Robust Semi-Supervised Deep Nonnegative Matrix Factorization with Constraint Propagation for Data Representation

Deep nonnegative matrix factorization (DNMF) technique has attached much great attention in recent year, since it can effectively discover the underlying hierarchical structure of complex data. However, most existing unsupervised and semi-supervised DNMF approaches not only suffer from the noisy data seriously, but also fail to enhance the decomposition quality of DNMF obviously by using the obtained supervisory information. To overcome these drawbacks, a robust semi-supervised DNMF method, called the correntropy based semi-supervised DNMF with constraint propagation (CSDCP), is proposed in this paper for learning a compact and meaningful data representation from the original data. Particularly, instead of adopting the traditional Frobenius norm, CSDCP employs the nonlinear and local similarity measure (e.g., correntropy) as the loss function in DNMF to enhance the robustness of DNMF for the noisy data. In addition, the hypergraph based constraint propagation (HCP) algorithm is adopted in CSDCP to exploit the limited supervisory information fully for capturing good data representation. Moreover, algorithm analysis of CSDCP is presented in this paper, including convergence analysis, robustness analysis supervised information analysis, and computational complexity. Extensive experimental results have illustrated that, in comparison to the most related DNMF approaches, CSDCP usually has better clustering results on six nonnegative datasets in clustering tasks.