text: # 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
  