multiclass.py

"""
Multiclass and multilabel classification strategies
===================================================

This module implements multiclass learning algorithms:
    - one-vs-the-rest / one-vs-all
    - one-vs-one
    - error correcting output codes

The estimators provided in this module are meta-estimators: they require a base
estimator to be provided in their constructor. For example, it is possible to
use these estimators to turn a binary classifier or a regressor into a
multiclass classifier. It is also possible to use these estimators with
multiclass estimators in the hope that their accuracy or runtime performance
improves.

All classifiers in scikit-learn implement multiclass classification; you
only need to use this module if you want to experiment with custom multiclass
strategies.

The one-vs-the-rest meta-classifier also implements a `predict_proba` method,
so long as such a method is implemented by the base classifier. This method
returns probabilities of class membership in both the single label and
multilabel case.  Note that in the multilabel case, probabilities are the
marginal probability that a given sample falls in the given class. As such, in
the multilabel case the sum of these probabilities over all possible labels
for a given sample *will not* sum to unity, as they do in the single label
case.
"""

# Author: Mathieu Blondel <mathieu@mblondel.org>
# Author: Hamzeh Alsalhi <93hamsal@gmail.com>
#
# License: BSD 3 clause

import array
import numpy as np
import warnings
import scipy.sparse as sp

from .base import BaseEstimator, ClassifierMixin, clone, is_classifier
from .base import MetaEstimatorMixin
from .preprocessing import LabelBinarizer
from .metrics.pairwise import euclidean_distances
from .utils import check_random_state
from .utils.validation import _num_samples
from .utils import deprecated
from .externals.joblib import Parallel
from .externals.joblib import delayed

__all__ = [
    "OneVsRestClassifier",
    "OneVsOneClassifier",
    "OutputCodeClassifier",
]

def _fit_binary(estimator, X, y, classes=None):
    """Fit a single binary estimator."""
    unique_y = np.unique(y)
    if len(unique_y) == 1:
        if classes is not None:
            if y[0] == -1:
                c = 0
            else:
                c = y[0]
            warnings.warn("Label %s is present in all training examples." %
                          str(classes[c]))
        estimator = _ConstantPredictor().fit(X, unique_y)
    else:
        estimator = clone(estimator)
        estimator.fit(X, y)
    return estimator


def _predict_binary(estimator, X):
    """Make predictions using a single binary estimator."""
    try:
        score = np.ravel(estimator.decision_function(X))
    except (AttributeError, NotImplementedError):
        # probabilities of the positive class
        score = estimator.predict_proba(X)[:, 1]
    return score


def _check_estimator(estimator):
    """Make sure that an estimator implements the necessary methods."""
    if (not hasattr(estimator, "decision_function") and
            not hasattr(estimator, "predict_proba")):
        raise ValueError("The base estimator should implement "
                         "decision_function or predict_proba!")


@deprecated("fit_ovr is deprecated and will be removed in 0.18."
            "Use the OneVsRestClassifier instead.")
def fit_ovr(estimator, X, y, n_jobs=1):
    """Fit a one-vs-the-rest strategy.

    Parameters
    ----------
    estimator : estimator object
        An estimator object implementing `fit` and one of `decision_function`
        or `predict_proba`.

    X : (sparse) array-like, shape = [n_samples, n_features]
        Data.

    y : (sparse) array-like, shape = [n_samples] or [n_samples, n_classes]
        Multi-class targets. An indicator matrix turns on multilabel
        classification.

    Returns
    -------
    estimators : list of estimators object
        The list of fitted estimator.

    lb : fitted LabelBinarizer

    """
    ovr =  OneVsRestClassifier(estimator, n_jobs=n_jobs).fit(X, y)
    return ovr.estimators_, ovr.label_binarizer_


@deprecated("predict_ovr is deprecated and will be removed in 0.18."
            "Use the OneVsRestClassifier instead.")
def predict_ovr(estimators, label_binarizer, X):
    """Predict multi-class targets using the one vs rest strategy.

