1.12. Multiclass and multioutput algorithms¶
This section of the user guide covers functionality related to multilearning problems, including multiclass, multilabel, and multioutput classification and regression.
The modules in this section implement metaestimators, which require a base estimator to be provided in their constructor. Metaestimators extend the functionality of the base estimator to support multilearning problems, which is accomplished by transforming the multilearning problem into a set of simpler problems, then fitting one estimator per problem.
This section covers two modules: sklearn.multiclass
and
sklearn.multioutput
. The chart below demonstrates the problem types
that each module is responsible for, and the corresponding metaestimators
that each module provides.
The table below provides a quick reference on the differences between problem types. More detailed explanations can be found in subsequent sections of this guide.
Number of targets 
Target cardinality 
Valid



Multiclass classification 
1 
>2 
‘multiclass’ 
Multilabel classification 
>1 
2 (0 or 1) 
‘multilabelindicator’ 
Multiclassmultioutput classification 
>1 
>2 
‘multiclassmultioutput’ 
Multioutput regression 
>1 
Continuous 
‘continuousmultioutput’ 
Below is a summary of scikitlearn estimators that have multilearning support builtin, grouped by strategy. You don’t need the metaestimators provided by this section if you’re using one of these estimators. However, metaestimators can provide additional strategies beyond what is builtin:
Inherently multiclass:
svm.LinearSVC
(setting multi_class=”crammer_singer”)linear_model.LogisticRegression
(setting multi_class=”multinomial”)linear_model.LogisticRegressionCV
(setting multi_class=”multinomial”)
Multiclass as OneVsOne:
gaussian_process.GaussianProcessClassifier
(setting multi_class = “one_vs_one”)
Multiclass as OneVsTheRest:
gaussian_process.GaussianProcessClassifier
(setting multi_class = “one_vs_rest”)svm.LinearSVC
(setting multi_class=”ovr”)linear_model.LogisticRegression
(setting multi_class=”ovr”)linear_model.LogisticRegressionCV
(setting multi_class=”ovr”)
Support multilabel:
Support multiclassmultioutput:
1.12.1. Multiclass classification¶
Warning
All classifiers in scikitlearn do multiclass classification
outofthebox. You don’t need to use the sklearn.multiclass
module
unless you want to experiment with different multiclass strategies.
Multiclass classification is a classification task with more than two classes. Each sample can only be labeled as one class.
For example, classification using features extracted from a set of images of fruit, where each image may either be of an orange, an apple, or a pear. Each image is one sample and is labeled as one of the 3 possible classes. Multiclass classification makes the assumption that each sample is assigned to one and only one label  one sample cannot, for example, be both a pear and an apple.
While all scikitlearn classifiers are capable of multiclass classification,
the metaestimators offered by sklearn.multiclass
permit changing the way they handle more than two classes
because this may have an effect on classifier performance
(either in terms of generalization error or required computational resources).
1.12.1.1. Target format¶
Valid multiclass representations for
type_of_target
(y
) are:
1d or column vector containing more than two discrete values. An example of a vector
y
for 4 samples:>>> import numpy as np >>> y = np.array(['apple', 'pear', 'apple', 'orange']) >>> print(y) ['apple' 'pear' 'apple' 'orange']Dense or sparse binary matrix of shape
(n_samples, n_classes)
with a single sample per row, where each column represents one class. An example of both a dense and sparse binary matrixy
for 4 samples, where the columns, in order, are apple, orange, and pear:>>> import numpy as np >>> from sklearn.preprocessing import LabelBinarizer >>> y = np.array(['apple', 'pear', 'apple', 'orange']) >>> y_dense = LabelBinarizer().fit_transform(y) >>> print(y_dense) [[1 0 0] [0 0 1] [1 0 0] [0 1 0]] >>> from scipy import sparse >>> y_sparse = sparse.csr_matrix(y_dense) >>> print(y_sparse) (0, 0) 1 (1, 2) 1 (2, 0) 1 (3, 1) 1
For more information about LabelBinarizer
,
refer to Transforming the prediction target (y).
