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# coding=utf8
"""
Label propagation in the context of this module refers to a set of
semi-supervised classification algorithms. At a high level, these algorithms
work by forming a fully-connected graph between all points given and solving
for the steady-state distribution of labels at each point.
These algorithms perform very well in practice. The cost of running can be very
expensive, at approximately O(N^3) where N is the number of (labeled and
unlabeled) points. The theory (why they perform so well) is motivated by
intuitions from random walk algorithms and geometric relationships in the data.
For more information see the references below.
Model Features
--------------
Label clamping:
The algorithm tries to learn distributions of labels over the dataset given
label assignments over an initial subset. In one variant, the algorithm does
not allow for any errors in the initial assignment (hard-clamping) while
in another variant, the algorithm allows for some wiggle room for the initial
assignments, allowing them to change by a fraction alpha in each iteration
(soft-clamping).
Kernel:
A function which projects a vector into some higher dimensional space. This
implementation supports RBF and KNN kernels. Using the RBF kernel generates
a dense matrix of size O(N^2). KNN kernel will generate a sparse matrix of
size O(k*N) which will run much faster. See the documentation for SVMs for
more info on kernels.
Examples
--------
>>> import numpy as np
>>> from sklearn import datasets
>>> from sklearn.semi_supervised import LabelPropagation
>>> label_prop_model = LabelPropagation()
>>> iris = datasets.load_iris()
>>> rng = np.random.RandomState(42)
>>> random_unlabeled_points = rng.rand(len(iris.target)) < 0.3
>>> labels = np.copy(iris.target)
>>> labels[random_unlabeled_points] = -1
>>> label_prop_model.fit(iris.data, labels)
LabelPropagation(...)
Notes
-----
References:
[1] Yoshua Bengio, Olivier Delalleau, Nicolas Le Roux. In Semi-Supervised
Learning (2006), pp. 193-216
[2] Olivier Delalleau, Yoshua Bengio, Nicolas Le Roux. Efficient
Non-Parametric Function Induction in Semi-Supervised Learning. AISTAT 2005
"""
# Authors: Clay Woolam <clay@woolam.org>
# Utkarsh Upadhyay <mail@musicallyut.in>
# License: BSD
from abc import ABCMeta, abstractmethod
import warnings
import numpy as np
from scipy import sparse
from scipy.sparse import csgraph
from ..base import BaseEstimator, ClassifierMixin
from ..metrics.pairwise import rbf_kernel
from ..neighbors import NearestNeighbors
from ..utils.extmath import safe_sparse_dot
from ..utils.multiclass import check_classification_targets
from ..utils.validation import check_is_fitted, check_array
from ..utils.validation import _deprecate_positional_args
from ..exceptions import ConvergenceWarning
class BaseLabelPropagation(ClassifierMixin, BaseEstimator, metaclass=ABCMeta):
"""Base class for label propagation module.
Parameters
----------
kernel : {'knn', 'rbf'} or callable, default='rbf'
String identifier for kernel function to use or the kernel function
itself. Only 'rbf' and 'knn' strings are valid inputs. The function
passed should take two inputs, each of shape (n_samples, n_features),
and return a (n_samples, n_samples) shaped weight matrix.
gamma : float, default=20
Parameter for rbf kernel.
n_neighbors : int, default=7
Parameter for knn kernel. Need to be strictly positive.
alpha : float, default=1.0
Clamping factor.
max_iter : int, default=30
Change maximum number of iterations allowed.
tol : float, default=1e-3
Convergence tolerance: threshold to consider the system at steady
state.
n_jobs : int, default=None
The number of parallel jobs to run.
``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
``-1`` means using all processors. See :term:`Glossary <n_jobs>`
for more details.
