624 lines
21 KiB
Python
624 lines
21 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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import warnings
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from abc import ABCMeta, abstractmethod
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from numbers import Integral, Real
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import numpy as np
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from scipy import sparse
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from ..base import BaseEstimator, ClassifierMixin, _fit_context
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from ..exceptions import ConvergenceWarning
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from ..metrics.pairwise import rbf_kernel
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from ..neighbors import NearestNeighbors
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from ..utils._param_validation import Interval, StrOptions
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from ..utils.extmath import safe_sparse_dot
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from ..utils.fixes import laplacian as csgraph_laplacian
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from ..utils.multiclass import check_classification_targets
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from ..utils.validation import check_is_fitted
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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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_parameter_constraints: dict = {
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"kernel": [StrOptions({"knn", "rbf"}), callable],
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"gamma": [Interval(Real, 0, None, closed="left")],
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"n_neighbors": [Interval(Integral, 0, None, closed="neither")],
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"alpha": [None, Interval(Real, 0, 1, closed="neither")],
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"max_iter": [Interval(Integral, 0, None, closed="neither")],
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"tol": [Interval(Real, 0, None, closed="left")],
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"n_jobs": [None, Integral],
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}
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def __init__(
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self,
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kernel="rbf",
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*,
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gamma=20,
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n_neighbors=7,
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alpha=1,
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max_iter=30,
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tol=1e-3,
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n_jobs=None,
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):
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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(
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n_neighbors=self.n_neighbors, n_jobs=self.n_jobs
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).fit(X)
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if y is None:
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return self.nn_fit.kneighbors_graph(
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self.nn_fit._fit_X, self.n_neighbors, mode="connectivity"
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)
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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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@abstractmethod
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def _build_graph(self):
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raise NotImplementedError(
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"Graph construction must be implemented to fit a label propagation model."
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)
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def predict(self, X):
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"""Perform 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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# Note: since `predict` does not accept semi-supervised labels as input,
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# `fit(X, y).predict(X) != fit(X, y).transduction_`.
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# Hence, `fit_predict` is not implemented.
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# See https://github.com/scikit-learn/scikit-learn/pull/24898
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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 = self._validate_data(
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X,
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accept_sparse=["csc", "csr", "coo", "dok", "bsr", "lil", "dia"],
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reset=False,
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)
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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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[
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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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]
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)
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else:
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weight_matrices = weight_matrices.T
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probabilities = safe_sparse_dot(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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@_fit_context(prefer_skip_nested_validation=True)
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def fit(self, X, y):
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"""Fit a semi-supervised label propagation model to X.
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The input samples (labeled and unlabeled) are provided by matrix X,
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and target labels are provided by matrix y. We conventionally apply the
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label -1 to unlabeled samples in matrix y in a semi-supervised
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classification.
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Parameters
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----------
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X : {array-like, sparse matrix} of shape (n_samples, n_features)
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Training data, where `n_samples` is the number of samples
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and `n_features` is the number of features.
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y : array-like of shape (n_samples,)
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Target class values with unlabeled points marked as -1.
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All unlabeled samples will be transductively assigned labels
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internally, which are stored in `transduction_`.
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Returns
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-------
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self : object
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Returns the instance itself.
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"""
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X, y = self._validate_data(
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X,
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y,
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accept_sparse=["csr", "csc"],
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reset=True,
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)
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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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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 - self.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.issparse(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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)
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if self._variant == "propagation":
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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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self.label_distributions_ = np.where(
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unlabeled, self.label_distributions_, y_static
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)
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else:
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# clamp
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self.label_distributions_ = (
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np.multiply(self.alpha, self.label_distributions_) + y_static
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)
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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_, 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_ : {array-like, sparse matrix} 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)
|
||
|
|
Categorical distribution for each item.
|
||
|
|
|
||
|
|
transduction_ : ndarray of shape (n_samples)
|
||
|
|
Label assigned to each item during :term:`fit`.