1.12.1.2. OneVsRestClassifier¶
The onevsrest strategy, also known as onevsall, is implemented in
OneVsRestClassifier
. The 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 only one
classifier, it is possible to gain knowledge about the class by inspecting its
corresponding classifier. This is the most commonly used strategy and is a fair
default choice.
Below is an example of multiclass learning using OvR:
>>> from sklearn import datasets
>>> from sklearn.multiclass import OneVsRestClassifier
>>> from sklearn.svm import LinearSVC
>>> X, y = datasets.load_iris(return_X_y=True)
>>> OneVsRestClassifier(LinearSVC(random_state=0)).fit(X, y).predict(X)
array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])
OneVsRestClassifier
also supports multilabel
classification. To use this feature, feed the classifier an indicator matrix,
in which cell [i, j] indicates the presence of label j in sample i.
Examples:
1.12.1.3. OneVsOneClassifier¶
OneVsOneClassifier
constructs one classifier per
pair of classes. At prediction time, the class which received the most votes
is selected. In the event of a tie (among two classes with an equal number of
votes), it selects the class with the highest aggregate classification
confidence by summing over the pairwise classification confidence levels
computed by the underlying binary classifiers.
Since it requires to fit n_classes * (n_classes  1) / 2
classifiers,
this method is usually slower than onevstherest, 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 onevstherest, the complete
dataset is used n_classes
times. The decision function is the result
of a monotonic transformation of the oneversusone classification.
Below is an example of multiclass learning using OvO:
>>> from sklearn import datasets
>>> from sklearn.multiclass import OneVsOneClassifier
>>> from sklearn.svm import LinearSVC
>>> X, y = datasets.load_iris(return_X_y=True)
>>> OneVsOneClassifier(LinearSVC(random_state=0)).fit(X, y).predict(X)
array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])
References:
“Pattern Recognition and Machine Learning. Springer”, Christopher M. Bishop, page 183, (First Edition)
1.12.1.4. OutputCodeClassifier¶
ErrorCorrecting Output Codebased strategies are fairly different from onevstherest and onevsone. With these strategies, each class is represented in a Euclidean space, where each dimension can only be 0 or 1. Another way to put it is that each class is represented by a binary code (an array of 0 and 1). The matrix which keeps track of the location/code of each class is called the code book. The code size is the dimensionality of the aforementioned space. Intuitively, each class should be represented by a code as unique as possible and a good code book should be designed to optimize classification accuracy. In this implementation, we simply use a randomlygenerated code book as advocated in 3 although more elaborate methods may be added in the future.
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.
In OutputCodeClassifier
, the code_size
attribute allows the user to control the number of classifiers which will be
used. It is a percentage of the total number of classes.
A number between 0 and 1 will require fewer classifiers than
onevstherest. In theory, log2(n_classes) / n_classes
is sufficient to
represent each class unambiguously. However, in practice, it may not lead to
good accuracy since log2(n_classes)
is much smaller than n_classes
.
A number greater than 1 will require more classifiers than onevstherest. In this case, some classifiers will in theory correct for the mistakes made by other classifiers, hence the name “errorcorrecting”. In practice, however, this may not happen as classifier mistakes will typically be correlated. The errorcorrecting output codes have a similar effect to bagging.
Below is an example of multiclass learning using OutputCodes:
>>> from sklearn import datasets
>>> from sklearn.multiclass import OutputCodeClassifier
>>> from sklearn.svm import LinearSVC
>>> X, y = datasets.load_iris(return_X_y=True)
>>> clf = OutputCodeClassifier(LinearSVC(random_state=0),
... code_size=2, random_state=0)
>>> clf.fit(X, y).predict(X)
array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1,
1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])
References:
“Solving multiclass learning problems via errorcorrecting output codes”, Dietterich T., Bakiri G., Journal of Artificial Intelligence Research 2, 1995.
 3
“The error coding method and PICTs”, James G., Hastie T., Journal of Computational and Graphical statistics 7, 1998.
“The Elements of Statistical Learning”, Hastie T., Tibshirani R., Friedman J., page 606 (secondedition) 2008.
