Matches in SemOpenAlex for { <https://semopenalex.org/work/W2307294673> ?p ?o ?g. }
- W2307294673 abstract "We study the Riemannian optimization methods on the embedded manifold of low rank matrices for the problem of matrix completion, which is about recovering a low rank matrix from its partial entries. Assume $m$ entries of an $ntimes n$ rank $r$ matrix are sampled independently and uniformly with replacement. We first prove that with high probability the Riemannian gradient descent and conjugate gradient descent algorithms initialized by one step hard thresholding are guaranteed to converge linearly to the measured matrix provided begin{align*} mgeq C_kappa n^{1.5}rlog^{1.5}(n), end{align*} where $C_kappa$ is a numerical constant depending on the condition number of the underlying matrix. The sampling complexity has been further improved to begin{align*} mgeq C_kappa nr^2log^{2}(n) end{align*} via the resampled Riemannian gradient descent initialization. The analysis of the new initialization procedure relies on an asymmetric restricted isometry property of the sampling operator and the curvature of the low rank matrix manifold. Numerical simulation shows that the algorithms are able to recover a low rank matrix from nearly the minimum number of measurements." @default.
- W2307294673 created "2016-06-24" @default.
- W2307294673 creator A5003735769 @default.
- W2307294673 creator A5057913701 @default.
- W2307294673 creator A5059208158 @default.
- W2307294673 creator A5068532103 @default.
- W2307294673 date "2016-03-21" @default.
- W2307294673 modified "2023-10-02" @default.
- W2307294673 title "Guarantees of Riemannian Optimization for Low Rank Matrix Completion" @default.
- W2307294673 cites W1484412996 @default.
- W2307294673 cites W1499670810 @default.
- W2307294673 cites W1804110266 @default.
- W2307294673 cites W1847121931 @default.
- W2307294673 cites W1884015253 @default.
- W2307294673 cites W1884359871 @default.
- W2307294673 cites W2000345836 @default.
- W2307294673 cites W2023101933 @default.
- W2307294673 cites W2034815954 @default.
- W2307294673 cites W2042182457 @default.
- W2307294673 cites W2058078260 @default.
- W2307294673 cites W2059283452 @default.
- W2307294673 cites W2060204507 @default.
- W2307294673 cites W2096154138 @default.
- W2307294673 cites W2098670069 @default.
- W2307294673 cites W2103972604 @default.
- W2307294673 cites W2116680824 @default.
- W2307294673 cites W2116837464 @default.
- W2307294673 cites W2118550318 @default.
- W2307294673 cites W2120564806 @default.
- W2307294673 cites W2120872934 @default.
- W2307294673 cites W2129908708 @default.
- W2307294673 cites W2140867429 @default.
- W2307294673 cites W2145179194 @default.
- W2307294673 cites W2165644552 @default.
- W2307294673 cites W2171046470 @default.
- W2307294673 cites W2200878340 @default.
- W2307294673 cites W2542482481 @default.
- W2307294673 cites W2611328865 @default.
- W2307294673 cites W2951597050 @default.
- W2307294673 cites W2952489973 @default.
- W2307294673 cites W2962761770 @default.
- W2307294673 cites W2963449128 @default.
- W2307294673 cites W2963684688 @default.
- W2307294673 cites W2963979747 @default.
- W2307294673 cites W3029645440 @default.
- W2307294673 cites W3113425034 @default.
- W2307294673 cites W2144730813 @default.
- W2307294673 doi "https://doi.org/10.48550/arxiv.1603.06610" @default.
- W2307294673 hasPublicationYear "2016" @default.
- W2307294673 type Work @default.
- W2307294673 sameAs 2307294673 @default.
- W2307294673 citedByCount "14" @default.
- W2307294673 countsByYear W23072946732015 @default.
- W2307294673 countsByYear W23072946732016 @default.
- W2307294673 countsByYear W23072946732017 @default.
- W2307294673 countsByYear W23072946732018 @default.
- W2307294673 countsByYear W23072946732019 @default.
- W2307294673 countsByYear W23072946732020 @default.
- W2307294673 countsByYear W23072946732021 @default.
- W2307294673 crossrefType "posted-content" @default.
- W2307294673 hasAuthorship W2307294673A5003735769 @default.
- W2307294673 hasAuthorship W2307294673A5057913701 @default.
- W2307294673 hasAuthorship W2307294673A5059208158 @default.
- W2307294673 hasAuthorship W2307294673A5068532103 @default.
- W2307294673 hasBestOaLocation W23072946731 @default.
- W2307294673 hasConcept C106487976 @default.
- W2307294673 hasConcept C11413529 @default.
- W2307294673 hasConcept C114466953 @default.
- W2307294673 hasConcept C114614502 @default.
- W2307294673 hasConcept C119857082 @default.
- W2307294673 hasConcept C121332964 @default.
- W2307294673 hasConcept C124851039 @default.
- W2307294673 hasConcept C153258448 @default.
- W2307294673 hasConcept C155281189 @default.
- W2307294673 hasConcept C159985019 @default.
- W2307294673 hasConcept C163716315 @default.
- W2307294673 hasConcept C164226766 @default.
- W2307294673 hasConcept C17902559 @default.
- W2307294673 hasConcept C192562407 @default.
- W2307294673 hasConcept C199360897 @default.
- W2307294673 hasConcept C202444582 @default.
- W2307294673 hasConcept C2778459887 @default.
- W2307294673 hasConcept C2779593128 @default.
- W2307294673 hasConcept C33923547 @default.
- W2307294673 hasConcept C41008148 @default.
- W2307294673 hasConcept C50644808 @default.
- W2307294673 hasConcept C62520636 @default.
- W2307294673 hasConcept C82457910 @default.
- W2307294673 hasConcept C90199385 @default.
- W2307294673 hasConceptScore W2307294673C106487976 @default.
- W2307294673 hasConceptScore W2307294673C11413529 @default.
- W2307294673 hasConceptScore W2307294673C114466953 @default.
- W2307294673 hasConceptScore W2307294673C114614502 @default.
- W2307294673 hasConceptScore W2307294673C119857082 @default.
- W2307294673 hasConceptScore W2307294673C121332964 @default.
- W2307294673 hasConceptScore W2307294673C124851039 @default.
- W2307294673 hasConceptScore W2307294673C153258448 @default.
- W2307294673 hasConceptScore W2307294673C155281189 @default.
- W2307294673 hasConceptScore W2307294673C159985019 @default.
- W2307294673 hasConceptScore W2307294673C163716315 @default.