Linear discriminant analysis (LDA) 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 the Gaussian class distributions and single-label data annotations. In this article, we propose a new variant of LDA to be used in multilabel classification tasks for dimensionality reduction on original data to enhance the subsequent performance of any multilabel classifier. A probabilistic class saliency estimation approach is introduced for computing saliency-based weights for all instances. We use the weights to redefine the between-class and within-class scatter matrices needed for calculating the projection matrix. We formulate six different variants of the proposed saliency-based multilabel LDA (SMLDA) based on different prior information on the importance of each instance for their class(es) extracted from labels and features. Our experiments show that the proposed SMLDA leads to performance improvements in various multilabel classification problems compared to several competing dimensionality reduction methods.