes=%d"
"length=%d" % (nb_classes, nb_ppc.size))
# initialize prototypes
if self.initial_prototypes is None:
self.w_ = np.empty([np.sum(nb_ppc), nb_features], dtype=np.double)
self.c_w_ = np.empty([nb_ppc.sum()], dtype=self.classes_.dtype)
pos = 0
for actClass in range(nb_classes):
nb_prot = nb_ppc[actClass]
mean = np.mean(
train_set[train_lab == self.classes_[actClass], :], 0)
self.w_[pos:pos + nb_prot] = mean + (
random_state.rand(nb_prot, nb_features) * 2 - 1)
self.c_w_[pos:pos + nb_prot] = self.classes_[actClass]
pos += nb_prot
else:
x = validation.check_array(self.initial_prototypes)
self.w_ = x[:, :-1]
self.c_w_ = x[:, -1]
if self.w_.shape != (np.sum(nb_ppc), nb_features):
raise ValueError("the initial prototypes have wrong shape\n"
"found=(%d,%d)\n"
"expected=(%d,%d)" % (
self.w_.shape[0], self.w_.shape[1],
nb_ppc.sum(), nb_features))
if set(self.c_w_) != set(self.classes_):
raise ValueError(
"prototype labels and test data classes do not match\n"
"classes={}\n"
"prototype labels={}\n".format(self.classes_, self.c_w_))
return train_set, train_lab, random_state
def _optimize(self, x, y, random_state):
label_equals_prototype = y[np.newaxis].T == self.c_w_
res = minimize(
fun=lambda vs: self._optfun(
variables=vs, training_data=x,
label_equals_prototype=label_equals_prototype),
jac=lambda vs: self._optgrad(
variables=vs, training_data=x,
label_equals_prototype=label_equals_prototype,
random_state=random_state),
method='l-bfgs-b', x0=self.w_,
options={'disp': self.display, 'gtol': self.gtol,
'maxiter': self.max_iter})
self.w_ = res.x.reshape(self.w_.shape)
self.n_iter_ = res.nit
[docs] def fit(self, x, y):
"""Fit the GLVQ model to the given training data and parameters using
l-bfgs-b.
Parameters
----------
x : array-like, shape = [n_samples, n_features]
Training vector, where n_samples in the number of samples and
n_features is the number of features.
y : array, shape = [n_samples]
Target values (integers in classification, real numbers in
regression)
Returns
--------
self
"""
x, y, random_state = self._validate_train_parms(x, y)
if len(np.unique(y)) == 1:
raise ValueError("fitting " + type(
self).__name__ + " with only one class is not possible")
self._optimize(x, y, random_state)
return self
def _compute_distance(self, x, w=None):
if w is None:
w = self.w_
return cdist(x, w, 'euclidean')
[docs] def predict(self, x):
"""Predict class membership index for each input sample.
This function does classification on an array of
test vectors X.
Parameters
----------
x : array-like, shape = [n_samples, n_features]
Returns
-------
C : array, shape = (n_samples,)
Returns predicted values.
"""
check_is_fitted(self, ['w_', 'c_w_'])
x = validation.check_array(x)
if x.shape[1] != self.w_.shape[1]:
raise ValueError("X has wrong number of features\n"
"found=%d\n"
"expected=%d" % (self.w_.shape[1], x.shape[1]))
dist = self._compute_distance(x)
return (self.c_w_[dist.argmin(1)])