Zhang Chihao, Zhang Shihua
IEEE Trans Pattern Anal Mach Intell. 2021 Apr;43(4):1184-1196. doi: 10.1109/TPAMI.2019.2946370. Epub 2021 Mar 4.
Matrix decomposition is a popular and fundamental approach in machine learning and data mining. It has been successfully applied into various fields. Most matrix decomposition methods focus on decomposing a data matrix from one single source. However, it is common that data are from different sources with heterogeneous noise. A few of the matrix decomposition methods have been extended for such multi-view data integration and pattern discovery while only a few methods were designed to consider the heterogeneity of noise in such multi-view data for data integration explicitly. To this end, in this article, we propose a joint matrix decomposition framework (BJMD), which models the heterogeneity of noise by the Gaussian distribution in a Bayesian framework. We develop two algorithms to solve this model: one is a variational Bayesian inference algorithm, which makes full use of the posterior distribution; and another is a maximum a posterior algorithm, which is more scalable and can be easily paralleled. Extensive experiments on synthetic and real-world datasets demonstrate that BJMD is superior or competitive to the state-of-the-art methods.
矩阵分解是机器学习和数据挖掘中一种流行且基础的方法。它已成功应用于各个领域。大多数矩阵分解方法专注于从单一数据源分解数据矩阵。然而，数据来自具有异质噪声的不同来源是很常见的。一些矩阵分解方法已扩展用于此类多视图数据集成和模式发现，而只有少数方法被设计用于在这种多视图数据中明确考虑噪声的异质性以进行数据集成。为此，在本文中，我们提出了一种联合矩阵分解框架（BJMD），它在贝叶斯框架中通过高斯分布对噪声的异质性进行建模。我们开发了两种算法来求解该模型：一种是变分贝叶斯推理算法，它充分利用后验分布；另一种是最大后验算法，它更具可扩展性且易于并行化。在合成数据集和真实世界数据集上的大量实验表明，BJMD 优于或可与现有最先进方法相竞争。