    Parameters
    ----------
    estimators : list of `n_classes` estimators, Estimators used for
        predictions. The list must be homogeneous with respect to the type of
        estimators. fit_ovr supplies this list as part of its output.

    label_binarizer : LabelBinarizer object, Object used to transform
        multiclass labels to binary labels and vice-versa. fit_ovr supplies
        this object as part of its output.

    X : (sparse) array-like, shape = [n_samples, n_features]
        Data.

    Returns
    -------
    y : (sparse) array-like, shape = [n_samples] or [n_samples, n_classes].
        Predicted multi-class targets.
    """
    e_types = set([type(e) for e in estimators if not
                   isinstance(e, _ConstantPredictor)])
    if len(e_types) > 1:
        raise ValueError("List of estimators must contain estimators of the"
                         " same type but contains types {0}".format(e_types))

    ovr = OneVsRestClassifier(clone(estimators[0]))
    ovr.estimators_ = estimators
    ovr.label_binarizer_ = label_binarizer

    return ovr.predict(X)


@deprecated("predict_proba_ovr is deprecated and will be removed in 0.18."
            "Use the OneVsRestClassifier instead.")
def predict_proba_ovr(estimators, X, is_multilabel):
    e_types = set([type(e) for e in estimators if not
                   isinstance(e, _ConstantPredictor)])
    if len(e_types) > 1:
        raise ValueError("List of estimators must contain estimators of the"
                         " same type but contains types {0}".format(e_types))

    Y = np.array([e.predict_proba(X)[:, 1] for e in estimators]).T

    if not is_multilabel:
        # Then, probabilities should be normalized to 1.
        Y /= np.sum(Y, axis=1)[:, np.newaxis]

    return Y


class _ConstantPredictor(BaseEstimator):
    def fit(self, X, y):
        self.y_ = y
        return self

    def predict(self, X):
        return np.repeat(self.y_, X.shape[0])

    def decision_function(self, X):
        return np.repeat(self.y_, X.shape[0])

    def predict_proba(self, X):
        return np.repeat([np.hstack([1 - self.y_, self.y_])],
                         X.shape[0], axis=0)


class OneVsRestClassifier(BaseEstimator, ClassifierMixin, MetaEstimatorMixin):
    """One-vs-the-rest (OvR) multiclass/multilabel strategy

    Also known as one-vs-all, this strategy consists in fitting one classifier
    per class. For each classifier, the class is fitted against all the other
    classes. In addition to its computational efficiency (only `n_classes`
    classifiers are needed), one advantage of this approach is its
    interpretability. Since each class is represented by one and one classifier
    only, it is possible to gain knowledge about the class by inspecting its
    corresponding classifier. This is the most commonly used strategy for
    multiclass classification and is a fair default choice.

    This strategy can also be used for multilabel learning, where a classifier
    is used to predict multiple labels for instance, by fitting on a 2-d matrix
    in which cell [i, j] is 1 if sample i has label j and 0 otherwise.

    In the multilabel learning literature, OvR is also known as the binary
    relevance method.

    Parameters
    ----------
    estimator : estimator object
        An estimator object implementing `fit` and one of `decision_function`
        or `predict_proba`.

    n_jobs : int, optional, default: 1
        The number of jobs to use for the computation. If -1 all CPUs are used.
        If 1 is given, no parallel computing code is used at all, which is
        useful for debugging. For n_jobs below -1, (n_cpus + 1 + n_jobs) are
        used. Thus for n_jobs = -2, all CPUs but one are used.

    Attributes
    ----------
    estimators_ : list of `n_classes` estimators
        Estimators used for predictions.

    classes_ : array, shape = [`n_classes`]
        Class labels.
    label_binarizer_ : LabelBinarizer object
        Object used to transform multiclass labels to binary labels and
        vice-versa.
    multilabel_ : boolean
        Whether a OneVsRestClassifier is a multilabel classifier.
    """

    def __init__(self, estimator, n_jobs=1):
        self.estimator = estimator
        self.n_jobs = n_jobs

    def fit(self, X, y):
        """Fit underlying estimators.

