Multi-dimensional multi-label classification: Towards encompassing heterogeneous label spaces and multi-label annotations

In traditional classification framework, the semantics of each object is usually characterized by annotating a single class label from one homogeneous label space. Nonetheless, objects with rich semantics naturally arise in real-world applications whose properties need to be characterized in a more sophisticated manner. In this paper, a new classification framework named Multi-Dimensional Multi-Label (MDML) classification is investigated which models objects with rich semantics by encompassing heterogeneous label spaces and multi-label annotations. Specifically, MDML generalizes the traditional classification framework by assuming a number of heterogeneous label spaces to characterize semantics from different dimensions, where each object is further annotated with multiple class labels from each heterogeneous label space. To learn from MDML training examples, a first attempt named CLIM is proposed based on an augmented stacking strategy. Firstly, CLIM induces a base multi-label predictive model w.r.t. each label space by maximizing the likelihood of the observed multiple class labels. Secondly, the thresholding predictions from all base models are used to augment the original feature space to yield stacked multi-label predictive models. The two-level models are refined alternately via empirical threshold tuning. Experiments on four real-world MDML data sets validate the effectiveness of CLIM in learning from training examples with heterogeneous label spaces and multi-label annotations.