Ganian, R, Kanj, I, Ordyniak, S orcid.org/0000-0003-1935-651X et al. (1 more author) (2020) On the Parameterized Complexity of Clustering Incomplete Data into Subspaces of Small Rank. In: AAAI-20 Technical Tracks 4. The Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI-20), 07-12 Feb 2020, New York, New York, USA. , pp. 3906-3913. ISBN 978-1-57735-835-0
Abstract
We consider a fundamental matrix completion problem where we are given an incomplete matrix and a set of constraints modeled as a CSP instance. The goal is to complete the matrix subject to the input constraints and in such a way that the complete matrix can be clustered into few subspaces with low rank. This problem generalizes several problems in data mining and machine learning, including the problem of completing a matrix into one with minimum rank. In addition to its ubiquitous applications in machine learning, the problem has strong connections to information theory, related to binary linear codes, and variants of it have been extensively studied from that perspective. We formalize the problem mentioned above and study its classical and parameterized complexity. We draw a detailed landscape of the complexity and parameterized complexity of the problem with respect to several natural parameters that are desirably small and with respect to several well-studied CSP fragments.
Metadata
Item Type: | Proceedings Paper |
---|---|
Authors/Creators: |
|
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/V00252X/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 21 Jul 2021 11:06 |
Last Modified: | 22 Jul 2021 07:50 |
Status: | Published |
Identification Number: | 10.1609/aaai.v34i04.5804 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:176330 |