        Parameters
        ----------
        X : (sparse) array-like, shape = [n_samples, n_features]
            Data.

        y : (sparse) array-like, shape = [n_samples] or [n_samples, n_classes]
            Multi-class targets. An indicator matrix turns on multilabel
            classification.

        Returns
        -------
        self
        """
        _check_estimator(self.estimator)
        # A sparse LabelBinarizer, with sparse_output=True, has been shown to
        # outpreform or match a dense label binarizer in all cases and has also
        # resulted in less or equal memory consumption in the fit_ovr function
        # overall.
        self.label_binarizer_ = LabelBinarizer(sparse_output=True)
        Y = self.label_binarizer_.fit_transform(y)
        Y = Y.tocsc()
        columns = (col.toarray().ravel() for col in Y.T)
        # In cases where individual estimators are very fast to train setting
        # n_jobs > 1 in can results in slower performance due to the overhead
        # of spawning threads.  See joblib issue #112.
        self.estimators_ = Parallel(n_jobs=self.n_jobs)(delayed(_fit_binary)
             (self.estimator, X, column,
              classes=["not %s" % self.label_binarizer_.classes_[i],
                       self.label_binarizer_.classes_[i]])
              for i, column in enumerate(columns))

        return self

    def _check_is_fitted(self):
        if not hasattr(self, "estimators_"):
            raise ValueError("The object hasn't been fitted yet!")

    def predict(self, X):
        """Predict multi-class targets using underlying estimators.

        Parameters
        ----------
        X : (sparse) array-like, shape = [n_samples, n_features]
            Data.

        Returns
        -------
        y : (sparse) array-like, shape = [n_samples] or [n_samples, n_classes].
            Predicted multi-class targets.
        """
        self._check_is_fitted()
        if (hasattr(self.estimators_[0], "decision_function") and
                is_classifier(self.estimators_[0])):
            thresh = 0
        else:
            thresh = .5

        if self.label_binarizer_.y_type_ == "multiclass":
            maxima = np.empty(X.shape[0], dtype=float)
            maxima.fill(-np.inf)
            argmaxima = np.zeros(X.shape[0], dtype=int)
            for i, e in enumerate(self.estimators_):
                pred = _predict_binary(e, X)
                np.maximum(maxima, pred, out=maxima)
                argmaxima[maxima == pred] = i
            return self.label_binarizer_.classes_[np.array(argmaxima.T)]
        else:
            n_samples = _num_samples(X)
            indices = array.array('i')
            indptr = array.array('i', [0])
            for e in self.estimators_:
                indices.extend(np.where(_predict_binary(e, X) > thresh)[0])
                indptr.append(len(indices))
            data = np.ones(len(indices), dtype=int)
            indicator = sp.csc_matrix((data, indices, indptr),
                                      shape=(n_samples, len(self.estimators_)))
            return self.label_binarizer_.inverse_transform(indicator)

    def predict_proba(self, X):
        """Probability estimates.

        The returned estimates for all classes are ordered by label of classes.

        Note that in the multilabel case, each sample can have any number of
        labels. This returns the marginal probability that the given sample has
        the label in question. For example, it is entirely consistent that two
        labels both have a 90% probability of applying to a given sample.

        In the single label multiclass case, the rows of the returned matrix
        sum to 1.

        Parameters
        ----------
        X : array-like, shape = [n_samples, n_features]

        Returns
        -------
        T : (sparse) array-like, shape = [n_samples, n_classes]
            Returns the probability of the sample for each class in the model,
            where classes are ordered as they are in `self.classes_`.
        """
        # Y[i,j] gives the probability that sample i has the label j.
        # In the multi-label case, these are not disjoint.
        Y = np.array([e.predict_proba(X)[:, 1] for e in self.estimators_]).T

        if not self.multilabel_:
            # Then, probabilities should be normalized to 1.
            Y /= np.sum(Y, axis=1)[:, np.newaxis]
        return Y


    def decision_function(self, X):
        """Returns the distance of each sample from the decision boundary for
        each class. This can only be used with estimators which implement the
        decision_function method.

