<p>In multi-dimensional multi-label classification (MDML), a number of heterogeneous label spaces are assumed to characterize the rich semantics of one object from different dimensions and a set of proper labels can be assigned to the object from each heterogeneous label space. In recent years, similarity-based framework has achieved a promising performance in classification tasks (e.g., multi-class/multi-label classification), while its effectiveness has not been investigated in solving the MDML problems. Moreover, existing similarity-based approaches only utilize either instance-based or label-based information which limits their generalization ability. In this paper, we propose a novel similarity-based MDML approach, naming S<span>idle</span> which attempts to utilize both instance-based and label-based information. To extract similarity information, S<span>idle</span> first identifies <i>k</i> nearest neighbors in instance space and enhanced label space, respectively. Then, with these identified samples, S<span>idle</span> calculates the simple counting statistics based on their labels as well as a bias based on distance between the sample and these identified samples. Finally, the instance space is enriched with extracted similarity information to update instance space and enhanced label space. These three steps are iteratively conducted until convergence. Experiments validate the effectiveness of the proposed S<span>idle</span> approach.</p>