In multi-dimensional classification (MDC), each instance is associated with multiple class variables characterizing the semantics of objects from different dimensions. To consider the dependencies among class variables and the specific characteristics contained in different semantic dimensions, a novel deep MDC approach named PIST is proposed to jointly deal with the two issues via learning pairwise dimension-specific features. Specifically, PIST conducts pairwise grouping to model the dependencies between each pair of class variables, which are more reliable with limited training samples. For extracting pairwise dimension-specific features, PIST weights the feature embedding with a feature importance vector, which is learned via utilizing a global loss measurement based on intra-class and inter-class covariance. Final prediction w.r.t. each dimension is determined by combining the joint probabilities related to this dimension. Comparative studies with eleven real-world MDC data sets clearly validate the effectiveness of the proposed approach.