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≪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=\diag\h+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
λmin−(\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.