Probabilistic matrix tri-factorization
Probabilistic matrix tri-factorization
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DOI：
10.1109/icassp.2009.4959893
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发表时间：
2009-04
期刊：
影响因子：
--
通讯作者：
Jiho Yoo;Seungjin Choi
中科院分区：
文献类型：
--
作者：
Jiho Yoo;Seungjin Choi
非负矩阵三因子分解 (NMTF) 是非负数据矩阵 X ≈ USV┬ 的三因子分解，其中因子矩阵 U、S 和 V 也被限制为非负。受用于二元数据分析以及概率潜在语义分析 (PLSA) 的方面模型的启发，我们提出了一种具有 NMTF 的两个相关潜在变量的概率模型，称为概率矩阵三因子分解 (PMTF)。模型中的每个潜在变量都与二元组中相应对象的聚类变量相关联，从而使模型适合共同聚类。我们开发了一种 EM 算法来学习 PMTF 模型，展示了它与代数方法导出的乘法更新的等价性。我们演示了 PMTF 在文档聚类任务中的有用行为。此外，我们将 PMTF 模型中的似然度合并到现有的信息标准中，以便可以检测簇的数量，而代数 NMTF 则不能。
Nonnegative matrix tri-factorization (NMTF) is a 3-factor decomposition of a nonnegative data matrix, X ≈ USV┬, where factor matrices, U, S, and V , are restricted to be nonnegative as well. Motivated by the aspect model used for dyadic data analysis as well as in probabilistic latent semantic analysis (PLSA), we present a probabilistic model with two dependent latent variables for NMTF, referred to as probabilistic matrix tri-factorization (PMTF). Each latent variable in the model is associated with the cluster variable for the corresponding object in the dyad, leading the model suited to co-clustering. We develop an EM algorithm to learn the PMTF model, showing its equivalence to multiplicative updates derived by an algebraic approach. We demonstrate the useful behavior of PMTF in a task of document clustering. Moreover, we incorporate the likelihood in the PMTF model into existing information criteria so that the number of clusters can be detected, while the algebraic NMTF cannot.