# 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_X_y, check_is_fitted, check_array
from ..exceptions import ConvergenceWarning


class BaseLabelPropagation(ClassifierMixin, BaseEstimator, metaclass=ABCMeta):
    """Base class for label propagation module.

    Parameters
    ----------
    kernel : {'knn', 'rbf', callable}
        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
        Parameter for rbf kernel

    n_neighbors : integer > 0
        Parameter for knn kernel

    alpha : float
        Clamping factor

    max_iter : integer
        Change maximum number of iterations allowed

    tol : float
        Convergence tolerance: threshold to consider the system at steady
        state

   n_jobs : int or None, optional (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.
    """

    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(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)

        Returns
        -------
        y : array_like, 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)

        Returns
        -------
        probabilities : array, 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 = np.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 {n_samples by n_samples} size matrix will be created from this

        y : array_like, shape = [n_samples]
            n_labeled_samples (unlabeled points are marked as -1)
            All unlabeled samples will be transductively assigned labels

        Returns
        -------
        self : returns an instance of self.
        """
        X, y = check_X_y(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]
        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', callable}
        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
        Parameter for rbf kernel

    n_neighbors : integer > 0
        Parameter for knn kernel

    max_iter : integer
        Change maximum number of iterations allowed

    tol : float
        Convergence tolerance: threshold to consider the system at steady
        state

    n_jobs : int or None, optional (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_ : array, shape = [n_samples, n_features]
        Input array.

    classes_ : array, shape = [n_classes]
        The distinct labels used in classifying instances.

    label_distributions_ : array, shape = [n_samples, n_classes]
        Categorical distribution for each item.

    transduction_ : array, 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'

    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', callable}
        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
      parameter for rbf kernel

    n_neighbors : integer > 0
      parameter for knn kernel

    alpha : float
      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 : integer
      maximum number of iterations allowed

    tol : float
      Convergence tolerance: threshold to consider the system at steady
      state

    n_jobs : int or None, optional (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_ : array, shape = [n_samples, n_features]
        Input array.

    classes_ : array, shape = [n_classes]
        The distinct labels used in classifying instances.

    label_distributions_ : array, shape = [n_samples, n_classes]
        Categorical distribution for each item.

    transduction_ : array, 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'

    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