Nonnegative matrix factorization (NMF) has been a vital data representation technique, and has demonstrated significant potential in the field of machine learning and data mining. Nonnegative matrix tri-factorization (NMTF) is an extension of NMF, and provides more degrees of freedom than NMF. In this paper, we propose the correntropy based orthogonal nonnegative matrix tri-factorization (CNMTF) algorithm, which is robust to noisy data contaminated by non-Gaussian noise and outliers. Different from previous NMF algorithms, CNMTF firstly applies correntropy to NMTF to measure the similarity, and preserves double orthogonality conditions and dual graph regularization. We adopt the half-quadratic technique to solve the optimization problem of CNMTF, and derive the multiplicative update rules. The complexity issue of CNMTF is also presented. Furthermore, the robustness of the proposed algorithm is analyzed, and the relationships between CNMTF and several previous NMF based methods are discussed. Experimental results demonstrate that the proposed CNMTF method has better performance on real world image and text datasets for clustering tasks, compared with several state-of-the-art methods.

非负矩阵分解（NMF）是一项至关重要的数据表示技术，在机器学习和数据挖掘领域已显示出巨大潜力。非负矩阵三因子分解（NMTF）是NMF的扩展，并且比NMF提供更多的自由度。在本文中，我们提出了基于熵的正交非负矩阵三因子分解（CNMTF）算法，该算法对于受非高斯噪声和离群值污染的嘈杂数据具有鲁棒性。与以前的NMF算法不同，CNMTF首先将熵应用于NMTF以测量相似性，并保留双正交性条件和双图正则化。我们采用半二次技术解决了CNMTF的优化问题，并推导了乘法更新规则。还介绍了CNMTF的复杂性问题。此外，分析了所提出算法的鲁棒性，并讨论了CNMTF与以前几种基于NMF的方法之间的关系。实验结果表明，与几种最新方法相比，所提出的CNMTF方法在现实世界中的图像和文本数据集上具有更好的聚类任务性能。