Fair graph clustering seeks partitions that respect network structure while maintaining proportional representation across sensitive groups, with applications spanning community detection, team formation, resource allocation, and social network analysis. Many existing approaches enforce rigid constraints or rely on multi-stage pipelines (e.g., spectral embedding followed by $k$-means), limiting trade-off control, interpretability, and scalability. We introduce \emph{DFNMF}, an end-to-end deep nonnegative tri-factorization tailored to graphs that directly optimizes cluster assignments with a soft statistical-parity regularizer. A single parameter $λ$ tunes the fairness--utility balance, while nonnegativity yields parts-based factors and transparent soft memberships. The optimization uses sparse-friendly alternating updates and scales near-linearly with the number of edges. Across synthetic and real networks, DFNMF achieves substantially higher group balance at comparable modularity, often dominating state-of-the-art baselines on the Pareto front. The code is available at https://github.com/SiamakGhodsi/DFNMF.git.

The major challenge of learning from multi-label data has arisen from the overwhelming size of label space which makes this problem NP-hard. This problem can be alleviated by gradually involving easy to hard tags into the learning process. Besides, the utilization of a diversity maintenance approach avoids overfitting on a subset of easy labels. In this paper, we propose a self-paced multi-label learning with diversity (SPMLD) which aims to cover diverse labels with respect to its learning pace. In addition, the proposed framework is applied to an efficient correlation-based multi-label method. The non-convex objective function is optimized by an extension of the block coordinate descent algorithm. Empirical evaluations on real-world datasets with different dimensions of features and labels imply the effectiveness of the proposed predictive model.