Abstract:  In multi-label learning, the correlation between labels has been more and more widely used, and it is necessary to show the relationship between them. Compared with previous studies, training process is extremely complicated and time-consuming due to the high dimensionality feature of multi-label data, so sparse optimization becomes essential; meanwhile, the relationship among labels has not been thoroughly excavated, so how to learn multi-label classification and study the correlation between all markers more effectively and conveniently becomes a necessity. This paper presents a method constraint on double sparse representation in multi-label classification, which first uses l₁/l₂-norm regularization to sparse multi-label data to convenient for following researches, and then applies l₁-norm into community detection to effectively detect communities. By this it shows the deep meaning of label relationship. Experiments show that this method can rapidly and accurately study and train multiple labels, and accurately display label connection at the same time.

Key words: multi-label, label relation, non-negative matrix factorization (NMF); l₁/l₂-norm; l₁-norm

摘要： 在多标记研究中，对于标记间相关性的利用已经越来越广泛，从而标记关系的展示就很有必要。相对以往的研究而言，由于多标记数据的高维特征，在训练过程中极为繁琐耗时，稀疏优化就尤为关键；同时标记相关性的内涵没有经过深入挖掘，因此如何更方便有效地进行多标记分类以及研究所有标记之间的相关性显得尤为必要。提出了一种基于两重稀疏约束的多标记社团分类算法，该算法首先将l₁/l₂正则化应用到多标记数据的稀疏表示过程，为后面的研究提供便利条件；其次在多标记关系基础上应用基于l₁]范数正则化的社团发现算法，有效地对标记进行社团划分，直观展示出标记关系的内涵。实验证明该方法能够快速、准确地进行多标记分类，并且能够准确展示标记关系。

关键词: 多标记, 标记关系, 非负矩阵分解（NMF）, l₁/l₂范数, l₁范数