Multilabel classification deals with the problem where each instance belongs to multiple labels simultaneously. The algorithm based on large margin loss with k nearest neighbor constraints (LM-kNN) is one of the most prominent multilabel classification algorithms. However, due to the use of square hinge loss, LM-kNN needs to iteratively solve a constrained quadratic programming at a high computational cost. To address this issue, we propose a novel metric learning-guided k nearest neighbor approach (MLG-kNN) for multilabel classification. Specifically, we first transform the original instance into the label space by least square regression. Then, we learn a metric matrix in the label space, which makes the predictions of an instance in the learned metric space close to its true class values while far away from others. Since our MLG-kNN can be formulated as an unconstrained strictly (geodesically) convex optimization problem and yield a closed-form solution, the computational complexity is reduced. An analysis of generalization error bound indicates that our MLG-kNN converges to the optimal solutions. Experimental results verify that the proposed approach is more effective than the existing ones for multilabel classification across many benchmark datasets.

多标签分类处理每个实例同时属于多个标签的问题。基于具有k个最近邻约束（LM- k NN）的大余量损失的算法是最著名的多标签分类算法之一。但是，由于使用了方形铰链损耗，LM- k NN需要以高计算量来迭代求解约束二次规划。为了解决这个问题，我们提出了一种新颖的度量学习指导的k最近邻方法（MLG- kNN）用于多标签分类。具体来说，我们首先通过最小二乘回归将原始实例转换为标签空间。然后，我们在标签空间中学习一个度量矩阵，该矩阵使学习的度量空间中的实例预测接近其真实类值，而与其他实例的预测值相距甚远。由于我们的MLG- k NN可以表示为无约束的严格（地学上）凸优化问题并产生封闭形式的解决方案，因此降低了计算复杂度。对泛化误差范围的分析表明，我们的MLG- k NN收敛于最优解。实验结果证明，对于许多基准数据集的多标签分类，该方法比现有方法更有效。