Sequential semi-orthogonal multi-level NMF with negative residual reduction for network embedding

Network embedding is intended to produce low-dimensional vector representations of nodes in a network to preserve and extract the latent network structure, which has higher robustness to noise, outliers, and redundant data. Although a recently proposed multi-level nonnegative matrix factorization (NMF)-based approach has exhibited superior performance on network analysis, it is adversely affected by performance degradation because of discarded negative residual and redundant base selection throughout sequential multiple factorization processes. To alleviate this shortcoming, this paper presents a proposal of a sequential semi-orthogonal NMF with negative residual reduction for the network embedding (SSO-NRR-NMF). The proposed approach reduces the negative residuals to be discarded, and avoids redundant bases with a semi-orthogonal constraint. Numerical evaluations conducted using several real-world datasets demonstrate the effectiveness of the proposed SSO-NRR-NMF.