We address the problem of finding closest matrix $$\tilde{\varvec{U}}$$ to a given $$\varvec{U}$$ under constraint that prescribed second-moment $$\tilde{\varvec{P}}$$ must be matched, i.e. $$\tilde{\varvec{U}}^{\mathrm {T}}\tilde{\varvec{U}}=\tilde{\varvec{P}}$$ . obtain closed-form formula for unique global optimizer full-rank case, is related by an SPD (symmetric positive definite) linear tr...

Video moment retrieval targets at retrieving a golden in video for given natural language query. The main challenges of this task include 1) the requirement accurately localizing (i.e., start time and end of) relevant an untrimmed stream, 2) bridging semantic gap between textual query contents. To tackle those problems, early approaches adopt sliding window or uniform sampling to collect clips ...

The problem of moment matching with preservation of port Hamiltonian and gradient structure is studied. Based on the time-domain approach to linear moment matching, we characterize the (subset of) port Hamiltonian/gradient models from the set of parameterized models that match the moments of a given port Hamiltonian/gradient system, at a set of finite points.