Abstract Nonnegative matrix factorization (NMF) is a powerful dimension reduction method, and has received increasing attention in various practical applications. However, most traditional NMF based algorithms are sensitive to noisy data, or fail to fully utilize the limited supervised information. In this paper, a novel robust semi-supervised NMF method, namely correntropy based semi-supervised NMF (CSNMF), is proposed to solve these issues. Specifically, CSNMF adopts a correntropy based loss function instead of the squared Euclidean distance (SED) in constrained NMF to suppress the influence of non-Gaussian noise or outliers contaminated in real world data, and simultaneously uses two types of supervised information, i.e., the pointwise and pairwise constraints, to obtain the discriminative data representation. The proposed method is analyzed in terms of convergence, robustness and computational complexity. The relationships between CSNMF and several previous NMF based methods are also discussed. Extensive experimental results show the effectiveness and robustness of CSNMF in image clustering tasks, compared with several state-of-the-art methods.

中文翻译：

---

用于图像聚类的鲁棒半监督非负矩阵分解

摘要 非负矩阵分解（NMF）是一种强大的降维方法，在各种实际应用中越来越受到关注。然而，大多数传统的基于 NMF 的算法对噪声数据很敏感，或者无法充分利用有限的监督信息。在本文中，提出了一种新颖的鲁棒半监督 NMF 方法，即基于相关熵的半监督 NMF (CSNMF)，以解决这些问题。具体来说，CSNMF采用基于相关熵的损失函数代替约束NMF中的平方欧几里德距离（SED）来抑制非高斯噪声或现实世界数据中污染的异常值的影响，同时使用两种类型的监督信息，即逐点和成对约束，以获得判别数据表示。从收敛性、鲁棒性和计算复杂度方面对所提出的方法进行了分析。还讨论了 CSNMF 和以前几种基于 NMF 的方法之间的关系。广泛的实验结果表明，与几种最先进的方法相比，CSNMF 在图像聚类任务中的有效性和鲁棒性。