|
||
|
|
|
||
|
|
n_features_in_ : int
|
||
|
|
Number of features seen during :term:`fit`.
|
||
|
|
|
||
|
|
.. versionadded:: 0.24
|
||
|
|
|
||
|
|
feature_names_in_ : ndarray of shape (`n_features_in_`,)
|
||
|
|
Names of features seen during :term:`fit`. Defined only when `X`
|
||
|
|
has feature names that are all strings.
|
||
|
|
|
||
|
|
.. versionadded:: 1.0
|
||
|
|
|
||
|
|
n_iter_ : int
|
||
|
|
Number of iterations run.
|
||
|
|
|
||
|
|
See Also
|
||
|
|
--------
|
||
|
|
LabelSpreading : Alternate label propagation strategy more robust to noise.
|
||
|
|
|
||
|
|
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
|
||
|
|
|
||
|
|
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(...)
|
||
|
|
"""
|
||
|
|
|
||
|
|
_variant = "propagation"
|
||
|
|
|
||
|
|
_parameter_constraints: dict = {**BaseLabelPropagation._parameter_constraints}
|
||
|
|
_parameter_constraints.pop("alpha")
|
||
|
|
|
||
|
|
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.issparse(affinity_matrix):
|
||
|
|
affinity_matrix.data /= np.diag(np.array(normalizer))
|
||
|
|
else:
|
||
|
|
affinity_matrix /= normalizer[:, np.newaxis]
|
||
|
|
return affinity_matrix
|
||
|
|
|
||
|
|
def fit(self, X, y):
|
||
|
|
"""Fit a semi-supervised label propagation model to X.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
X : {array-like, sparse matrix} of shape (n_samples, n_features)
|
||
|
|
Training data, where `n_samples` is the number of samples
|
||
|
|
and `n_features` is the number of features.
|
||
|
|
|
||
|
|
y : array-like of shape (n_samples,)
|
||
|
|
Target class values with unlabeled points marked as -1.
|
||
|
|
All unlabeled samples will be transductively assigned labels
|
||
|
|
internally, which are stored in `transduction_`.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
self : object
|
||
|
|
Returns the instance itself.
|
||
|
|
"""
|
||
|
|
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 during :term:`fit`.
|
||
|
|
|
||
|
|
n_features_in_ : int
|
||
|
|
Number of features seen during :term:`fit`.
|
||
|
|
|
||
|
|
.. versionadded:: 0.24
|
||
|
|
|
||
|
|
feature_names_in_ : ndarray of shape (`n_features_in_`,)
|
||
|
|
Names of features seen during :term:`fit`. Defined only when `X`
|
||
|
|
has feature names that are all strings.
|
||
|
|
|
||
|
|
.. versionadded:: 1.0
|
||
|
|
|
||
|
|
n_iter_ : int
|
||
|
|
Number of iterations run.
|
||
|
|
|
||
|
|
See Also
|
||
|
|
--------
|
||
|
|
LabelPropagation : Unregularized graph based semi-supervised learning.
|
||
|
|
|
||
|
|
References
|
||
|
|
----------
|
||
|
|
`Dengyong Zhou, Olivier Bousquet, Thomas Navin Lal, Jason Weston,
|
||
|
|
Bernhard Schoelkopf. Learning with local and global consistency (2004)
|
||
|
|
<https://citeseerx.ist.psu.edu/doc_view/pid/d74c37aabf2d5cae663007cbd8718175466aea8c>`_
|
||
|
|
|
||
|
|
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(...)
|
||
|
|
"""
|
||
|
|
|
||
|
|
_variant = "spreading"
|
||
|
|
|
||
|
|
_parameter_constraints: dict = {**BaseLabelPropagation._parameter_constraints}
|
||
|
|
_parameter_constraints["alpha"] = [Interval(Real, 0, 1, closed="neither")]
|
||
|
|
|
||
|
|
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.issparse(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
|