# -*- coding: utf-8 -*-
# Author: Joris Jensen <jjensen@techfak.uni-bielefeld.de>
#
# License: BSD 3 clause
from __future__ import division
import math
from math import log
import numpy as np
from scipy.optimize import minimize
from .glvq import GlvqModel, _squared_euclidean
from sklearn.utils import validation
[docs]class GmlvqModel(GlvqModel):
"""Generalized Matrix 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_matrix : array-like, shape = [dim, n_features], optional
Relevance matrix to start with.
If not given random initialization for rectangular matrix and unity
for squared matrix.
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.
dim : int, optional (default=nb_features)
Maximum rank or projection dimensions
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.
display : boolean, optional (default=False)
Print information about the bfgs steps.
random_state : int, RandomState instance or None, optional (default=None)
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.
dim_ : int
Maximum rank or projection dimensions
omega_ : array-like, shape = [dim, n_features]
Relevance matrix
See also
--------
GlvqModel, GrlvqModel, LgmlvqModel
"""
[docs] def __init__(self, prototypes_per_class=1, initial_prototypes=None,
initial_matrix=None, regularization=0.0,
dim=None, max_iter=2500, gtol=1e-5, display=False,
random_state=None):
super(GmlvqModel, self).__init__(prototypes_per_class,
initial_prototypes, max_iter, gtol,
display, random_state)
self.regularization = regularization
self.initial_matrix = initial_matrix
self.initialdim = dim
def _optgrad(self, variables, training_data, label_equals_prototype,
random_state, lr_relevances=0, lr_prototypes=1):
n_data, n_dim = training_data.shape
variables = variables.reshape(variables.size // n_dim, n_dim)
nb_prototypes = self.c_w_.shape[0]
omega_t = variables[nb_prototypes:].conj().T
dist = _squared_euclidean(training_data.dot(omega_t),
variables[:nb_prototypes].dot(omega_t))
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(variables.shape)
distcorrectpluswrong = 4 / distcorrectpluswrong ** 2
if lr_relevances > 0:
gw = np.zeros([omega_t.shape[0], n_dim])
for i in range(nb_prototypes):
idxc = i == pidxcorrect
idxw = i == pidxwrong
dcd = distcorrect[idxw] * distcorrectpluswrong[idxw]
dwd = distwrong[idxc] * distcorrectpluswrong[idxc]
if lr_relevances > 0:
difc = training_data[idxc] - variables[i]
difw = training_data[idxw] - variables[i]
gw = gw - np.dot(difw * dcd[np.newaxis].T, omega_t).T \
.dot(difw) + np.dot(difc * dwd[np.newaxis].T,
omega_t).T.dot(difc)
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)) * variables[i]
f3 = 0
if self.regularization:
f3 = np.linalg.pinv(omega_t.conj().T).conj().T
if lr_relevances > 0:
g[nb_prototypes:] = 2 / n_data \
* lr_relevances * gw - self.regularization * f3
if lr_prototypes > 0:
g[:nb_prototypes] = 1 / n_data * lr_prototypes \
* g[:nb_prototypes].dot(omega_t.dot(omega_t.T))
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
variables = variables.reshape(variables.size // n_dim, n_dim)
nb_prototypes = self.c_w_.shape[0]
omega_t = variables[nb_prototypes:] # .conj().T
dist = _squared_euclidean(training_data.dot(omega_t),
variables[:nb_prototypes].dot(omega_t))
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
if self.regularization > 0:
reg_term = self.regularization * log(
np.linalg.det(omega_t.conj().T.dot(omega_t)))
return mu.sum(0) - reg_term # f
return 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.initialdim is None:
self.dim_ = nb_features
elif not isinstance(self.initialdim, int) or self.initialdim <= 0:
raise ValueError("dim must be an positive int")
else:
self.dim_ = self.initialdim
if self.initial_matrix is None:
if self.dim_ == nb_features:
self.omega_ = np.eye(nb_features)
else:
self.omega_ = random_state.rand(self.dim_, nb_features) * 2 - 1
else:
self.omega_ = validation.check_array(self.initial_matrix)
if self.omega_.shape[1] != nb_features: # TODO: check dim
raise ValueError(
"initial matrix has wrong number of features\n"
"found=%d\n"
"expected=%d" % (self.omega_.shape[1], nb_features))
variables = np.append(self.w_, self.omega_, 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,
random_state=random_state,
lr_prototypes=1, lr_relevances=0),
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,
random_state=random_state,
lr_prototypes=0, lr_relevances=1),
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,
random_state=random_state,
lr_prototypes=1, lr_relevances=1),
method=method, x0=res.x,
options={'disp': self.display, 'gtol': self.gtol,
'maxiter': self.max_iter})
n_iter = max(n_iter, res.nit)
out = res.x.reshape(res.x.size // nb_features, nb_features)
self.w_ = out[:nb_prototypes]
self.omega_ = out[nb_prototypes:]
self.omega_ /= math.sqrt(
np.sum(np.diag(self.omega_.T.dot(self.omega_))))
self.n_iter_ = n_iter
def _compute_distance(self, x, w=None, omega=None):
if w is None:
w = self.w_
if omega is None:
omega = self.omega_
nb_samples = x.shape[0]
nb_prototypes = w.shape[0]
distance = np.zeros([nb_prototypes, nb_samples])
for i in range(nb_prototypes):
distance[i] = np.sum((x - w[i]).dot(omega.T) ** 2, 1)
return distance.T
[docs] def project(self, x, dims, print_variance_covered=False):
"""Projects the data input data X using the relevance matrix 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.
"""
v, u = np.linalg.eig(self.omega_.conj().T.dot(self.omega_))
idx = v.argsort()[::-1]
if print_variance_covered:
print('variance coverd by projection:',
v[idx][:dims].sum() / v.sum() * 100)
return x.dot(u[:, idx][:, :dims].dot(np.diag(np.sqrt(v[idx][:dims]))))