Jia Yuheng, Liu Hui, Hou Junhui, Kwong Sam
IEEE Trans Cybern. 2021 May;51(5):2550-2562. doi: 10.1109/TCYB.2020.2969684. Epub 2021 Apr 15.
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.
作为非负矩阵分解（NMF）的一种变体，对称非负矩阵分解（SymNMF）通过将相似性矩阵分解为聚类指示矩阵与其转置的乘积，无需额外的后处理即可生成聚类结果。然而，传统SymNMF方法中的相似性矩阵通常是预先定义的，导致聚类性能有限。考虑到相似性图的质量对最终聚类性能至关重要，我们提出了一种新的半监督模型，该模型能够同时利用监督信息学习相似性矩阵并生成聚类结果，使得这两个任务的相互增强效应能够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进行传播，以获得信息丰富的相似性矩阵。最终，所提出的模型被表述为一个非负约束优化问题。此外，我们提出了一种迭代方法来求解该问题，并从理论上证明了其收敛性。大量实验验证了所提出模型与九个最新的NMF模型相比的优越性。