        Parameters
        ----------
        X : array-like, shape = [n_samples, n_features]

        Returns
        -------
        T : array-like, shape = [n_samples, n_classes]
        """
        if not hasattr(self.estimators_[0], "decision_function"):
            raise AttributeError(
                "Base estimator doesn't have a decision_function attribute.")
        return np.array([est.decision_function(X).ravel()
                         for est in self.estimators_]).T

    @property
    def multilabel_(self):
        """Whether this is a multilabel classifier"""
        return self.label_binarizer_.y_type_.startswith('multilabel')

    @property
    def classes_(self):
        return self.label_binarizer_.classes_

    @property
    def coef_(self):
        self._check_is_fitted()
        if not hasattr(self.estimators_[0], "coef_"):
            raise AttributeError(
                "Base estimator doesn't have a coef_ attribute.")
        return np.array([e.coef_.ravel() for e in self.estimators_])

    @property
    def intercept_(self):
        self._check_is_fitted()
        if not hasattr(self.estimators_[0], "intercept_"):
            raise AttributeError(
                "Base estimator doesn't have an intercept_ attribute.")
        return np.array([e.intercept_.ravel() for e in self.estimators_])


def _fit_ovo_binary(estimator, X, y, i, j):
    """Fit a single binary estimator (one-vs-one)."""
    cond = np.logical_or(y == i, y == j)
    y = y[cond]
    y_binary = np.empty(y.shape, np.int)
    y_binary[y == i] = 0
    y_binary[y == j] = 1
    ind = np.arange(X.shape[0])
    return _fit_binary(estimator, X[ind[cond]], y_binary, classes=[i, j])


@deprecated("fit_ovo is deprecated and will be removed in 0.18."
            "Use the OneVsRestClassifier instead.")
def fit_ovo(estimator, X, y, n_jobs=1):
    ovo =  OneVsOneClassifier(estimator, n_jobs=n_jobs).fit(X, y)
    return ovo.estimators_, ovo.classes_


@deprecated("predict_ovo is deprecated and will be removed in 0.18."
            "Use the OneVsRestClassifier instead.")
def predict_ovo(estimators, classes, X):
    """Make predictions using the one-vs-one strategy."""

    e_types = set([type(e) for e in estimators if not
                   isinstance(e, _ConstantPredictor)])
    if len(e_types) > 1:
        raise ValueError("List of estimators must contain estimators of the"
                         " same type but contains types {0}".format(e_types))

    ovo = OneVsOneClassifier(clone(estimators[0]))
    ovo.estimators_ = estimators
    ovo.classes_ = classes
    return ovo.predict(X)


class OneVsOneClassifier(BaseEstimator, ClassifierMixin, MetaEstimatorMixin):
    """One-vs-one multiclass strategy

    This strategy consists in fitting one classifier per class pair.
    At prediction time, the class which received the most votes is selected.
    Since it requires to fit `n_classes * (n_classes - 1) / 2` classifiers,
    this method is usually slower than one-vs-the-rest, due to its
    O(n_classes^2) complexity. However, this method may be advantageous for
    algorithms such as kernel algorithms which don't scale well with
    `n_samples`. This is because each individual learning problem only involves
    a small subset of the data whereas, with one-vs-the-rest, the complete
    dataset is used `n_classes` times.

    Parameters
    ----------
    estimator : estimator object
        An estimator object implementing `fit` and one of `decision_function`
        or `predict_proba`.

    n_jobs : int, optional, default: 1
        The number of jobs to use for the computation. If -1 all CPUs are used.
        If 1 is given, no parallel computing code is used at all, which is
        useful for debugging. For n_jobs below -1, (n_cpus + 1 + n_jobs) are
        used. Thus for n_jobs = -2, all CPUs but one are used.

    Attributes
    ----------
    estimators_ : list of `n_classes * (n_classes - 1) / 2` estimators
        Estimators used for predictions.

    classes_ : numpy array of shape [n_classes]
        Array containing labels.
    """

    def __init__(self, estimator, n_jobs=1):
        self.estimator = estimator
        self.n_jobs = n_jobs

    def fit(self, X, y):
        """Fit underlying estimators.

