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