  In this paper, we propose a new variant of Linear Discriminant Analysis (LDA)
to solve multi-label classification tasks. The proposed method is based on a
probabilistic model for defining the weights of individual samples in a
weighted multi-label LDA approach. Linear Discriminant Analysis is a classical
statistical machine learning method, which aims to find a linear data
transformation increasing class discrimination in an optimal discriminant
subspace. Traditional LDA sets assumptions related to Gaussian class
distributions and single-label data annotations. To employ the LDA technique in
multi-label classification problems, we exploit intuitions coming from a
probabilistic interpretation of class saliency to redefine the between-class
and within-class scatter matrices. The saliency-based weights obtained based on
various kinds of affinity encoding prior information are used to reveal the
probability of each instance to be salient for each of its classes in the
multi-label problem at hand. The proposed Saliency-based weighted Multi-label
LDA approach is shown to lead to performance improvements in various
multi-label classification problems.
