Graph Unfolding and Sampling for Transitory Video Keyframe Selection via Gershgorin Disc Alignment

User-generated videos (UGVs) uploaded from mobile phones to social media sites like YouTube and TikTok are short and non-repetitive. We summarize a transitory UGV into several keyframes in linear-time via fast graph sampling based on Gershgorin disc alignment (GDA). Specifically, we first model a sequence of N frames in a UGV as an M-hop path graph cGo for M ll N, where the similarity between two frames within M time instants is encoded as a positive edge based on feature similarity. Towards efficient sampling, we then ``unfold'' cGo to a 1-hop path graph cG, specified by a generalized graph Laplacian matrix cL, via one of two graph unfolding procedures with provable performance bounds. We show that maximizing the smallest eigenvalue λmin(B) of a coefficient matrix B = diagh + μ cL, where h is the binary keyframe selection vector, is equivalent to minimizing a worst-case signal reconstruction error. We maximize instead the Gershgorin circle theorem (GCT) lower bound λ^-min(B) by choosing h via a new fast graph sampling algorithm that iteratively aligns left-ends of Gershgorin discs for all graph nodes (frames). Experiments on multiple short video datasets show that our algorithm achieves comparable or better keyframe selection performance compared to state-of-the-art methods, at a substantially reduced complexity.