Nonnegative matrix factorization (NMF) has found many applications including topic modeling and document analysis. Hierarchical NMF (HNMF) variants are able to learn topics at various levels of granularity and illustrate their hierarchical relationship. Recently, nonnegative tensor factorization (NTF) methods have been applied in a similar fashion in order to handle data sets with complex, multi-modal structure. Hierarchical NTF (HNTF) methods have been proposed, however these methods do not naturally generalize their matrix-based counterparts. Here, we propose a new HNTF model which directly generalizes a HNMF model special case, and provide a supervised extension. We also provide a multiplicative updates training method for this model. Our experimental results show that this model more naturally illuminates the topic hierarchy than previous HNMF and HNTF methods.
翻译:非负式矩阵因子化(NMF)发现许多应用,包括主题模型和文件分析。等级型NMF(HNMF)变量能够在不同颗粒层面学习专题并展示其等级关系。最近,以类似的方式应用了非负式的指数因子化(NTF)方法,以便处理复杂、多模式结构的数据集。提出了等级型NTF(HNTF)方法,但这些方法并不自然地将其基于矩阵的对应方法概括化。在这里,我们提议一个新的HNTF模型模型,直接概括HNMF模式的特例,并提供受监督的扩展。我们还为这一模型提供了一种多复制式更新培训方法。我们的实验结果表明,这一模型比以前的HNMF和HNTF方法更自然地说明了主题等级。