A Generalized Hierarchical Nonnegative Tensor Decomposition
A Generalized Hierarchical Nonnegative Tensor Decomposition
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DOI：
10.1109/icassp43922.2022.9747810
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发表时间：
2021-09
期刊：
影响因子：
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通讯作者：
Joshua Vendrow;Jamie Haddock;D. Needell
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文献类型：
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作者：
Joshua Vendrow;Jamie Haddock;D. Needell
非负矩阵分解在主题建模、文档分析等领域有着广泛的应用。分层NMF（HNMF）变体能够以各种粒度级别学习主题，并说明它们的层次关系。最近，非负张量因子分解（NTF）方法已经以类似的方式应用，以处理具有复杂的多模态结构的数据集。分层NTF（HNTF）方法已经提出，但是这些方法并不自然地推广他们的基于矩阵的同行。在这里，我们提出了一个新的HNTF模型，它直接推广了HNMF模型的特殊情况，并提供了一个监督扩展。我们还为该模型提供了一种乘法更新训练方法。我们的实验结果表明，该模型比以前的HNMF和HNTF方法更自然地阐明了主题层次。
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.