        Parameters
        ----------
        X : (sparse) array-like, shape = [n_samples, n_features]
            Data.

        y : numpy array of shape [n_samples]
            Multi-class targets.

        Returns
        -------
        self
        """
        self.classes_ = np.unique(y)
        n_classes = self.classes_.shape[0]
        self.estimators_ = Parallel(n_jobs=self.n_jobs)(
            delayed(_fit_ovo_binary)(
                self.estimator, X, y, self.classes_[i], self.classes_[j])
            for i in range(n_classes) for j in range(i + 1, n_classes))

        return self

    def predict(self, X):
        """Predict multi-class targets using underlying estimators.

        Parameters
        ----------
        X : (sparse) array-like, shape = [n_samples, n_features]
            Data.

        Returns
        -------
        y : numpy array of shape [n_samples]
            Predicted multi-class targets.
        """
        if not hasattr(self, "estimators_"):
            raise ValueError("The object hasn't been fitted yet!")

        n_samples = X.shape[0]
        n_classes = self.classes_.shape[0]
        votes = np.zeros((n_samples, n_classes))
        scores = np.zeros((n_samples, n_classes))

        k = 0
        for i in range(n_classes):
            for j in range(i + 1, n_classes):
                pred = self.estimators_[k].predict(X)
                score = _predict_binary(self.estimators_[k], X)
                scores[:, i] -= score
                scores[:, j] += score
                votes[pred == 0, i] += 1
                votes[pred == 1, j] += 1
                k += 1

        # find all places with maximum votes per sample
        maxima = votes == np.max(votes, axis=1)[:, np.newaxis]

        # if there are ties, use scores to break them
        if np.any(maxima.sum(axis=1) > 1):
            scores[~maxima] = -np.inf
            prediction = scores.argmax(axis=1)
        else:
            prediction = votes.argmax(axis=1)
        return self.classes_[prediction]


@deprecated("fit_ecoc is deprecated and will be removed in 0.18."
            "Use the OutputCodeClassifier instead.")
def fit_ecoc(estimator, X, y, code_size=1.5, random_state=None, n_jobs=1):
    """Fit an error-correcting output-code strategy.

    Parameters
    ----------
    estimator : estimator object
        An estimator object implementing `fit` and one of `decision_function`
        or `predict_proba`.

    code_size : float, optional
        Percentage of the number of classes to be used to create the code book.

    random_state : numpy.RandomState, optional
        The generator used to initialize the codebook. Defaults to
        numpy.random.


    Returns
    --------
    estimators : list of `int(n_classes * code_size)` estimators
        Estimators used for predictions.

    classes : numpy array of shape [n_classes]
        Array containing labels.

    code_book_ : numpy array of shape [n_classes, code_size]
        Binary array containing the code of each class.
    """
    ecoc =  OutputCodeClassifier(estimator, random_state=random_state,
                                 n_jobs=n_jobs).fit(X, y)
    return ecoc.estimators_, ecoc.classes_, ecoc.code_book_


@deprecated("predict_ecoc is deprecated and will be removed in 0.18."
            "Use the OutputCodeClassifier instead.")
def predict_ecoc(estimators, classes, code_book, X):
    """Make predictions using the error-correcting output-code strategy."""
    ecoc =  OutputCodeClassifier(clone(estimators[0]))
    ecoc.classes_ = classes
    ecoc.estimators_ = estimators
    ecoc.code_book_ = code_book

    return ecoc.predict(X)


class OutputCodeClassifier(BaseEstimator, ClassifierMixin, MetaEstimatorMixin):
    """(Error-Correcting) Output-Code multiclass strategy

    Output-code based strategies consist in representing each class with a
    binary code (an array of 0s and 1s). At fitting time, one binary
    classifier per bit in the code book is fitted.  At prediction time, the
    classifiers are used to project new points in the class space and the class
    closest to the points is chosen. The main advantage of these strategies is
    that the number of classifiers used can be controlled by the user, either
    for compressing the model (0 < code_size < 1) or for making the model more
    robust to errors (code_size > 1). See the documentation for more details.

