  This paper looks into the problem of handling imbalanced data in a
multi-label classification problem. The problem is solved by proposing two
novel methods that primarily exploit the geometric relationship between the
feature vectors. The first one is an undersampling algorithm that uses angle
between feature vectors to select more informative samples while rejecting the
less informative ones. A suitable criterion is proposed to define the
informativeness of a given sample. The second one is an oversampling algorithm
that uses a generative algorithm to create new synthetic data that respects all
class boundaries. This is achieved by finding \emph{no man's land} based on
Euclidean distance between the feature vectors. The efficacy of the proposed
methods is analyzed by solving a generic multi-class recognition problem based
on mixture of Gaussians. The superiority of the proposed algorithms is
established through comparison with other state-of-the-art methods, including
SMOTE and ADASYN, over ten different publicly available datasets exhibiting
high-to-extreme data imbalance. These two methods are combined into a single
data processing framework and is labeled as ``GICaPS'' to highlight the role of
geometry-based information (GI) sampling and Class-Prioritized Synthesis (CaPS)
in dealing with multi-class data imbalance problem, thereby making a novel
contribution in this field.
