Efficient Detection of Short-Lived Communities via Spectral-Bound Guided Incremental NMF

Short-lived communities refer to groups of nodes in a network that form suddenly, persist briefly, and dissolve as the network evolves. These communities in real-world networks play a crucial role in capturing transient consumer interests that emerge around events, trends, or campaigns, making them essential for time-sensitive decision-making. Such interaction and transactional networks evolve over time and can be naturally modeled as temporal networks. Detecting such temporal communities in these evolving networks is critical for understanding their underlying temporal structures. However, most existing temporal community detection methods integrate all snapshots into a single community structure, thereby overlooking short-lived communities that form and dissolve around specific events or transient interests. These temporally localized groups are particularly important in applications where timing and contextual relevance are essential. To address these challenges, a novel approach called graph regularized incremental learning nonnegative matrix factorization (GRIL-NMF) is proposed. This method selects core-periphery subgraphs that exhibit the most significant topological changes at each time step. These selected subgraphs are then combined with adjacent snapshots to create an incremental learning framework. To effectively detect short-lived temporal communities and estimate their optimal duration, a cluster potential spectral bound is introduced that leverages the Courant–Fischer min–max principle. Extensive experiments on both real and synthetic datasets show that GRIL-NMF achieves an average runtime improvement of 8%–10%, with higher gains in later timesteps due to effective pruning of inactive subnetworks, compared to most state-of-the-art methods.