Network Embedding Using Deep Robust Nonnegative Matrix Factorization

As an effective technique to learn low-dimensional node features in complicated network environment, network embedding has become a promising research direction in the field of network analysis. Due to the virtues of better interpretability and flexibility, matrix factorization based methods for network embedding have received increasing attentions. However, most of them are inadequate to learn more complicated hierarchical features hidden in complex networks because of their mechanisms of single-layer factorization structure. Besides, their original feature matrices used for factorization and their robustness against noises also need to be further improved. To solve these problems, we propose a novel network embedding method named DRNMF (deep robust nonnegative matrix factorization), which is formed by multi-layer NMF learning structure. Meanwhile, DRNMF employs the combination of high-order proximity matrices of the network as the original feature matrix for the factorization. To improve the robustness against noises, we use $\ell _{2,1}$ norm to devise the objective function for the DRNMF network embedding model. Effective iterative update rules are derived to resolve the model, and the convergence of these rules are strictly proved. Moreover, we introduce a pre-training strategy to improve the efficiency of convergence. Extensive experiments on several benchmarks of complex networks demonstrate that our proposed method DRNMF is effective and has better performance than the state-of-the-art matrix factorization based methods for network embedding.