Multi-label classification aims to assign a set of proper labels for each instance, where distance metric learning can help improve the generalization ability of instance-based multi-label classification models. Existing multi-label metric learning techniques work by utilizing pairwise constraints to enforce that examples with similar label assignments should have close distance in the embedded feature space. In this paper, a novel distance metric learning approach for multi-label classification is proposed by modeling structural interactions between instance space and label space. On one hand, compositional distance metric is employed which adopts the representation of a weighted sum of rank-1 PSD matrices based on component bases. On the other hand, compositional weights are optimized by exploiting triplet similarity constraints derived from both instance and label spaces. Due to the compositional nature of employed distance metric, the resulting problem admits quadratic programming formulation with linear optimization complexity w.r.t. the number of training examples. We also derive the generalization bound for the proposed approach based on algorithmic robustness analysis of the compositional metric. Extensive experiments on sixteen benchmark data sets clearly validate the usefulness of compositional metric in yielding effective distance metric for multi-label classification.

多标签分类旨在为每个实例分配一组适当的标签，其中距离度量学习可以帮助提高基于实例的多标签分类模型的泛化能力。现有的多标签度量学习技术通过利用成对约束来强制具有相似标签分配的示例在嵌入式特征空间中应具有近距离。本文通过对实例空间和标签空间之间的结构相互作用进行建模，提出了一种用于多标签分类的新型距离度量学习方法。一方面，采用组成距离度量，该组成距离度量采用基于分量基的秩-1 PSD矩阵的加权和表示。另一方面，通过利用从实例空间和标签空间派生的三元组相似性约束来优化组合权重。由于所采用距离度量的组成性质，所产生的问题允许采用具有线性优化复杂度和训练示例数量的二次规划公式。我们还根据组成指标的算法鲁棒性分析，得出了该方法的推广界。在16个基准数据集上进行的大量实验清楚地证明了组成度量在产生用于多标签分类的有效距离度量中的有用性。培训实例的数量。我们还根据组成指标的算法鲁棒性分析，得出了该方法的推广界。在16个基准数据集上进行的大量实验清楚地证明了组合度量在产生用于多标签分类的有效距离度量中的有用性。培训实例的数量。我们还根据组成指标的算法鲁棒性分析，得出了该方法的推广界。在16个基准数据集上进行的大量实验清楚地证明了组成度量在产生用于多标签分类的有效距离度量中的有用性。