    Parameters
    ----------
    estimator : estimator object
        An estimator object implementing `fit` and one of `decision_function`
        or `predict_proba`.

    code_size : float
        Percentage of the number of classes to be used to create the code book.
        A number between 0 and 1 will require fewer classifiers than
        one-vs-the-rest. A number greater than 1 will require more classifiers
        than one-vs-the-rest.

    random_state : numpy.RandomState, optional
        The generator used to initialize the codebook. Defaults to
        numpy.random.

    n_jobs : int, optional, default: 1
        The number of jobs to use for the computation. If -1 all CPUs are used.
        If 1 is given, no parallel computing code is used at all, which is
        useful for debugging. For n_jobs below -1, (n_cpus + 1 + n_jobs) are
        used. Thus for n_jobs = -2, all CPUs but one are used.

    Attributes
    ----------
    estimators_ : list of `int(n_classes * code_size)` estimators
        Estimators used for predictions.

    classes_ : numpy array of shape [n_classes]
        Array containing labels.

    code_book_ : numpy array of shape [n_classes, code_size]
        Binary array containing the code of each class.

    References
    ----------

    .. [1] "Solving multiclass learning problems via error-correcting output
       codes",
       Dietterich T., Bakiri G.,
       Journal of Artificial Intelligence Research 2,
       1995.

    .. [2] "The error coding method and PICTs",
       James G., Hastie T.,
       Journal of Computational and Graphical statistics 7,
       1998.

    .. [3] "The Elements of Statistical Learning",
       Hastie T., Tibshirani R., Friedman J., page 606 (second-edition)
       2008.
    """

    def __init__(self, estimator, code_size=1.5, random_state=None, n_jobs=1):
        self.estimator = estimator
        self.code_size = code_size
        self.random_state = random_state
        self.n_jobs = n_jobs

    def fit(self, X, y):
        """Fit underlying estimators.

        Parameters
        ----------
        X : (sparse) array-like, shape = [n_samples, n_features]
            Data.

        y : numpy array of shape [n_samples]
            Multi-class targets.

        Returns
        -------
        self
        """
        if self.code_size <= 0:
            raise ValueError("code_size should be greater than 0, got {1}"
                             "".format(self.code_size))

        _check_estimator(self.estimator)
        random_state = check_random_state(self.random_state)

        self.classes_ = np.unique(y)
        n_classes = self.classes_.shape[0]
        code_size_ = int(n_classes * self.code_size)

        # FIXME: there are more elaborate methods than generating the codebook
        # randomly.
        self.code_book_ = random_state.random_sample((n_classes, code_size_))
        self.code_book_[self.code_book_ > 0.5] = 1

        if hasattr(self.estimator, "decision_function"):
            self.code_book_[self.code_book_ != 1] = -1
        else:
            self.code_book_[self.code_book_ != 1] = 0

        classes_index = dict((c, i) for i, c in enumerate(self.classes_))

        Y = np.array([self.code_book_[classes_index[y[i]]]
                      for i in range(X.shape[0])], dtype=np.int)

        self.estimators_ = Parallel(n_jobs=self.n_jobs)(
            delayed(_fit_binary)(self.estimator, X, Y[:, i])
            for i in range(Y.shape[1]))

        return self

    def predict(self, X):
        """Predict multi-class targets using underlying estimators.

        Parameters
        ----------
        X : (sparse) array-like, shape = [n_samples, n_features]
            Data.

        Returns
        -------
        y : numpy array of shape [n_samples]
            Predicted multi-class targets.
        """
        if not hasattr(self, "estimators_"):
            raise ValueError("The object hasn't been fitted yet!")

        Y = np.array([_predict_binary(e, X) for e in self.estimators_]).T
        pred = euclidean_distances(Y, self.code_book_).argmin(axis=1)
        return self.classes_[pred]