"""
@_deprecate_positional_args
def __init__(self, kernel='rbf', *, gamma=20, n_neighbors=7,
alpha=1, max_iter=30, tol=1e-3, n_jobs=None):
self.max_iter = max_iter
self.tol = tol
# kernel parameters
self.kernel = kernel
self.gamma = gamma
self.n_neighbors = n_neighbors
# clamping factor
self.alpha = alpha
self.n_jobs = n_jobs
def _get_kernel(self, X, y=None):
if self.kernel == "rbf":
if y is None:
return rbf_kernel(X, X, gamma=self.gamma)
else:
return rbf_kernel(X, y, gamma=self.gamma)
elif self.kernel == "knn":
if self.nn_fit is None:
self.nn_fit = NearestNeighbors(n_neighbors=self.n_neighbors,
n_jobs=self.n_jobs).fit(X)
if y is None:
return self.nn_fit.kneighbors_graph(self.nn_fit._fit_X,
self.n_neighbors,
mode='connectivity')
else:
return self.nn_fit.kneighbors(y, return_distance=False)
elif callable(self.kernel):
if y is None:
return self.kernel(X, X)
else:
return self.kernel(X, y)
else:
raise ValueError("%s is not a valid kernel. Only rbf and knn"
" or an explicit function "
" are supported at this time." % self.kernel)
@abstractmethod
def _build_graph(self):
raise NotImplementedError("Graph construction must be implemented"
" to fit a label propagation model.")
def predict(self, X):
"""Performs inductive inference across the model.
Parameters
----------
X : array-like of shape (n_samples, n_features)
The data matrix.
Returns
-------
y : ndarray of shape (n_samples,)
Predictions for input data.
"""
probas = self.predict_proba(X)
return self.classes_[np.argmax(probas, axis=1)].ravel()
def predict_proba(self, X):
"""Predict probability for each possible outcome.
Compute the probability estimates for each single sample in X
and each possible outcome seen during training (categorical
distribution).
Parameters
----------
X : array-like of shape (n_samples, n_features)
The data matrix.
Returns
-------
probabilities : ndarray of shape (n_samples, n_classes)
Normalized probability distributions across
class labels.
"""
check_is_fitted(self)
X_2d = check_array(X, accept_sparse=['csc', 'csr', 'coo', 'dok',
'bsr', 'lil', 'dia'])
weight_matrices = self._get_kernel(self.X_, X_2d)
if self.kernel == 'knn':
probabilities = np.array([
np.sum(self.label_distributions_[weight_matrix], axis=0)
for weight_matrix in weight_matrices])
else:
weight_matrices = weight_matrices.T
probabilities = safe_sparse_dot(
weight_matrices, self.label_distributions_)
normalizer = np.atleast_2d(np.sum(probabilities, axis=1)).T
probabilities /= normalizer
return probabilities
def fit(self, X, y):
"""Fit a semi-supervised label propagation model based
All the input data is provided matrix X (labeled and unlabeled)
and corresponding label matrix y with a dedicated marker value for
unlabeled samples.
Parameters
----------
X : array-like of shape (n_samples, n_features)
A matrix of shape (n_samples, n_samples) will be created from this.
y : array-like of shape (n_samples,)
`n_labeled_samples` (unlabeled points are marked as -1)
All unlabeled samples will be transductively assigned labels.
