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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.