Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 10 min ago
PreprintarXiv licencearXiv

Matrix Completion Discriminants

  • Yoshiyuki Sekiguchi
  • Shin-ichi Tanigawa
Open at sourcePDFDOICite

Abstract

We introduce the matrix completion discriminant of a graph as the Zariski closure of the set of partial symmetric matrices whose completion fibers fail to meet a rank stratum transversely. A clique-sum formula for the matrix completion discriminant is established for arbitrary graphs, while explicit defining equations for cycles are obtained in terms of iterated resultants. Using these results together with the analysis of K4-minor-free graphs, we prove that for every cycle-completable graph, the discriminant factors into determinant factors from maximal cliques and resultant factors from chordless cycles.

Related

  1. Empirical Bayes 1-bit matrix completion
    Takeru Matsuda
    arXivPreprintCC BY 4.0Full textStatisticsarXiv
  2. Near-Optimal Nonconvex Matrix Completion
    Jian-Feng Cai, Xiliang Lu, Juntao You
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  3. Hyperbolic distance matrix completion
    Mihai Putinar, Prateek Kumar Vishwakarma
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  4. Synthetic Nearest Neighbors: Extending Synthetic Controls for Matrix Completion with Missing Not at Random Data
    Anish Agarwal, Munther Dahleh, Devavrat Shah +1
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  5. Noisy Matrix Completion under Informative Missingness
    Xuanyu Chen, Xiaoyue Niu, Gongjun Xu +1
    arXivPreprintarXiv licenceFull textStatisticsarXiv

Cite

BibTeXRIS
BibTeX
@misc{sekiguchi2026matrix,
  title = {{Matrix Completion Discriminants}},
  author = {Yoshiyuki Sekiguchi and Shin-ichi Tanigawa},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.21341},
  eprint = {2610.21341},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.21341},
}
RIS
TY  - UNPB
TI  - Matrix Completion Discriminants
AU  - Yoshiyuki Sekiguchi
AU  - Shin-ichi Tanigawa
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.21341
UR  - https://arxiv.org/abs/2610.21341
AB  - We introduce the matrix completion discriminant of a graph as the Zariski closure of the set of partial symmetric matrices whose completion fibers fail to meet a rank stratum transversely. A clique-sum formula for the matrix completion discriminant is established for arbitrary graphs, while explicit defining equations for cycles are obtained in terms of iterated resultants. Using these results together with the analysis of K_4-minor-free graphs, we prove that for every cycle-completable graph, the discriminant factors into determinant factors from maximal cliques and resultant factors from chordless cycles.
ER  -