  Multi-label learning is concerned with the classification of data with
multiple class labels. This is in contrast to the traditional classification
problem where every data instance has a single label. Due to the exponential
size of output space, exploiting intrinsic information in feature and label
spaces has been the major thrust of research in recent years and use of
parametrization and embedding have been the prime focus. Researchers have
studied several aspects of embedding which include label embedding, input
embedding, dimensionality reduction and feature selection. These approaches
differ from one another in their capability to capture other intrinsic
properties such as label correlation, local invariance etc. We assume here that
the input data form groups and as a result, the label matrix exhibits a
sparsity pattern and hence the labels corresponding to objects in the same
group have similar sparsity. In this paper, we study the embedding of labels
together with the group information with an objective to build an efficient
multi-label classification. We assume the existence of a low-dimensional space
onto which the feature vectors and label vectors can be embedded. In order to
achieve this, we address three sub-problems namely; (1) Identification of
groups of labels; (2) Embedding of label vectors to a low rank-space so that
the sparsity characteristic of individual groups remains invariant; and (3)
Determining a linear mapping that embeds the feature vectors onto the same set
of points, as in stage 2, in the low-dimensional space. We compare our method
with seven well-known algorithms on twelve benchmark data sets. Our
experimental analysis manifests the superiority of our proposed method over
state-of-art algorithms for multi-label learning.
