As a variant of non-negative matrix factorization (NMF), symmetric NMF (SymNMF) can generate the clustering result without additional post-processing, by decomposing a similarity matrix into the product of a clustering indicator matrix and its transpose. However, the similarity matrix in the traditional SymNMF methods is usually predefined, resulting in limited clustering performance. Considering that the quality of the similarity graph is crucial to the final clustering performance, we propose a new semisupervised model, which is able to simultaneously learn the similarity matrix with supervisory information and generate the clustering results, such that the mutual enhancement effect of the two tasks can produce better clustering performance. Our model fully utilizes the supervisory information in the form of pairwise constraints to propagate it for obtaining an informative similarity matrix. The proposed model is finally formulated as a non-negativity-constrained optimization problem. Also, we propose an iterative method to solve it with the convergence theoretically proven. Extensive experiments validate the superiority of the proposed model when compared with nine state-of-the-art NMF models.

中文翻译：

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半监督自适应对称非负矩阵分解


作为非负矩阵分解（NMF）的一种变体，对称 NMF（SymNMF）可以通过将相似性矩阵分解为聚类指标矩阵与其转置的乘积来生成聚类结果，而无需额外的后处理。然而，传统SymNMF方法中的相似度矩阵通常是预定义的，导致聚类性能有限。考虑到相似图的质量对最终的聚类性能至关重要，我们提出了一种新的半监督模型，该模型能够同时学习带有监督信息的相似度矩阵并生成聚类结果，使得两者的相互增强效果任务可以产生更好的聚类性能。我们的模型充分利用成对约束形式的监督信息来传播它以获得信息丰富的相似度矩阵。所提出的模型最终被表述为非负约束优化问题。此外，我们提出了一种迭代方法来解决它，并在理论上证明了收敛性。与九种最先进的 NMF 模型相比，大量实验验证了所提出模型的优越性。