Matrix factorization (MF) methods decompose a data matrix into a product of two-factor matrices (denoted as U and V ) which are with low ranks. In this article, we propose a generative latent variable model for the data matrix, in which each entry is assumed to be a Gaussian with mean to be the inner product of the corresponding columns of U and V . The prior of each column of U and V is assumed to be as a finite mixture of Gaussians. Further, we propose to model the attribute matrix with the data matrix jointly by considering them as conditional independence with respect to the factor matrix U , building upon previously defined model for the data matrix. Due to the intractability of the proposed models, we employ variational Bayes to infer the posteriors of the factor matrices and the clustering relationships, and to optimize for the model parameters. In our development, the posteriors and model parameters can be readily computed in closed forms, which is much more computationally efficient than existing sampling-based probabilistic MF models. Comprehensive experimental studies of the proposed methods on collaborative filtering and community detection tasks demonstrate that the proposed methods achieve the state-of-the-art performance against a great number of MF-based and non-MF-based algorithms.

中文翻译：

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基于有限混合建模的具有属性的数据的概率矩阵分解。

矩阵分解 (MF) 方法将数据矩阵分解为具有低秩的双因子矩阵（表示为 U 和 V ）的乘积。在本文中，我们提出了一个数据矩阵的生成隐变量模型，其中每个条目被假定为高斯，其均值是 U 和 V 对应列的内积。假设 U 和 V 的每一列的先验是高斯的有限混合。此外，我们建议将属性矩阵与数据矩阵联合建模，将它们视为相对于因子矩阵 U 的条件独立，建立在先前定义的数据矩阵模型的基础上。由于所提出模型的难处理性，我们采用变分贝叶斯来推断因子矩阵的后验和聚类关系，并优化模型参数。在我们的开发中，后验和模型参数可以很容易地以封闭形式计算，这比现有的基于采样的概率 MF 模型的计算效率要高得多。对所提出的协同过滤和社区检测任务方法的综合实验研究表明，所提出的方法在大量基于 MF 和非基于 MF 的算法中实现了最先进的性能。