""" 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 # 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, is_regressor from .preprocessing import LabelBinarizer from .metrics.pairwise import euclidean_distances from .utils import check_random_state from .utils.validation import _num_samples from .utils.validation import check_consistent_length from .utils.validation import check_is_fitted 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.""" if is_regressor(estimator): return estimator.predict(X) 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): check_is_fitted(self, 'y_') return np.repeat(self.y_, X.shape[0]) def decision_function(self, X): check_is_fitted(self, 'y_') return np.repeat(self.y_, X.shape[0]) def predict_proba(self, X): check_is_fitted(self, 'y_') 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. Read more in the :ref:`User Guide `. 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 """ # 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 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. """ check_is_fitted(self, 'estimators_') if (hasattr(self.estimators_[0], "decision_function") and is_classifier(self.estimators_[0])): thresh = 0 else: thresh = .5 n_samples = _num_samples(X) if self.label_binarizer_.y_type_ == "multiclass": maxima = np.empty(n_samples, dtype=float) maxima.fill(-np.inf) argmaxima = np.zeros(n_samples, 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: 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_`. """ check_is_fitted(self, 'estimators_') # 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 len(self.estimators_) == 1: # Only one estimator, but we still want to return probabilities # for two classes. Y = np.concatenate(((1 - Y), Y), axis=1) 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] """ check_is_fitted(self, 'estimators_') 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): check_is_fitted(self, 'estimators_') if not hasattr(self.estimators_[0], "coef_"): raise AttributeError( "Base estimator doesn't have a coef_ attribute.") coefs = [e.coef_ for e in self.estimators_] if sp.issparse(coefs[0]): return sp.vstack(coefs) return np.vstack(coefs) @property def intercept_(self): check_is_fitted(self, 'estimators_') 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 OneVsOneClassifier 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 OneVsOneClassifier 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. Read more in the :ref:`User Guide `. 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 : array-like, shape = [n_samples] Multi-class targets. Returns ------- self """ y = np.asarray(y) check_consistent_length(X, y) 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): """Estimate the best class label for each sample in X. This is implemented as ``argmax(decision_function(X), axis=1)`` which will return the label of the class with most votes by estimators predicting the outcome of a decision for each possible class pair. Parameters ---------- X : (sparse) array-like, shape = [n_samples, n_features] Data. Returns ------- y : numpy array of shape [n_samples] Predicted multi-class targets. """ Y = self.decision_function(X) return self.classes_[Y.argmax(axis=1)] def decision_function(self, X): """Decision function for the OneVsOneClassifier. The decision values for the samples are computed by adding the normalized sum of pair-wise classification confidence levels to the votes in order to disambiguate between the decision values when the votes for all the classes are equal leading to a tie. Parameters ---------- X : array-like, shape = [n_samples, n_features] Returns ------- Y : array-like, shape = [n_samples, n_classes] """ check_is_fitted(self, 'estimators_') predictions = np.vstack([est.predict(X) for est in self.estimators_]).T confidences = np.vstack([_predict_binary(est, X) for est in self.estimators_]).T return _ovr_decision_function(predictions, confidences, len(self.classes_)) def _ovr_decision_function(predictions, confidences, n_classes): """Compute a continuous, tie-breaking ovr decision function. It is important to include a continuous value, not only votes, to make computing AUC or calibration meaningful. Parameters ---------- predictions : array-like, shape (n_samples, n_classifiers) Predicted classes for each binary classifier. confidences : array-like, shape (n_samples, n_classifiers) Decision functions or predicted probabilities for positive class for each binary classifier. n_classes : int Number of classes. n_classifiers must be ``n_classes * (n_classes - 1 ) / 2`` """ n_samples = predictions.shape[0] votes = np.zeros((n_samples, n_classes)) sum_of_confidences = np.zeros((n_samples, n_classes)) k = 0 for i in range(n_classes): for j in range(i + 1, n_classes): sum_of_confidences[:, i] -= confidences[:, k] sum_of_confidences[:, j] += confidences[:, k] votes[predictions[:, k] == 0, i] += 1 votes[predictions[:, k] == 1, j] += 1 k += 1 max_confidences = sum_of_confidences.max() min_confidences = sum_of_confidences.min() if max_confidences == min_confidences: return votes # Scale the sum_of_confidences to (-0.5, 0.5) and add it with votes. # The motivation is to use confidence levels as a way to break ties in # the votes without switching any decision made based on a difference # of 1 vote. eps = np.finfo(sum_of_confidences.dtype).eps max_abs_confidence = max(abs(max_confidences), abs(min_confidences)) scale = (0.5 - eps) / max_abs_confidence return votes + sum_of_confidences * scale @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. Read more in the :ref:`User Guide `. 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. """ check_is_fitted(self, 'estimators_') 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]