{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/sparse-generalized-eigenvalue-problem-via","title":"Sparse Generalized Eigenvalue Problem via Smooth Optimization","arxiv_id":"1408.6686","date":"2014-08-28","proceeding":null,"authors":["Junxiao Song","Prabhu Babu","Daniel P. Palomar"],"abstract":"In this paper, we consider an $\\ell_{0}$-norm penalized formulation of the\ngeneralized eigenvalue problem (GEP), aimed at extracting the leading sparse\ngeneralized eigenvector of a matrix pair. The formulation involves maximization\nof a discontinuous nonconcave objective function over a nonconvex constraint\nset, and is therefore computationally intractable. To tackle the problem, we\nfirst approximate the $\\ell_{0}$-norm by a continuous surrogate function. Then\nan algorithm is developed via iteratively majorizing the surrogate function by\na quadratic separable function, which at each iteration reduces to a regular\ngeneralized eigenvalue problem. A preconditioned steepest ascent algorithm for\nfinding the leading generalized eigenvector is provided. A systematic way based\non smoothing is proposed to deal with the \"singularity issue\" that arises when\na quadratic function is used to majorize the nondifferentiable surrogate\nfunction. For sparse GEPs with special structure, algorithms that admit a\nclosed-form solution at every iteration are derived. Numerical experiments show\nthat the proposed algorithms match or outperform existing algorithms in terms\nof computational complexity and support recovery.","url_abs":"http://arxiv.org/abs/1408.6686v2","url_pdf":"http://arxiv.org/pdf/1408.6686v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"sparse-generalized-eigenvalue-problem-via","repo_url":"https://github.com/aseyboldt/covadapt","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1408.6686","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1408.6686"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/aseyboldt/covadapt","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":7},"by_repo_kind":{"listed":{"samples":7,"ran":0,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"3826e5b889cb3aab","entry":"eigvals_from_window","repo":"aseyboldt/covadapt","repo_kind":"listed","path":"covadapt/potential.py","file_url":"https://github.com/aseyboldt/covadapt/blob/HEAD/covadapt/potential.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"3826e5b889cb3aab"}},{"code_sha256_prefix":"ab677e35720d613f","entry":"expit","repo":"aseyboldt/covadapt","repo_kind":"listed","path":"covadapt/eigvals_reg.py","file_url":"https://github.com/aseyboldt/covadapt/blob/HEAD/covadapt/eigvals_reg.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"ab677e35720d613f"}},{"code_sha256_prefix":"c231043414cca350","entry":"kondition_number","repo":"aseyboldt/covadapt","repo_kind":"listed","path":"covadapt/matrix.py","file_url":"https://github.com/aseyboldt/covadapt/blob/HEAD/covadapt/matrix.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"c231043414cca350"}},{"code_sha256_prefix":"1b86c018d466a06e","entry":"matmul_eigs","repo":"aseyboldt/covadapt","repo_kind":"listed","path":"covadapt/spd_manifold.py","file_url":"https://github.com/aseyboldt/covadapt/blob/HEAD/covadapt/spd_manifold.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"1b86c018d466a06e"}},{"code_sha256_prefix":"0ead7d0aad3089c4","entry":"matmul_eigs_single","repo":"aseyboldt/covadapt","repo_kind":"listed","path":"covadapt/spd_manifold.py","file_url":"https://github.com/aseyboldt/covadapt/blob/HEAD/covadapt/spd_manifold.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"0ead7d0aad3089c4"}},{"code_sha256_prefix":"df09c8907b02f16b","entry":"soft_l1","repo":"aseyboldt/covadapt","repo_kind":"listed","path":"covadapt/eigvals_reg.py","file_url":"https://github.com/aseyboldt/covadapt/blob/HEAD/covadapt/eigvals_reg.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"df09c8907b02f16b"}},{"code_sha256_prefix":"d9ed6406e1adf03f","entry":"softplus","repo":"aseyboldt/covadapt","repo_kind":"listed","path":"covadapt/eigvals_reg.py","file_url":"https://github.com/aseyboldt/covadapt/blob/HEAD/covadapt/eigvals_reg.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"d9ed6406e1adf03f"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}