1.12.2. Multilabel classification¶
Multilabel classification (closely related to multioutput
classification) is a classification task labeling each sample with m
labels from n_classes
possible classes, where m
can be 0 to
n_classes
inclusive. This can be thought of as predicting properties of a
sample that are not mutually exclusive. Formally, a binary output is assigned
to each class, for every sample. Positive classes are indicated with 1 and
negative classes with 0 or 1. It is thus comparable to running n_classes
binary classification tasks, for example with
MultiOutputClassifier
. This approach treats
each label independently whereas multilabel classifiers may treat the
multiple classes simultaneously, accounting for correlated behavior among
them.
For example, prediction of the topics relevant to a text document or video. The document or video may be about one of ‘religion’, ‘politics’, ‘finance’ or ‘education’, several of the topic classes or all of the topic classes.
1.12.2.1. Target format¶
A valid representation of multilabel y
is an either dense or sparse
binary matrix of shape (n_samples, n_classes)
. Each column
represents a class. The 1
’s in each row denote the positive classes a
sample has been labeled with. An example of a dense matrix y
for 3
samples:
>>> y = np.array([[1, 0, 0, 1], [0, 0, 1, 1], [0, 0, 0, 0]])
>>> print(y)
[[1 0 0 1]
[0 0 1 1]
[0 0 0 0]]
Dense binary matrices can also be created using
MultiLabelBinarizer
. For more information,
refer to Transforming the prediction target (y).
An example of the same y
in sparse matrix form:
>>> y_sparse = sparse.csr_matrix(y)
>>> print(y_sparse)
(0, 0) 1
(0, 3) 1
(1, 2) 1
(1, 3) 1
1.12.2.2. MultiOutputClassifier¶
Multilabel classification support can be added to any classifier with
MultiOutputClassifier
. This strategy consists of
fitting one classifier per target. This allows multiple target variable
classifications. The purpose of this class is to extend estimators
to be able to estimate a series of target functions (f1,f2,f3…,fn)
that are trained on a single X predictor matrix to predict a series
of responses (y1,y2,y3…,yn).
You can find a usage example for
MultiOutputClassifier
as part of the section on Multiclassmultioutput classification
since it is a generalization of multilabel classification to
multiclass outputs instead of binary outputs.
1.12.2.3. ClassifierChain¶
Classifier chains (see ClassifierChain
) are a way
of combining a number of binary classifiers into a single multilabel model
that is capable of exploiting correlations among targets.
For a multilabel classification problem with N classes, N binary classifiers are assigned an integer between 0 and N1. These integers define the order of models in the chain. Each classifier is then fit on the available training data plus the true labels of the classes whose models were assigned a lower number.
When predicting, the true labels will not be available. Instead the predictions of each model are passed on to the subsequent models in the chain to be used as features.
Clearly the order of the chain is important. The first model in the chain has no information about the other labels while the last model in the chain has features indicating the presence of all of the other labels. In general one does not know the optimal ordering of the models in the chain so typically many randomly ordered chains are fit and their predictions are averaged together.
References:
 Jesse Read, Bernhard Pfahringer, Geoff Holmes, Eibe Frank,
“Classifier Chains for Multilabel Classification”, 2009.
1.12.3. Multiclassmultioutput classification¶
Multiclassmultioutput classification (also known as multitask classification) is a classification task which labels each sample with a set of nonbinary properties. Both the number of properties and the number of classes per property is greater than 2. A single estimator thus handles several joint classification tasks. This is both a generalization of the multilabel classification task, which only considers binary attributes, as well as a generalization of the multiclass classification task, where only one property is considered.
For example, classification of the properties “type of fruit” and “colour” for a set of images of fruit. The property “type of fruit” has the possible classes: “apple”, “pear” and “orange”. The property “colour” has the possible classes: “green”, “red”, “yellow” and “orange”. Each sample is an image of a fruit, a label is output for both properties and each label is one of the possible classes of the corresponding property.
