IEEE Trans Cybern. 2021 Aug;51(8):3952-3963. doi: 10.1109/TCYB.2020.3000799. Epub 2021 Aug 4.
Non-negative matrix factorization (NMF) has become one of the most powerful methods for clustering and feature selection. However, the performance of the traditional NMF method severely degrades when the data contain noises and outliers or the manifold structure of the data is not taken into account. In this article, a novel method called correntropy-based hypergraph regularized NMF (CHNMF) is proposed to solve the above problem. Specifically, we use the correntropy instead of the Euclidean norm in the loss term of CHNMF, which will improve the robustness of the algorithm. And the hypergraph regularization term is also applied to the objective function, which can explore the high-order geometric information in more sample points. Then, the half-quadratic (HQ) optimization technique is adopted to solve the complex optimization problem of CHNMF. Finally, extensive experimental results on multi-cancer integrated data indicate that the proposed CHNMF method is superior to other state-of-the-art methods for clustering and feature selection.
非负矩阵分解（NMF）已成为聚类和特征选择的最强大方法之一。然而，当数据包含噪声和离群值或未考虑数据的流形结构时，传统的 NMF 方法的性能会严重下降。在本文中，提出了一种称为基于相关熵的超图正则化 NMF（CHNMF）的新方法来解决上述问题。具体来说，我们在 CHNMF 的损失项中使用相关熵代替欧几里得范数，这将提高算法的鲁棒性。并且还将超图正则化项应用于目标函数，这可以在更多样本点中探索高阶几何信息。然后，采用半二次（HQ）优化技术来解决 CHNMF 的复杂优化问题。最后，在多癌症综合数据上的广泛实验结果表明，所提出的 CHNMF 方法在聚类和特征选择方面优于其他最先进的方法。
