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Penalized nonnegative nonnegative matrix tri-factorization for co-clustering

机译：罚聚类非负非负矩阵三因子分解

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Nonnegative matrix factorization has been widely used in co-clustering tasks which group data points and features simultaneously. In recent years, several proposed co-clustering algorithms have shown their superiorities over traditional one-side clustering, especially in text clustering and gene expression. Due to the NP-completeness of the co-clustering problems, most existing methods relaxed the orthogonality constraint as nonnegativity, which often deteriorates performance and robustness as a result. In this paper, penalized nonnegative matrix tri-factorization is proposed for co-clustering problems, where three penalty terms are introduced to guarantee the near orthogonality of the clustering indicator matrices. An iterative updating algorithm is proposed and its convergence is proved. Furthermore, the high-order nonnegative matrix tri-factorization technique is provided for symmetric co-clustering tasks and a corresponding algorithm with proved convergence is also developed. Finally, extensive experiments in six real-world datasets demonstrate that the proposed algorithms outperform the compared state-of-the-art co-clustering methods. (C) 2017 Elsevier Ltd. All rights reserved.
机译：非负矩阵分解已广泛用于将数据点和特征同时分组的共聚任务。近年来，一些提议的共聚算法已显示出它们优于传统的单侧聚类的优势，尤其是在文本聚类和基因表达方面。由于共聚问题的NP完全性，大多数现有方法放宽了正交性约束，因为它们是非负性，因此通常会降低性能和鲁棒性。针对共聚问题，提出了惩罚非负矩阵三因子分解方法，引入了三个惩罚项来保证聚类指标矩阵的近正交性。提出了一种迭代更新算法，并证明了其收敛性。此外，为对称共聚任务提供了高阶非负矩阵三因子分解技术，并开发了一种具有证明的收敛性的相应算法。最后，在六个真实世界的数据集中进行的广泛实验表明，所提出的算法优于已比较的最先进的共聚方法。 （C）2017 Elsevier Ltd.保留所有权利。

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