Note that all classifiers handling multiclassmultioutput (also known as multitask classification) tasks, support the multilabel classification task as a special case. Multitask classification is similar to the multioutput classification task with different model formulations. For more information, see the relevant estimator documentat
Below is an example of multiclassmultioutput classification:
>>> from sklearn.datasets import make_classification
>>> from sklearn.multioutput import MultiOutputClassifier
>>> from sklearn.ensemble import RandomForestClassifier
>>> from sklearn.utils import shuffle
>>> import numpy as np
>>> X, y1 = make_classification(n_samples=10, n_features=100,
... n_informative=30, n_classes=3,
... random_state=1)
>>> y2 = shuffle(y1, random_state=1)
>>> y3 = shuffle(y1, random_state=2)
>>> Y = np.vstack((y1, y2, y3)).T
>>> n_samples, n_features = X.shape # 10,100
>>> n_outputs = Y.shape[1] # 3
>>> n_classes = 3
>>> forest = RandomForestClassifier(random_state=1)
>>> multi_target_forest = MultiOutputClassifier(forest, n_jobs=2)
>>> multi_target_forest.fit(X, Y).predict(X)
array([[2, 2, 0],
[1, 2, 1],
[2, 1, 0],
[0, 0, 2],
[0, 2, 1],
[0, 0, 2],
[1, 1, 0],
[1, 1, 1],
[0, 0, 2],
[2, 0, 0]])
Warning
At present, no metric in sklearn.metrics
supports the multiclassmultioutput classification task.
1.12.3.1. Target format¶
A valid representation of multioutput y
is a dense matrix of shape
(n_samples, n_classes)
of class labels. A column wise concatenation of 1d
multiclass variables. An example of y
for 3 samples:
>>> y = np.array([['apple', 'green'], ['orange', 'orange'], ['pear', 'green']])
>>> print(y)
[['apple' 'green']
['orange' 'orange']
['pear' 'green']]
1.12.4. Multioutput regression¶
Multioutput regression predicts multiple numerical properties for each
sample. Each property is a numerical variable and the number of properties
to be predicted for each sample is greater than or equal to 2. Some estimators
that support multioutput regression are faster than just running n_output
estimators.
For example, prediction of both wind speed and wind direction, in degrees, using data obtained at a certain location. Each sample would be data obtained at one location and both wind speed and direction would be output for each sample.
1.12.4.1. Target format¶
A valid representation of multioutput y
is a dense matrix of shape
(n_samples, n_output)
of floats. A column wise concatenation of
continuous variables. An example of y
for 3 samples:
>>> y = np.array([[31.4, 94], [40.5, 109], [25.0, 30]])
>>> print(y)
[[ 31.4 94. ]
[ 40.5 109. ]
[ 25. 30. ]]
1.12.4.2. MultiOutputRegressor¶
Multioutput regression support can be added to any regressor with
MultiOutputRegressor
. This strategy consists of
fitting one regressor per target. Since each target is represented by exactly
one regressor it is possible to gain knowledge about the target by
inspecting its corresponding regressor. As
MultiOutputRegressor
fits one regressor per
target it can not take advantage of correlations between targets.
Below is an example of multioutput regression:
>>> from sklearn.datasets import make_regression
>>> from sklearn.multioutput import MultiOutputRegressor
>>> from sklearn.ensemble import GradientBoostingRegressor
>>> X, y = make_regression(n_samples=10, n_targets=3, random_state=1)
>>> MultiOutputRegressor(GradientBoostingRegressor(random_state=0)).fit(X, y).predict(X)
array([[154.75474165, 147.03498585, 50.03812219],
[ 7.12165031, 5.12914884, 81.46081961],
[187.8948621 , 100.44373091, 13.88978285],
[141.62745778, 95.02891072, 191.48204257],
[ 97.03260883, 165.34867495, 139.52003279],
[ 123.92529176, 21.25719016, 7.84253 ],
[122.25193977, 85.16443186, 107.12274212],
[ 30.170388 , 94.80956739, 12.16979946],
[ 140.72667194, 176.50941682, 17.50447799],
[ 149.37967282, 81.15699552, 5.72850319]])
1.12.4.3. RegressorChain¶
Regressor chains (see RegressorChain
) is
analogous to ClassifierChain
as a way of
combining a number of regressions into a single multitarget model that is
capable of exploiting correlations among targets.