Returns
-------
self : object
"""
X, y = self._validate_data(X, y)
self.X_ = X
check_classification_targets(y)
# actual graph construction (implementations should override this)
graph_matrix = self._build_graph()
# label construction
# construct a categorical distribution for classification only
classes = np.unique(y)
classes = (classes[classes != -1])
self.classes_ = classes
n_samples, n_classes = len(y), len(classes)
alpha = self.alpha
if self._variant == 'spreading' and \
(alpha is None or alpha <= 0.0 or alpha >= 1.0):
raise ValueError('alpha=%s is invalid: it must be inside '
'the open interval (0, 1)' % alpha)
y = np.asarray(y)
unlabeled = y == -1
# initialize distributions
self.label_distributions_ = np.zeros((n_samples, n_classes))
for label in classes:
self.label_distributions_[y == label, classes == label] = 1
y_static = np.copy(self.label_distributions_)
if self._variant == 'propagation':
# LabelPropagation
y_static[unlabeled] = 0
else:
# LabelSpreading
y_static *= 1 - alpha
l_previous = np.zeros((self.X_.shape[0], n_classes))
unlabeled = unlabeled[:, np.newaxis]
if sparse.isspmatrix(graph_matrix):
graph_matrix = graph_matrix.tocsr()
for self.n_iter_ in range(self.max_iter):
if np.abs(self.label_distributions_ - l_previous).sum() < self.tol:
break
l_previous = self.label_distributions_
self.label_distributions_ = safe_sparse_dot(
graph_matrix, self.label_distributions_)
if self._variant == 'propagation':
normalizer = np.sum(
self.label_distributions_, axis=1)[:, np.newaxis]
self.label_distributions_ /= normalizer
self.label_distributions_ = np.where(unlabeled,
self.label_distributions_,
y_static)
else:
# clamp
self.label_distributions_ = np.multiply(
alpha, self.label_distributions_) + y_static
else:
warnings.warn(
'max_iter=%d was reached without convergence.' % self.max_iter,
category=ConvergenceWarning
)
self.n_iter_ += 1
normalizer = np.sum(self.label_distributions_, axis=1)[:, np.newaxis]
normalizer[normalizer == 0] = 1
self.label_distributions_ /= normalizer
# set the transduction item
transduction = self.classes_[np.argmax(self.label_distributions_,
axis=1)]
self.transduction_ = transduction.ravel()
return self
class LabelPropagation(BaseLabelPropagation):
"""Label Propagation classifier
Read more in the :ref:`User Guide <label_propagation>`.
Parameters
----------
kernel : {'knn', 'rbf'} or callable, default='rbf'
String identifier for kernel function to use or the kernel function
itself. Only 'rbf' and 'knn' strings are valid inputs. The function
passed should take two inputs, each of shape (n_samples, n_features),
and return a (n_samples, n_samples) shaped weight matrix.
gamma : float, default=20
Parameter for rbf kernel.
n_neighbors : int, default=7
Parameter for knn kernel which need to be strictly positive.
max_iter : int, default=1000
Change maximum number of iterations allowed.
tol : float, 1e-3
Convergence tolerance: threshold to consider the system at steady
state.
n_jobs : int, default=None
The number of parallel jobs to run.
``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
``-1`` means using all processors. See :term:`Glossary <n_jobs>`
for more details.
Attributes
----------
X_ : ndarray of shape (n_samples, n_features)
Input array.
classes_ : ndarray of shape (n_classes,)
The distinct labels used in classifying instances.
label_distributions_ : ndarray of shape (n_samples, n_classes)
Categorical distribution for each item.
transduction_ : ndarray of shape (n_samples)
Label assigned to each item via the transduction.
n_iter_ : int
Number of iterations run.
Examples
--------
>>> import numpy as np
>>> from sklearn import datasets
>>> from sklearn.semi_supervised import LabelPropagation
>>> label_prop_model = LabelPropagation()
>>> iris = datasets.load_iris()
>>> rng = np.random.RandomState(42)
>>> random_unlabeled_points = rng.rand(len(iris.target)) < 0.3
>>> labels = np.copy(iris.target)
>>> labels[random_unlabeled_points] = -1
>>> label_prop_model.fit(iris.data, labels)
LabelPropagation(...)
References
----------
Xiaojin Zhu and Zoubin Ghahramani. Learning from labeled and unlabeled data
with label propagation. Technical Report CMU-CALD-02-107, Carnegie Mellon
University, 2002 http://pages.cs.wisc.edu/~jerryzhu/pub/CMU-CALD-02-107.pdf
See Also
--------
LabelSpreading : Alternate label propagation strategy more robust to noise
"""
_variant = 'propagation'
@_deprecate_positional_args
def __init__(self, kernel='rbf', *, gamma=20, n_neighbors=7,
max_iter=1000, tol=1e-3, n_jobs=None):
super().__init__(kernel=kernel, gamma=gamma,
n_neighbors=n_neighbors, max_iter=max_iter,
tol=tol, n_jobs=n_jobs, alpha=None)
def _build_graph(self):
"""Matrix representing a fully connected graph between each sample
This basic implementation creates a non-stochastic affinity matrix, so
class distributions will exceed 1 (normalization may be desired).
