Provably optimal sparse solutions to overdetermined linear systems with non-negativity constraints in a least-squares sense by implicit enumeration
buir.contributor.author | Aktaş, Fatih Selim | |
buir.contributor.author | Ekmekcioglu, Ömer | |
buir.contributor.author | Pinar, Mustafa Çelebi | |
buir.contributor.orcid | Pinar, Mustafa Çelebi|0000-0002-8307-187X | |
dc.citation.epage | 2535 | en_US |
dc.citation.spage | 2505 | en_US |
dc.citation.volumeNumber | 22 | en_US |
dc.contributor.author | Aktaş, Fatih Selim | |
dc.contributor.author | Ekmekcioglu, Ömer | |
dc.contributor.author | Pinar, Mustafa Çelebi | |
dc.date.accessioned | 2022-02-10T11:13:36Z | |
dc.date.available | 2022-02-10T11:13:36Z | |
dc.date.issued | 2021-12 | |
dc.department | Department of Industrial Engineering | en_US |
dc.description.abstract | Computing sparse solutions to overdetermined linear systems is a ubiquitous problem in several fields such as regression analysis, signal and image processing, information theory and machine learning. Additional non-negativity constraints in the solution are useful for interpretability. Most of the previous research efforts aimed at approximating the sparsity constrained linear least squares problem, and/or finding local solutions by means of descent algorithms. The objective of the present paper is to report on an efficient and modular implicit enumeration algorithm to find provably optimal solutions to the NP-hard problem of sparsity-constrained non-negative least squares. We focus on the problem where the system is assumed to be over-determined where the matrix has full column rank. Numerical results with real test data as well as comparisons of competing methods and an application to hyperspectral imaging are reported. Finally, we present a Python library implementation of our algorithm. | en_US |
dc.description.provenance | Submitted by Dilan Ayverdi (dilan.ayverdi@bilkent.edu.tr) on 2022-02-10T11:13:36Z No. of bitstreams: 1 Provably_optimal_sparse_solutions_to_overdetermined_linear_systems_with_non‑negativity_constraints_in_a_least‑squares_sense_by_implicit_enumeration.pdf: 2905823 bytes, checksum: a94b95019d4b7c04c6fac2c95fee10f8 (MD5) | en |
dc.description.provenance | Made available in DSpace on 2022-02-10T11:13:36Z (GMT). No. of bitstreams: 1 Provably_optimal_sparse_solutions_to_overdetermined_linear_systems_with_non‑negativity_constraints_in_a_least‑squares_sense_by_implicit_enumeration.pdf: 2905823 bytes, checksum: a94b95019d4b7c04c6fac2c95fee10f8 (MD5) Previous issue date: 2021-12 | en |
dc.identifier.doi | 10.1007/s11081-021-09676-2 | en_US |
dc.identifier.eissn | 1573-2924 | |
dc.identifier.issn | 1389-4420 | |
dc.identifier.uri | http://hdl.handle.net/11693/77222 | |
dc.language.iso | English | en_US |
dc.publisher | Springer | en_US |
dc.relation.isversionof | https://doi.org/10.1007/s11081-021-09676-2 | en_US |
dc.source.title | Optimization and Engineering | en_US |
dc.subject | Inverse problems | en_US |
dc.subject | Sparse approximation | en_US |
dc.subject | Overdetermined linear systems | en_US |
dc.subject | Sparse solutions | en_US |
dc.subject | Branch and bound | en_US |
dc.subject | Implicit enumeration | en_US |
dc.subject | Non negative least squares | en_US |
dc.title | Provably optimal sparse solutions to overdetermined linear systems with non-negativity constraints in a least-squares sense by implicit enumeration | en_US |
dc.type | Article | en_US |
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