Bayesian non-negative matrix factorization (BNMF) has been widely used in different applications. In this article, we propose a novel BNMF technique dedicated to semibounded data where each entry of the observed matrix is supposed to follow an Inverted Beta distribution. The model has two parameter matrices with the same size as the observation matrix which we factorize into a product of excitation and basis matrices. Entries of the corresponding basis and excitation matrices follow a Gamma prior. To estimate the parameters of the model, variational Bayesian inference is used. A lower bound approximation for the objective function is used to find an analytically tractable solution for the model. An online extension of the algorithm is also proposed for more scalability and to adapt to streaming data. The model is evaluated on five different applications: part-based decomposition, collaborative filtering, market basket analysis, transactions prediction and items classification, topic mining, and graph embedding on biomedical networks.

中文翻译：

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半有界数据的贝叶斯矩阵分解


贝叶斯非负矩阵分解（BNMF）已广泛应用于不同的应用中。在本文中，我们提出了一种专门用于半有界数据的新型 BNMF 技术，其中观察到的矩阵的每个条目都应该遵循倒贝塔分布。该模型有两个与观测矩阵大小相同的参数矩阵，我们将其分解为激励矩阵和基矩阵的乘积。相应的基矩阵和激励矩阵的条目遵循伽玛先验。为了估计模型的参数，使用变分贝叶斯推理。目标函数的下界近似用于寻找模型的分析易处理解。还提出了该算法的在线扩展，以提高可扩展性并适应流数据。该模型在五种不同的应用程序上进行评估：基于部分的分解、协同过滤、购物篮分析、交易预测和项目分类、主题挖掘以及生物医学网络上的图嵌入。