Orthogonal Nonnegative Matrix Factorization (ONMF) offers an important analytical vehicle for addressing many problems. Encouraged by record-breaking successes attained by neural computing models in solving an assortment of data analytics tasks, a rich collection of neural computing models has been proposed to perform ONMF with compelling performance. Such existing models can be broadly classified into the shallow-layered structure (SLS) based and deep-layered structure (DLS) based models. However, SLS models cannot capture complex relationships and hierarchical information latent in a matrix due to their simple network structures and DLS models rely on an iterative procedure to derive weights, leading to a less efficient solution process and cannot be reused to factorize new matrices. To overcome these shortcomings, this paper proposes a novel deep autoencoder network for ONMF, which is abbreviated as DAutoED-ONMF. Compared with SLS models, the newly proposed model is capable of generating solutions with good interpretability and solution uniqueness like original SLS models, yet the new model attains a superior learning capability thanks to its deep structure employed. In comparison with DLS models, the new model trains a reusable encoder network to directly factorize any given matrix with no need to repeatedly retrain the model for factorizing multiple matrices using a tailor-designed network training procedure. Proof of the procedure’s convergence is presented with an analysis of its computational complexity. The numerical experiments conducted on several publicly data sets convincingly demonstrate that the proposed DAutoED-ONMF model gains promising performance in terms of multiple metrics.

正交非负矩阵分解 (ONMF) 为解决许多问题提供了重要的分析工具。受到神经计算模型在解决各种数据分析任务方面取得的破纪录成功的鼓舞，已经提出了丰富的神经计算模型集合来以引人注目的性能执行 ONMF。此类现有模型可以大致分为基于浅层结构 (SLS) 和基于深层结构 (DLS) 的模型。然而，SLS 模型由于其简单的网络结构而无法捕获矩阵中潜在的复杂关系和层次信息，并且 DLS 模型依赖于迭代过程来推导权重，导致求解过程效率较低，并且不能重复用于分解新矩阵。为了克服这些缺点，本文为ONMF提出了一种新颖的深度自动编码器网络，缩写为DAutoED-ONMF。与 SLS 模型相比，新提出的模型能够像原始 SLS 模型一样生成具有良好解释性和解唯一性的解，但由于采用了深度结构，新模型获得了卓越的学习能力。与 DLS 模型相比，新模型训练可重复使用的编码器网络以直接分解任何给定矩阵，而无需使用量身定制的网络训练程序重复重新训练模型以分解多个矩阵。通过分析其计算复杂性来证明该过程的收敛性。