# Developing a label space clusterer¶

One of the approaches to multi-label classification is to cluster the label space into subspaces and perform classification in smaller subproblems to reduce the risk of under/overfitting.

scikit-multilearn follows scikit-learn’s ClustererMixin interface API for a clustering class. scikit-learn concentrates on single-label classification in which one usually performs clustering of the input space X and not the output class space. In scikit-learn the clusterer class is expected to take X and y and provide a clustering of X as an ndarray of n_samples elements, each element corresponding to the id of the cluster to which the observation is assigned, thus if sample no. 3 is assigned to cluster no. 1: result[3] should be equal to 1.

The clusterer for the label space in scikit-multilearn follows this interface, in order to create your own label space clusterer you need to inherit LabelSpaceClustererBase and implement the fit_predict(X, y) class method. Expect X and y to be sparse matrices, you and also use skmultilearn.utils.get_matrix_in_format() to convert to a desired matrix format. fit_predict(X, y) should return an array-like, preferably an ndarray or list of n_labels of integers indicating the no. of cluster a given label is assigned to similarly as it is performed in scikit-learn clusterers.

## Example classifier¶

Let us look at a toy example, where a clusterer divides the label space based on how a given label’s ordinal divides modulo a given number of clusters.

from skmultilearn.ensemble import LabelCooccurenceClustererBase

class ModuloClusterer(LabelSpaceClustererBase):
def __init__(self, number_of_clusters = None):
super(ModuloClusterer, self).__init__()
self.number_of_clusters = number_of_clusters

def fit_predict(self, X, y):
number_of_labels = y.shape[1]
# assign a label to a cluster no. label ordinal %  number of labeSls
return map(lambda x: x % self.number_of_clusters, xrange(number_of_labels))


## Label co-occurence graph¶

A feature present currently only in scikit-multilearn is the possibility to divide the label space based on analysing a label co-occurence graph. In such a graph labels are represented as nodes, and edges are generated based on how labels co-occur together among samples. In other words an edge between label no. a and number b is present if there exists a sample in X that is labeled with both a and b. The LabelCooccurenceClustererBase provides a method LabelCooccurenceClustererBase.generate_coocurence_adjacency_matrix(X, y)() which generates a dict containing label pairs as keys, and a float as edge weight value:

• 1.0 in an unweighted setting
• number of samples in X that are labeled with both labels in a weighted setting (when self.is_weighted is True)

The edge_map is both returned and stored in the class as self.edge_map. This is a base class for building label co-occurence graphs. Subclass LabelCooccurenceClustererBase and use generate_coocurence_adjacency_matrix at the beginning of your fit_predict as shown below, than build a graph using the edge_map property, and infer the communities from the graph. Interfaces for two popular Python graph libraries already exist:

• skmultilearn.ensemble.GraphToolCooccurenceClusterer that constructs the graph-tool graph object and uses stochastic block modelling for clustering
• skmultilearn.ensemble.IGraphLabelCooccurenceClusterer that constructs an igraph graph object and allows the use of a variety of igraph’s community detection methods for clustering

to use them, just subclass the class and start your fit_predict method like this:

def fit_predict(self, X, y):

Your graph object (a graphtool Graph or an igraph Graph) is available at self.coocurence_graph after those two lines.