"""
if self.kernel == 'knn':
self.nn_fit = None
affinity_matrix = self._get_kernel(self.X_)
normalizer = affinity_matrix.sum(axis=0)
if sparse.isspmatrix(affinity_matrix):
affinity_matrix.data /= np.diag(np.array(normalizer))
else:
affinity_matrix /= normalizer[:, np.newaxis]
return affinity_matrix
def fit(self, X, y):
return super().fit(X, y)
class LabelSpreading(BaseLabelPropagation):
"""LabelSpreading model for semi-supervised learning
This model is similar to the basic Label Propagation algorithm,
but uses affinity matrix based on the normalized graph Laplacian
and soft clamping across the labels.
Read more in the :ref:`User Guide <label_propagation>`.
Parameters
----------
kernel : {'knn', 'rbf'} or callable, default='rbf'
String identifier for kernel function to use or the kernel function
itself. Only 'rbf' and 'knn' strings are valid inputs. The function
passed should take two inputs, each of shape (n_samples, n_features),
and return a (n_samples, n_samples) shaped weight matrix.
gamma : float, default=20
Parameter for rbf kernel.
n_neighbors : int, default=7
Parameter for knn kernel which is a strictly positive integer.
alpha : float, default=0.2
Clamping factor. A value in (0, 1) that specifies the relative amount
that an instance should adopt the information from its neighbors as
opposed to its initial label.
alpha=0 means keeping the initial label information; alpha=1 means
replacing all initial information.
max_iter : int, default=30
Maximum number of iterations allowed.
tol : float, default=1e-3
Convergence tolerance: threshold to consider the system at steady
state.
n_jobs : int, default=None
The number of parallel jobs to run.
``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
``-1`` means using all processors. See :term:`Glossary <n_jobs>`
for more details.
Attributes
----------
X_ : ndarray of shape (n_samples, n_features)
Input array.
classes_ : ndarray of shape (n_classes,)
The distinct labels used in classifying instances.
label_distributions_ : ndarray of shape (n_samples, n_classes)
Categorical distribution for each item.
transduction_ : ndarray of shape (n_samples,)
Label assigned to each item via the transduction.
n_iter_ : int
Number of iterations run.
Examples
--------
>>> import numpy as np
>>> from sklearn import datasets
>>> from sklearn.semi_supervised import LabelSpreading
>>> label_prop_model = LabelSpreading()
>>> iris = datasets.load_iris()
>>> rng = np.random.RandomState(42)
>>> random_unlabeled_points = rng.rand(len(iris.target)) < 0.3
>>> labels = np.copy(iris.target)
>>> labels[random_unlabeled_points] = -1
>>> label_prop_model.fit(iris.data, labels)
LabelSpreading(...)
References
----------
Dengyong Zhou, Olivier Bousquet, Thomas Navin Lal, Jason Weston,
Bernhard Schoelkopf. Learning with local and global consistency (2004)
http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.115.3219
See Also
--------
LabelPropagation : Unregularized graph based semi-supervised learning
"""
_variant = 'spreading'
@_deprecate_positional_args
def __init__(self, kernel='rbf', *, gamma=20, n_neighbors=7, alpha=0.2,
max_iter=30, tol=1e-3, n_jobs=None):
# this one has different base parameters
super().__init__(kernel=kernel, gamma=gamma,
n_neighbors=n_neighbors, alpha=alpha,
max_iter=max_iter, tol=tol, n_jobs=n_jobs)
def _build_graph(self):
"""Graph matrix for Label Spreading computes the graph laplacian"""
# compute affinity matrix (or gram matrix)
if self.kernel == 'knn':
self.nn_fit = None
n_samples = self.X_.shape[0]
affinity_matrix = self._get_kernel(self.X_)
laplacian = csgraph.laplacian(affinity_matrix, normed=True)
laplacian = -laplacian
if sparse.isspmatrix(laplacian):
diag_mask = (laplacian.row == laplacian.col)
laplacian.data[diag_mask] = 0.0
else:
laplacian.flat[::n_samples + 1] = 0.0 # set diag to 0.0
return laplacian