In multi-label learning, each instance is associated with a subset of predefined labels. One common approach for multi-label classification has been proposed in Godbole and Sarawagi (2004) based on stacking which is called as Meta Binary Relevance (MBR). It uses two layers of binary models and feeds the outputs of the first layer to all binary models of the second layer. Hence, initial predicted class labels (in the first layer) are attached to the original features to have a new prediction of the classes in the second layer. To predict a specific label in the second layer, irrelevant labels are also used as the noisy features. This is why; Nearest Neighbor (NN) as a sensitive classifier to noisy features had been not, up to now, a proper base classifier in stacking method and all of its merits including simplicity, interpretability, global stability to noisy labels and good performance, are lost. As the first contribution, a popular feature weighting in NN classification is used here to solve uncorrelated labels problem. It tunes a parametric distance function by gradient descent to minimize the classification error on training data. However, it is known that some other objectives including F-measure are more suitable than classification error on learning imbalanced data. The second contribution of this paper is extending this method in order to improve F-measure. In our experimental study, the proposed method has been compared with and outperforms state-of-the-art multi-label classifiers in the literature.

在多标签学习中，每个实例都与预定义标签的子集相关联。一种基于多标签分类的通用方法已在Godbole和Sarawagi（2004）中提出，该方法基于堆叠，即所谓的元二进制相关性（MBR）。它使用两层二进制模型，并将第一层的输出提供给第二层的所有二进制模型。因此，将初始预测的类别标签（在第一层中）附加到原始要素上，以对第二层中的类别进行新的预测。为了预测第二层中的特定标签，不相关的标签也用作噪声特征。这就是为什么; 迄今为止，最近邻（NN）作为噪声特征的敏感分类器还不是堆叠方法及其所有优点（包括简单性，可解释性，嘈杂标签的全局稳定性和良好的性能都丢失了。作为第一项贡献，此处使用了NN分类中流行的特征加权来解决不相关标签的问题。它通过梯度下降来调整参数距离函数，以最小化训练数据上的分类误差。但是，众所周知，其他一些目标包括对于学习不平衡数据，F度量比分类误差更合适。本文的第二个贡献是扩展了该方法，以改进F测度。在我们的实验研究中，所提出的方法已与文献中最先进的多标签分类器进行了比较，并优于后者。