Combinatorial Conditions for the Unique Completability of Low-Rank Matrices
نویسندگان
چکیده
منابع مشابه
Combinatorial Conditions for the Unique Completability of Low-Rank Matrices
We consider the problems of completing a low-rank positive semidefinite square matrix M or a low-rank rectangular matrix N from a given subset of their entries. Following the approach initiated by Singer and Cucuringu [20] we study the local and global uniqueness of such completions by analysing the structure of the graphs determined by the positions of the known entries of M or N . We present ...
متن کاملUnique low rank completability of partially filled matrices
We consider the problems of completing a low-rank positive semidefinite square matrix M or a low-rank rectangular matrix N from a given subset of their entries. We study the local and global uniqueness of such completions by analysing the structure of the graphs determined by the positions of the known entries of M or N . We show that the unique completability testing of rectangular matrices is...
متن کاملDeterministic and Probabilistic Conditions for Finite Completability of Low-rank Multi-View Data
We consider the multi-view data completion problem, i.e., to complete a matrix U = [U1|U2] where the ranks of U,U1, and U2 are given. In particular, we investigate the fundamental conditions on the sampling pattern, i.e., locations of the sampled entries for finite completability of such a multi-view data given the corresponding rank constraints. In contrast with the existing analysis on Grassm...
متن کاملDeterministic and Probabilistic Conditions for Finite Completability of Low Rank Tensor
We investigate the fundamental conditions on the sampling pattern, i.e., locations of the sampled entries, for finite completability of a low-rank tensor given some components of its Tucker rank. In order to find the deterministic necessary and sufficient conditions, we propose an algebraic geometric analysis on the Tucker manifold, which allows us to incorporate multiple rank components in the...
متن کاملCharacterization of Deterministic and Probabilistic Sampling Patterns for Finite Completability of Low Tensor-Train Rank Tensor
In this paper, we analyze the fundamental conditions for low-rank tensor completion given the separation or tensor-train (TT) rank, i.e., ranks of unfoldings. We exploit the algebraic structure of the TT decomposition to obtain the deterministic necessary and sufficient conditions on the locations of the samples to ensure finite completability. Specifically, we propose an algebraic geometric an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2014
ISSN: 0895-4801,1095-7146
DOI: 10.1137/140960098