Multi-label classification (MLC) is a problem that each given sample is associated with more than one label simultaneously. There is a variety of application in our daily life, such as text categorization and image annotation. To date, many methodologies are proposed to do a multi-label learning task. According to the MLC setting, we put forward an MLC method called TPMLC (an MLC method with Two Parts) and propose a uniform loss function based on the variational inference with Bayesian and Gaussian distribution assumption. Moreover, this uniform loss function is composed of two parts. On one hand, the first part is about the determination of the relationship between sample and multiple labels, so we adopt a set of multiple support vector machines (SVMs) to determine this relationship. On the other hand, the second part in this uniform loss function is about the determination of the relationship among multiple labels, and thus we construct a projection matrix model to determine this relationship. Furthermore, this uniform loss function is optimized simultaneously, such that the two kinds of relationships can be optimized at the same time. Besides, we also present the convergence analysis and computational complexity analysis of the method. After that, in the experiment part, the comparison of TPMLC with state-of-the-art approaches manifests the feasibility and the competitive performance in classification. In addition, the statistic results show that the proposed method performs better than the state-of-the-art methods.

多标签分类（MLC）是一个问题，每个给定样本同时与多个标签相关联。在我们的日常生活中，有各种各样的应用程序，例如文本分类和图像注释。迄今为止，提出了许多方法来完成多标签学习任务。根据MLC的设置，我们提出了一种称为TPMLC的MLC方法（一种T wo P并提出基于贝叶斯和高斯分布假设的变分推断的统一损失函数。而且，该均匀损耗函数由两部分组成。一方面，第一部分是关于样本与多个标签之间关系的确定，因此我们采用一组多个支持向量机（SVM）来确定这种关系。另一方面，该均匀损失函数的第二部分是关于确定多个标签之间关系的，因此我们构建了一个投影矩阵模型来确定这种关系。此外，该均匀损失函数被同时优化，从而可以同时优化两种关系。此外，我们还介绍了该方法的收敛性分析和计算复杂度分析。之后，在实验部分，TPLMC与最新方法的比较表明了分类的可行性和竞争性能。此外，统计结果表明，该方法的性能优于最新方法。